Chapter 11 of Understanding Chemical Bonding: The development of A level students' understanding of the concept of chemical bonding
Learners' application of 'octet thinking'
§11.0: The full shells explanatory principle
In the present research it was found that one of the most significant factors influencing learners' developing understanding of chemical bonding was the presence of complexes of alternative conceptions which were not consistent with curriculum science, and which provided learners with alternative rationales for the formation of chemical bonds. These complexes were based around the octet rule heuristic, but developed into a fundamental explanatory principle. Each learner's thinking was to some extent unique, as the case studies of Annie and Tajinder demonstrate (see chapters 7 and 8 respectively). However, as with Annie and Tajinder, all the colearners in the study showed some aspects of what I will loosely term octet thinking. In this chapter the main features of octet thinking will be described and illustrated. In the final chapter I will suggest that, on the evidence of the present research, the full shells explanatory principle forms the basis of a common alternative conceptual framework applied by learners in chemistry (§12.3). However, I would suggest that the presence in learners' cognitive structures of the set of related alternative conceptions discussed in this chapter has implications for learning about bonding, and other aspects of chemistry (§12.5), regardless of whether the label of alternative framework is considered appropriate.
§11.1: An atomic ontology: atoms as the units of matter – the building block metaphor
The research suggests that atoms are ascribed a special ontological significance by learners, so that chemical systems tend to be conceptualised in terms of combinations of atoms, although this may not always be the most useful and appropriate approach. The notion of electrons belonging to atoms (see below, §11.1.4) may be associated with this tendency to perceive discrete neutral atoms as some sort of 'natural' unit of matter. The evidence from the data collected suggests that the metaphor of atoms as the building blocks of matter may be adopted by learners, without consideration of the ways in which atoms are not analogous to building blocks.
One colearner in the study, Kabul, seemed unable to conceive of the possibility of an ion existing unless it had been formed by electron transfer between neutral atoms (see appendix 32, §A32.1.1).
Evidence from tasks set to new A level students as induction exercises demonstrate that Kabul's view was not idiosyncratic. When new students were asked to define the term 'atom' as part of an induction exercise, several suggested that atoms were indivisible or the smallest components in matter (see appendix 32, §A32.1.2). Although these comments reflect the original meaning of atomos, they are contrary to a model of chemistry that understands bonding as the electrostatic interactions between sub-atomic units (i.e. cores, electrons). Some students' definitions seemed to reflect this tension between the atom as indivisible, and as a compound entity, referring to the atom as both the 'smallest particle' possible, or the 'simplest structure in chemistry', and then going on to describe its subatomic components (see appendix 32, §A32.1.3).
Some students seem to explicitly use the metaphor of atom as building block, so the atom is seen as the "building block of all substances" (induction exercise, September 1995), or put even more strongly, the "atom is a particle which is the building block of everything" (induction exercise, September 1993).
Seeing an atom as the basic unit means that molecules are seen as combinations of atoms, rather than as basic entities, or as systems of atomic nuclei/cores and electrons (see appendix 32, §A32.1.4, c.f. chapter 12, §12.4.5).
The same phenomena may be found in many students' definitions of ions, that is – as with Kabul – ions are seen as altered atoms. Rather than ions being viewed as entities in their own right, they may be seen as atoms (or molecules, which are derived from atoms) that have had electrons added or removed (see appendix 32, §A32.1.5).
§11.1.1: The assumption of initial atomicity
This research suggests that in A level chemistry some learners may assume that any chemical system they are asked to consider has evolved from discrete atoms. For learners who assign atoms the ontological status of being the basic units of matter, it is perhaps understandable that this is so: i.e., that they should conceptualise information presented to them, in terms of what they perceive to be the basic level of analysis for the subject.
For example, in Tajinder's third interview he apparently brought to mind an isolated atom (that has "four" outer shell electrons) when he was asked about an atom in a piece of carbon (see appendix 32, §A32.2.1). A similar example occurred in Kabul's fifth interview when he discussed hybridisation. He talked about diamond as though there were atomic orbitals present, that could be hybridised when bonds were to be formed (see appendix 32, §A32.2.2).
In an interview shortly before his A level examinations Kabul explained that sodium would react with hydrogen as the hydrogen atoms had "just one electron" and could accommodate another, thus conceptualising hydrogen as if it existing as isolated atoms rather than molecules. It would appear that throughout his A level course, when thinking of such reactions, Kabul assumed the reactants initially existed as atoms. When this was challenged he appeared to have no other rationale for explaining the reaction (see appendix 32, §A32.2.3).
Incidental data collected from induction exercises with A level chemistry classes demonstrate that it is not uncommon for learners to make an assumption that reactions occur between elements which are in the form of discrete atoms (see appendix 32, §A32.2.4).
In the following example, the atomic status of the reactants is emphasised with an illustration,
"Sodium has to get rid of an electron to achieve a full outer shell status and Chlorine has to try to gain an electron to complete its outer shell. Therefore Na and Cl combine in an ionic bond where Na gives Cl an electron to complete both shells and both atoms stay together in an ionic bond because they both [sic] have opposite charges."
Induction exercise, September 1994
The assumption of initial atomicity is not restricted to students commencing their A level studies, and the following examples were collected from students who had completed one term of A level study,
"Sodium atom has one electron more while chlorine atom needs one electron to complete an inert electronic configuration. Hence both atoms react with each other …"
"Carbon needs 4 electrons while oxygen needs 2 electrons to complete its outer shell. Hence to gain inert gas configuration, 1 molecule of carbon combines with 2 molecules of oxygen to form carbon dioxide which has covalent bonding"
First year coursework exercise, January 1995
The potency of octet thinking may be seen in the second example above, where the explicit acknowledgement that the reactants are in the form of molecules does not prevent the students applying the assumption of reagent atomicity.
Although the assumption of initial atomicity is inappropriate from a curriculum science perspective, a perusal of some school text books soon revealed examples of authors' explanations that seemed to support such an interpretation (see appendix 32, §A32.5).
§11.1.2: Atoms as hard spheres
Atoms are sometimes compared to billiard balls. This is an analogy made in physics when the elastic nature of collisions between particles is important for developing the kinetic model of a gas. (Of course if all collisions between particles were elastic there would be no chemical reactions.) In chemistry it is important for learners to realise that in some situations atomic particles do behave similarly to hard spheres, but in other contexts the mutual penetration of atoms and molecules is very important.
In her third interview Annie was asked why in sodium chloride (focal figure 5) the ions do not move any closer, if they are attracted together. Annie suggests "they could only get so, so close, because of the size of the atoms" (A3.202). This answer implies that atoms have size in the same sense as a billiard ball, whereas an atom is a 'fuzzy' object, where the notion of size is more problematic. Her answer also reflects some of the comments presented in chapter 10, where an object may be perceived to rest on the ground when acted upon by the (unbalanced) force of gravity, because it can not fall any further: in other words support (or in this case integrity) is seen as self evident, and the learners does not need to invoke the action of a force.
§11.1.3: Isolated electrons
The high ontological status learners appear to ascribe to atoms may mean that electrons, as parts of atoms, may not be considered to be stable outside the atom. So, in his first interview Tajinder suggested that an electron could not be removed from an atom, unless it could "go to another atom", "because it just can't exist by itself" (T1.A421). Later in the interview Tajinder did change his mind when he thought about a metal as there would be "free electrons roaming around" (T1.B074). However, in the case of a single sodium atom, Tajinder explained that an electron "wouldn't just roam off by itself" (T1.B094). In his second interview Tajinder reiterated that an electron "would be able to move about in the lump of metal … it wouldn't just float off by itself" (T2.A168).
§11.1.4: Ownership of electrons
It was found in the research that electrons were commonly seen to belong to particular atoms. When an isolated atom is considered this notion of 'belonging to' could be equated with 'being part of' an atom. In the case of a molecule those electrons classed as core, or lone-pair ('non-bonding') electrons might be considered – from a curriculum science perspective – to belong to a particular atom in a sense that relates to the extent to which the atomic orbitals are perturbed (i.e. the extent to which the molecular orbitals occupied by the electrons are similar to the atomic orbitals that would be occupied in the absence of the rest of the molecule, see §12.5). However it was found that for learners, the notion of electron ownership was applied to bonding electrons that – from a curriculum science perspective – could not be said to have a particular association with one specific atomic core in the molecule.
It is conventional in school science and chemistry texts, and to some extent in A level texts, to use variations on 'dot and cross' diagrams, where electrons are shown by different symbols according to which atom that are said to have originated. (This may be useful to pupils to draw attention to the point that the number of electrons has not changed during a reaction). Focal figure 3 followed this convention:
focal figure 3
A number of the colearners interviewed interpreted the distinction between the electrons in terms of which atom they 'belonged' to. Further questioning suggested that in some cases the word 'belong' was being used casually, but for others the ownership of the electrons was more significant (see appendix 32, §A32.3.1).
Where the term 'belong' is used as no more than a way of indicating which electron originated from where, then it may not be seen as important. However, later in this chapter (§11.4) it will be shown that although from a curriculum science perspective, there is no significance to an electron's history – the electron has no memory of where it has previously been – for some learners the electron's 'history' is seen as having consequences. In Paminder's first interview she suggested that the protons in the chlorine nucleus were only attracted to chlorine electrons, and the protons in the carbon nucleus were only attracted to carbon electrons (see appendix 32, §A32.3.2).
It will be shown below (§11.4.2) that electron history is considered a determinant of whether ionic bonds exist between adjacent sodium and chloride ions in a sodium chloride lattice. When Mike discussed sodium chloride in his first interview, he described the conjectured electron transfer event as "the sodium atom is lending chlorine one of its electrons" (M1.A375). In Carol's second interview she suggested that electron transfer in sodium chloride was not complete as "the sodium will still want its electrons back" (C2.211).
§11.1.5: Covalent bonding as sharing of electrons
In this research it was found that the covalent bond was often described in terms of atoms sharing electrons. This is a term which is often used in books, and therefore has some currency within curriculum science. However during an A level course learners are expected to develop more sophisticated models of the bond, and it is therefore of interest if they continue to use this level of description as they undertake their A level studies. This is particularly so if learners define the covalent bond as 'sharing electrons' as though this is a full and sufficient description.
The significance of the use of this description may be clear from Tajinder's case (chapter 8). By the end of his course Tajinder had three alternative explanatory principles he would use to discuss bonding. To describe a bond as electrons being 'shared' has little relevance to either his coulombic forces explanatory principle, nor his minimum energy explanatory principle, the bases of the two more sophisticated complexes of ideas he developed through A level study. Rather sharing of electrons is a definition of the covalent bond which derives from Tajinder's octet rule explanatory principle, the deficient basis for explaining bonding that he brought from his school level study.
Indeed this terminology derives from the notion of atoms owning electrons (see above, §11.1.4). The term 'sharing' derives is potency from a scheme such that by sharing electrons, an atom may count both its own electrons, and the electrons donated to be shared by atoms bonded to it, towards having a full outer shell. It is interesting to note that the term 'sharing' is anthropomorphic – that is, atoms share by analogy with human social behaviour – and in such a scheme the agents bringing about sharing (and therefore bonding) appear to be the atoms themselves. (Later in this chapter more widespread anthropomorphism in discussing bonding will be identified, §11.3.)
Of course, if a learner uses the term 'atoms share electrons' as shorthand for, say, 'a pair of negatively charged electrons are attracted to, and by, a pair of positively charged atomic cores, and the electrostatic forces bind the atoms together', or alternatively to mean something like, 'a pair of electrons occupy a bonding molecular orbital formed by the overlap of two atomic orbitals that were at higher energy levels, and therefore the energy of the molecular species is lower compared with the atoms', then the term is not problematic. However in some of the discussions with learners undertaken for this research it was clear that the term 'sharing' was used more literally, and was seen as a sufficient explanation for the covalent bond.
The use of the term 'sharing' was ubiquitous amongst the colearners in this study near the beginning of their A level study (see appendix 32, §A32.4.1), and was also found in data collected from other learners starting out on A level (see appendix 32, §A32.4.2). Most of the colearners continued to talk of 'sharing' even when they had been taught about bonding at A level (see appendix 32, §A32.4.3).
In some cases the definition of the covalent bond as sharing of electrons is probably little more than habit, and does not exclude the presence of alternative models of description (as seen with Tajinder in chapter 8, §8.4.5). However, in at least some cases, sharing is seen to be an explanation of the bond in itself. This seemed to be the case in Paminder's first interview where the sharing itself was described as a link and "like a force" (see appendix 32, §A32.4.4). Similarly in Umar's first interview he appeared to think that the sharing held atoms together simply because they were combined as one whole thing (see appendix 32, §A32.4.5).
For a student who does not share a curriculum science typology of forces (c.f. §3.1.3 and chapter 10), such 'sharing' may be seen as the cause of a force, rather than as a metaphor for describing a system of interacting electrostatic charges. So one learner setting out on an A level course explained that "when two or more atoms join their electrons are shared (covalent) or given (ionic) this makes a force between the atoms" (induction exercise, September 1995).
§11.2: The octet rule as the basis of an explanatory principle
"bonding is when 2 atoms chemically combine to become a molecule of sorts. The 2 types of bonding are IONIC (donating electrons) and COVALENT (sharing electrons). It is done in order to try to achieve a stable structure i.e. 8 electrons in the outer shell of the atom"
From an A level induction exercise, September 1995
In chapters 7 and 8 it was suggested that Annie and Tajinder's understanding of chemical bonding could be interpreted in terms of key 'explanatory principles' which formed the basis of many of their interview responses. In both cases one explanatory principle was related to the octet rule, and was used throughout the course. The two principles were similar, but to emphasise the unique nature of learners' ideas, they were given distinct labels: the stable shells explanatory principle (Annie), and the octet rule explanatory principle (Tajinder). In the present chapter it is suggested that this research suggests that the application of ideas based on the octet rule as the basis for explaining chemical bonding – and related phenomena – is ubiquitous among chemistry learners at this level.
The case studies in chapters 7 and 8 have demonstrated that although Annie and Tajinder used similar explanatory principles, they developed a different range of explanatory schemes from them, so that the complex of ideas elicited from Annie based on her stable shells explanatory principle, does not match absolutely with the set of ideas elicited from Tajinder based on his octet rule explanatory principle. In a similar way, the other colearners in the study also used 'octet thinking' to different extents, and in varying ways, and in somewhat different contexts during their interviews. However all of the colearners in the study seemed to hold in their cognitive structures something akin to Annie's stable shells explanatory principle and Tajinder's octet rule explanatory principle, which will be given the generic label of the full shells explanatory principle.
The basis of 'octet thinking' is the full shells explanatory principle: that atoms form bonds in order to achieve stable electronic configurations (variously referred to as octets, full outer shells or noble gas configurations/structures).
Each of the colearners may be shown to be applying a variant of this principle at some point during the interviews (see appendix 33, §A33.1.1), so for example Noor explained that bonding "involves obtaining a full outer shell", and that "in all cases what an atom is trying to do is to become stable, and so obtain a full outer shell" (N3.A150). Incidental data provides some evidence that other chemistry learners also apply this principle (see appendix 33, §A33.1.2).
Although using the octet rule as an explanatory principle is inappropriate from a curriculum science perspective, a perusal of some school text books soon revealed examples of authors' explanations that seemed to support such an interpretation (see appendix 33, §A33.11).
§11.2.1: Explaining the covalent bond
In terms of the full shells explanatory principle, a covalent bond enables atoms to obtain stable electronic structures by sharing electrons, which are then 'counted' towards both of the sharing atoms.
In the data collected there were many examples of colearners explaining covalent bonds being described in terms of "the sharing of electrons between two species, in order to gain fully full outer shell" (see appendix 33, §A33.2.1).
In terms of the full shells explanatory principle, a double bond is simply the sharing of two pairs of electrons, and in the research there were several examples of the bond in an oxygen molecule being described in these terms (see appendix 33, §A33.2.2).
'Incidental data' collected from chemistry students suggests that the notion of the covalent bond as sharing of electrons to give full electron shells is not restricted to the colearners in this study. For example comments reflecting the full shells explanatory principle have been elicited in relation to a number of different molecules in induction exercises by students embarking on A level study (see appendix 33, §A33.2.3). As has been seen with the colearners interviewed for this research, the full shells explanatory principle is retained and applied by chemistry students after they have been taught the more sophisticated models of the A level curriculum (see appendix 33, §A33.2.4).
An interesting variation on the model of covalent bonding discussed here was found in the case of Mike. For most learners applying the full shells explanatory principle, shared electrons are counted fully towards the octets of both sharing atoms. However in his second interview Mike revealed his own interpretation was different, i.e. that a shared electron only counted as half an electron for each atom, so that more electrons would need to be shared to reach the required number (see appendix 33, §A33.2.5).
§11.2.2: Explaining the ionic bond
In terms of the full shells explanatory principle, ionic bonding occurs when atoms achieve stable electronic configurations through electron transfer. There were many examples of colearners explaining the ionic bond in this way (see appendix 33, §A33.3.1), and these were not limited to students just commencing the A level course. So at the end of her first year Jagdish explained how a sodium atom could "form a more stable configuration by giving one of the electrons to the chlorine and forming a bond, and so it would be at lower energy level" (J3.A376); and at the end of her course Annie explained how ionic bonding involved one atom donating electrons, to another which is "sort of deficient in electrons", so that it would have the "number it needs, to like have a full stable outer shell which is what all sort of compounds are aiming for" (A4.14).
The notion of the ionic bond being an electron transfer to give full shells is reflected in evidence collected from other chemistry learners, such as the following datum presented in an induction exercise,
"Sodium loses one electron to complete the outer shell for chlorine."
From an induction exercise, September 1995
and the following definition, taken from a revision exercise at the end of one year of study,
Ionic bonding is the exchange of electrons in two or more atoms to achieve the result of a full valent shell.
concept map on chemical bonding, June 1994
§11.2.3: Explaining the metallic bond
The metallic bond cannot be explained in terms of the full shells explanatory principle as readily as the covalent and ionic cases, as in a metal the mean number of valent electrons per atom is unchanged from the isolated atom. (It is suggested later in the chapter that this may explain why pure metals are sometimes considered not to involve chemical bonds, or at least not 'proper' bonds, see §11.7.2.) However, some colearners in the study were able to construe the metallic bond in terms consistent with the full shells explanatory principle. So electrons were conceptualised as being shared, or being moved around so that the atoms took turns in having full shells (either by gaining enough, or losing enough), or the electrons were considered to have been donated to the lattice and so they were no longer on the atoms (see appendix 33, §A33.4.1).
§11.2.4: Explaining the dative bond
Colearners in this study also used the full shells explanatory principle to explain dative bonds. So Kabul explained that aluminium chloride dimerised as "in order to attain a stable state you must have eight electrons" (K4.B414). Similar explanations were given by several other colearners (see appendix 33, §A33.5.1).
§11.2.5: Rationale for chemical reactions
Chemical reactions may be described at the molecular scale in terms of bond breaking and bond making: bond fission and bond formation. The full shells explanatory principle may therefore be used to explain chemical reactions, as well as bonds in themselves.
At the end of her course Debra explained the monatomic nature of noble gas molecules in terms of the atoms already having full shells (D3.37) and a similar argument was put by Lovesh in his second interview (see appendix 33, §A33.6.1). Similarly, at the end of Kabul's course he attempted to explain the reaction between sodium and hydrogen in terms of the hydrogen atoms being able to accommodate another electron (see appendix 33, §A33.6.2).
§11.2.6: Octets, or full shells, or noble gas electronic configurations?
It was suggested above (§11.2) that when learners apply the full shells explanatory principle some refer to octets, others to full shells, and yet others to noble (or inert) gas structures, and this is illustrated by the various examples given in appendix 33, §A33.7). These terms seem to often be used as if synonymous. However according to curriculum science only two of the noble gas structures have full outer shells (as the first four shells would be full with 2, 8, 18 and 32 electrons respectively), and helium does not have an octet.
Some colearners demonstrated confusion over this aspect of atomic structure. So although Edward was able to report that the maximum number of electrons in a shell was given by the formula 2n2, on another occasion he stated that the third atomic shell could only contain four orbitals, i.e. a maximum of eight electrons (see appendix 33, §A33.7.1).
Jagdish and Paminder also thought that the third shell could only hold a maximum of eight electrons (see appendix 33, §A33.7.2).
Although from a curriculum science perspective the terms octets, full shells, and noble (or inert) gas electronic configurations are not synonymous, several school science texts perused during this research presented statements which – like some of my colearners – clearly used incorrect terminology (see appendix 33, §A33.12).
§11.2.7: Bond polarity and electronegativity
Bond polarity is an important concept in A level chemistry, but one which is not explained by the full shells explanatory principle. The concept of electronegativity may be seen as allowing learners to move beyond the dichotomous classification of elements as metal/non-metal, and consequently to allow a classification of bonding with various degrees of polarity, rather than covalent/ionic.
However, in this research it was found that some of the colearners would attempt to rationalise polarity in terms of octets. At the end of her first year Jagdish discussed the polarity of a bond as being due to the extent to which the elements involved "pull electrons in a bond" (J3.A136), but she was only able to construe this in terms of the more electronegative element having to take electrons to form a full outer shell (see appendix 33, §A33.8.1). Similarly, when Noor gave an account of electronegativity at the end of her first year her explanation was in terms of octets and only discriminated metals from non-metals,
"in all cases what an atom is trying to do is to become stable, and so, er, obtain a full outer shell. In the case of metals it's easier for them to become stable by losing electrons, and, by doing this they become positive, so they're gonna be more electropositive, whereas [non-metals] to become stable, erm, would acquire those electrons, and hence become more electronegative, 'cause they've gained electrons"
N3.A150
At the end of Kabul's his course he understood the most electronegative and electropositive elements to be those that needed to gain or lose the least number of electrons to gain an octet (see appendix 33, §A33.8.2).
§11.2.8: Stable electronic structures
Although the full shell explanatory principle is used by colearners in ways that are here considered invalid (such as a rationale for chemical reactions occurring, and artificially distinguishing between equivalent between-ion interactions in lattices), and although it may be considered to act as an impediment to progression (as it does not provide a basis for understanding bond polarity or hydrogen bonds for example), it is none-the-less based on an established principle from curriculum science, that some electronic structures appear to be associated with particular stability.
The noble gases were – and often still are – referred to as inert, as they tend to be unreactive. This may be explained in the following terms:
- the noble gas atoms are electrically neutral, and therefore do not attract charged species (including polarised species) at a distance.
- the charge distribution of a noble gas atom is symmetrical so that the atom 'presents' no permanent areas of higher negative or positive charge (i.e. the electron cloud is equitably distributed, and the nuclear charge is effectively shielded).
- the noble gases do not have any singularly occupied orbitals in the ground state that can overlap with orbitals on other atoms to form lower energy molecular orbitals, and thus bonds. (The exclusion principle does not allow them to overlap in the ground state.)
- the noble gases do not generally have available empty orbitals suitable (in particular at similar energy level) for promoting electrons to provide singularly occupied orbitals for overlap.
Points 3 and 4 refer to the energetic (thermodynamic) considerations that may be understood as the driving force for reactions. Points 1 and 2 refer to the mechanisms by which species may interact.
Point 1 applies to all atoms, of course, but point 2 does not, because the distribution of charge in an atom is restricted by quantization: that electrons must occupy orbitals that are solutions to the Schrödinger equation. Point 2 would therefore not apply to any atom that had sub-shells that were other than full, or half-full. In other words configurations such as s1, s2, p3, p6, d5, d10 etc., would be inert in these terms. However point 3 would suggest that s1, p3, and d5, configurations would be relatively inert, but not particularly stable. However one would expect particular stability to be associated with configurations such as s2, s2p6, s2d10, s2p6d10, and generally this what is found. That point 4 is not absolute is reflected in the existence of several compounds of the heavier inert gases.
This analysis is somewhat sophisticated and may be too subtle for some A level students. This is reflected in the colearners' applications of the full shells explanatory principle. Lovesh thought that is was not possible for one sodium atom to exist alone as it did not have a full outer shell (see appendix 33, §A33.9.1).
In Lovesh's final interview, near the end of the second year of his course he explained how a sodium atom is not stable "because it hasn't got a, a full outer electron shell, [the] outer electron shell hasn't got eight electrons in" (L4.A067). Indeed Lovesh thought that "it's not possible to have one on its own" (L4.A26). Other colearners also suggested that single atoms would not be stable where they did not have full shells (see appendix 33, §A33.9.2).
§11.2.9: Ionisation energies
The full shells explanatory principle criterion of atomic stability may be seen to effect learners' understanding of ionisation energies.
So, for example, Lovesh had studied patterns in ionisation energies, but when asked about the stability of the sodium ion he appeared to be operating from his full shells explanatory principle perspective, and he did not think a second ionisation of sodium was possible (see appendix 33, §A33.10.1).
Data collected from students' responses to a past examination question about ionisation energies reflected the same perspective. It would seem that when a question concerns one of the noble gases then the observed stability of the noble gas electronic configurations may be invoked as an explanation, rather than as a phenomena to be explained. The question, used in the end-of-first-year examination given to A level chemistry students in June 1994, asked why neon had the highest molar first ionisation energy of the elements in period 2. The most appropriate answer from a curriculum science perspective would focus on the core charge, which increases across the period. However, even when this is invoked, the full outer shell status may also be mentioned as another reason. A number of students, however, gave a response that suggested that the high ionisation energy could be explained completely in terms of the full shells explanatory principle. Once again the precise wording varies considerably, with full shells, eight electrons, octets and unspecified stable configurations variously used to make the point (see appendix 33, §A33.10.2).
The theme of this thesis is Understanding Chemical Bonding, and ionisation energy could seem to be something outside of this topic (although ionisation energy is a term in the Born-Häber cycles that also includes the energy changes on bond formation such as lattice energy). However, it would seem that in this research learners may construe ionisation energy in terms of the same full shells explanatory principle used to explain bonding itself. Moreover, whereas in explaining the inert behaviour of the noble gases, arguments that these atoms have 'full shells' or 'octets' could be considered as an oversimplification of the analysis in points 1-4 given above (§11.2.8), in the case of ionisation energy it is much clearer that explaining the high first ionisation energy of neon in these terms is clearly not a less sophisticated version of curriculum science. Where Lovesh's comments about sodium are concerned, it is seen that the full shells explanatory principle is applied, even though it leads to a prediction that clearly contradicts work Lovesh has previously studied.
Appendix 3 gives details of a pencil-and-paper that was developed to diagnose the extent of some of the alternative notions about ionisation energy elicited from learners in this study. The truth about ionisation energy diagnostic instrument was used with a sample of 110 A level chemistry students who had studied the topic of ionisation energy.
The responses to some of the items in the instrument suggested that the application of a full shells explanatory principle is much more widespread than just the colearners in the interview study. The respondents were shown a copy of focal figure 1, and 35% of respondents thought, like Lovesh above, that only one electron can be removed from the atom, as it then has a stable electronic configuration. 75% of respondents agreed with the statement that the atom would be more stable if it 'lost' an electron, and 56% of respondents agreed that if the outermost electron is removed from the atom it will not return because there will be a stable electronic configuration, although presumably they were aware that positive and negative charges attract each other.
Perhaps most significantly 83% of respondents agreed that the atom would become stable if it either lost one electron or gained seven electrons. If these students were interpreting the statement as intended, they were overwhelmingly suggesting that not only would Na+ (electronic configuration, 2.8) be stable, but so would the species Na7- (electronic configuration, 2.8.8), which is highly unstable from a curriculum science perspective. In case this last result was due to an ambiguity in the statement, a separate question about atomic stability was prepared and presented to a class of A level chemistry students (further details are again given in appendix 3).
They were asked to compare the stability of the three species concerned,
three figures used to elicit views on chemical stability (reproduced at 75% of original linear dimensions)
Ten students in this class (63% of respondents) thought that "B is less stable than C", a conclusion that may follow from the full shells explanatory principle, but gives scant regard to a consideration for electrical neutrality. The association of full shells/octets with stability was clear in the respondents explanations, such as,
B is less stable than C because … the outer shell of C is full with eight electrons but B only has 1 electron in its outer shell and is less stable.
B is not as stable as C because it needs [sic] another 7 electrons to fill the outer shell
In the comparison between the sodium atom and the cation, 13 students (81%) thought the cation more stable, and only 1 thought it was less stable than the atom, again reflecting the responses to the diagnostic instrument, and again ignoring the curriculum science principle that in the absence of an effective electron acceptor the neutral atom would be a stable species.
When the same question was used as an induction exercise with a class new to A level work, the option B is less stable than C was selected by 11 of 13 respondents (85%), and the same number of respondents also selected A is more stable than B.
One of the explanations given makes a fitting quotation to underline this section on how the octet rule is used by learners as an explanatory principle,
"If an atom has been filled up or all ready full up (of 8 outer electrons) it beA level student, written induction exercise, September 1995comes stable and therefore it is unreactive. The atom will stay that way forever and not react or loose or gain any electrons."
A level student, written induction exercise, September 1995
§11.3: The use of anthropomorphic language to discuss atomic phenomena
"This reaction occurs because both Hydrogen and Oxygen atoms wish to become stable. By bonding they both become stable. Hydrogen now has 2 electrons in its first and outer shell, oxygen now has 8 electrons in its outer shell; so both are chemically stable. At first neither the Hydrogen (H) or oxygen (O) atoms are stable. Each Hydrogen atom needs one more electron in order to be stable (i.e. have 2 electrons in first shell). The Oxygen atom already has 6 electrons in its outer shell, so needs 2 more in order to be stable (i.e. 8 electrons in outer shell.) The atoms now bond covalently, by both Hydrogen atoms sharing 1 electron, and oxygen by sharing 2 electrons."
Induction exercise, September 1995
Whereas curriculum science provides a mechanism for chemical processes to occur, i.e. electrostatic forces, the full shells explanatory principle is not associated with any particular type of force. In the interview study it was found that colearners tended to give explanations based on this principle in language that was anthropomorphic. That is, atoms were spoken of as if they were sentient actors that had perceptions and desires, and were able to act accordingly. Such language may represent either anthropomorphic thinking on the part of the learner (thinking in terms of the atom being a sentient actor), or alternatively, a metaphorical description where the best way the learner can find to explain their thinking is to speak as if atoms were conscious agents.
Some of the language used by colearners in the interviews, which could be considered as anthropomorphic, might be better classified as 'dead metaphor', i.e. terms that at one time had metaphorical weight, but with familiarity of use have taken on a new, and now literal, meaning. It could certainly be argued that in chemistry the notion of atoms sharing electrons in bonds is an example of such usage. For electrons to be shared, donated or accepted by atoms implies some sense of ownership – a concept relating to human social affairs – and this may be considered to have originally been a way of conceptualising molecular systems by analogy with human experience. As these terms are accepted and ubiquitous in chemistry, it would be inappropriate to suggest that they are evidence for anthropomorphic thinking among my colearners. Rather, these terms are akin to technical terms that soon become habitual when reading and talking chemistry. It is suggested that the widespread use of these terms has more significance for the construction of learners' atomic ontologies (as discussed earlier in this chapter, §11.1), than for being evidence of their anthropomorphic thought.
Other language used by colearners, however, such as suggesting that atoms 'like', 'want' or 'need', should not be explained as dead metaphor. There were many examples of such comments in the data collected from colearners, and the extent and range of contexts of anthropomorphism may be gauged from the examples below. In some cases this use of language was actually discussed with the colearners to explore their awareness of the anthropomorphisms (§11.3.3).
§11.3.1: What atoms want: anthropomorphism in place of physical mechanisms
The emphasis placed on colearners' anthropomorphic language in this thesis is due to the way such language seemed to stand in place of physical causes. In other words, it often seemed that when a colearner suggested that a bond formed because that was what atoms wanted, the colearner did not seek to look for an alternative explanation.
The extent to which having an anthropomorphic 'explanation' impeded the learner's quest for a physical explanation, rather than just being used because no alternative was available, or due to habit, is a question that may benefit further research (see chapter 12, §12.6). However, it is clear that a great deal of anthropomorphic language was used by learners, and much – although by no means all – of this was related to the application of the full shells explanatory principle. Put simply colearners suggested that bonds form because atoms want to have full shells.
One common way in which the full shells explanatory principle was applied by the colearners was by referring to how atoms needed to acquire (or lose) electrons to become stable (see appendix 34, §A34.1.1). Other examples of this use of 'needs' were found in incidental data collected from other chemistry students. The following explanation of the reaction between oxygen and hydrogen involves the assumption that the reactants are atoms (see §11.1.1), and refers to their needs, the 'needed' noble gas structure, and the sharing of electrons that satisfies the atoms,
"This reaction occurs due to the covalent bonding which takes place. Hydrogen needs an extra electron to copy He [helium] and have a stable condition. Oxygen needs two electrons, and so two hydrogens and one oxygen bond together covalently so that each hydrogen shares an electron with oxygen so that their outer shells are all stable."
Induction exercise, September 1995
However a range of other examples were also uncovered (see appendix 34, §A34.1.2) In the following example, 'require' is used rather than 'need',
"oxygen has 6 outer electrons so it requires another two electrons to fill the outer shell. Hydrogen has 1 spare electron so 2 hydrogen electron is required to fill oxygens outer shell [by] combining to make a full shell.
Induction exercise, September 1995
A way of expressing similar ideas was in terms of the slightly less imperative reference to what an atom 'wants'. Again this was used widely amongst the colearners in this study, as when Kabul suggested that chlorine "wants to become a stable atom" (Kabul, K6.A322), but there were many other examples (see appendix 34, §A34.1.3). Again this use of anthropomorphism was reflected in incidental data collected from other learners' course work (see appendix 34, §A34.1.4) as in the examination answer suggesting that an aluminium ion "wants to have a full shell". For most learners there is probably little significance to the choice of 'needs' or 'wants', despite the literal difference in meaning, and there were examples in the data collected where the two words seemed to be used interchangeably (see appendix 34, §A34.1.5).
Besides 'need' and 'want', the colearners interviewed used a number of other similar terms (so that atoms "like to achieve a stable noble gas configuration" and "prefer to have eight electrons") implying that atoms had human feelings (see appendix 34,§A34.1.6). Once more, similar examples (such as the hydrogen atom that was "very eager to get the 1 electron to complete its outer shell") were found amongst other chemistry students (see appendix 34, §A34.1.7).
Tajinder (chapter 8) sometimes referred to atoms 'thinking', and in particular that bonding took place so that the atoms could 'think' they had full shells (see appendix 34, §A34.1.8). As far as achieving full shells was concerned, Tajinder suggests that it is indeed the atom's perception of its octet status which is critical, so when aluminium chloride formed a dimer "the aluminium thinks that it's stable because it's got eight outer electrons, but really it hasn't, but it thinks that it has" (T10.A524).
So, according to the colearners, atoms want, or even need full shells, and according to Tajinder at least they are aware of their octet status or otherwise. Some colearners also talked as though the atoms then deliberately went about obtaining full electron shells. As Noor and Tajinder both explained, "in all cases what an atom is trying to do is to become stable, and so obtain a full outer shell" (N3.A150), or "all elements try to gain noble gas configurations to become stable" (T4.A062). There were other references to atoms 'trying' in the interviews (see appendix 34, §A34.1.9) and in the incidental data collected from other students (see appendix 34, §A34.1.10).
§11.3.2: Anthropomorphism in other contexts
I have demonstrated, above, that learners' discussions of bonding in terms of the full shells explanatory principle are often anthropomorphic. I have argued that the full shells explanatory principle is by its very nature anthropomorphic, in that anthropomorphic language stands in place of the physical mechanisms which explain bonding processes in curriculum science. Further, it may be conjectured that without the availability of such anthropomorphic language the limitations of explanations of bond formation in terms of full shells would be clear to learners, and thus this mode of discourse may be a factor inhibiting their progression towards alternative explanatory schemes with more currency in curriculum science.
It is therefore illuminating to consider whether learners' anthropomorphic explanations about bonding and related phenomena are limited to arguments based on the full shells explanatory principle. In the present research it was found that whilst anthropomorphic language was widely used in explanations based on full shells, it was also commonly used in other types of explanation. The interaction between electrical charges was often discussed in anthropomorphic terms by the colearners, in particular with various species said to be trying to attract or get apart from one another (see appendix 34, §A34.2.1). Further examples of anthropomorphic language used to describe electrostatic phenomena were collected from the end-of-first-year examination given to A level chemistry students in the College in June 1994 (see appendix 34, §A34.2.2). These various examples of learners explaining electrostatic interactions as though charged particles are sentient actors should be considered in the context of the evidence presented in the previous chapter (chapter 10) which suggests that chemistry learners may be ignorant of fundamental ideas in electrostatics. The anthropomorphic explanations of bonding based on the full shells explanatory principle may be considered part of a wider tendency to discuss electrostatic phenomena as though due to the desires and deliberate actions of charged species.
Chapter 9 demonstrated that learners may find some quantum ideas difficult to grasp, and this is another area where colearners in this study were found to use anthropomorphic language, so that Edward suggests that "an electron always tries to achieve its ground state" (E2.A157). A number of other examples were elicited during the interviews (see appendix 34, §A34.2.3).
§11.3.3: The extent of learners’ awareness of their anthropomorphic language
In view of the widespread use of anthropomorphic language found in this research, it is important to know whether learners mean their anthropomorphic expressions to be literal or figurative. On some occasions during the interviews this aspect of some of the colearners' talk was probed.
In her second interview Debra suggested that a covalent bond would hold atoms together "because they, they gain the full shell then, so they're stable molecules, so it's sort of desirable to be like that" (D2.111). The anthropomorphic aspect of this suggestion was challenged. Debra's response is interesting because although she refers to minimising energy, and a "random" process, she seems to accept the anthropomorphic language of the question. Indeed even when her comments are interpreted in situ as negating the suggestions of a sentient atom, Debra herself seems less sure,
I: Do you think the carbon atom is aware of the fact that it's got four electrons in its outer shell? And aware of the fact that it's desirable to have eight? And so is it some sort of tension that makes it go round and search out electrons and when it's got eight it says, 'right, I can relax now'?
D: Yeah, if, if the erm energy of the sort of molecule would be lower than the energy of you know when it's, on its own, it will.
I: But does the carbon actively seek to do this?
D: No, it's sort of random.
I: So it's not like a carbon atom's got some sort of consciousness, of a very low level, whereby it has some sort of awareness, that it's missing some electrons, and it actively seeks them out, and when it gets them it says 'right, that's it – work done for the day'?
••
D: I don't know.
I: Does that sound feasible for a carbon atom, to sort of > work in that mode? >
D: < Well, < not really, no.
D2.114
Edward used anthropomorphic language when asked to explain his comments about noble gas configurations. He explained that on "ionic bonding, and covalent bonding as well" atoms,
"like to achieve a stable noble gas configuration. Which are, two in the first shell, eight in the second, and it goes up according to 2n2, depending on the shell."
E1.231
He explained this with a tautology, that "each orbital in each shell is filled, and it doesn't need to acquire electrons, or, lose electrons, to fill all its shells" (E1.233). Edward was asked for further explanation. At first Edward seems to be going to repeat his tautology that the atom "doesn't require anything else" (E1.235), but he switches to an anthropomorphic response, that "atoms are, happiest … when they've got full orbitals. And … that's what they always, try and, achieve" (E1.235). Edward considers that somehow atoms are aware of their electronic configurations, and are active agents in seeking full shells (E1.237), but is unable to suggest what form this awareness may take (E1.238-45, see appendix 34, §A34.3.1). Edward was then asked if it is reasonable that atoms should somehow have a kind of awareness, and he still thought it was (E1.249), although he did not believe atoms could think (E1.253). On further questioning Edward suggested that "there has to be some mechanism" (E1.265) by which the atoms could form a molecule, and suggested "it must be something to do with the achieving a sort of equilibrium charge, force … between the, particles" (E1.273). Edward still thought there was a requirement of the 'full shells' type, as "electrostatic" forces (E1.294) "would pull all the electrons in, closer to the nucleus, so that all these levels were filled, from the nucleus outwards", as,m"in the atom [there are] defined orbitals and if the nucleus attracts the electrons, then there's going to be a vacancy outside the last electron to be attracted. And these need to be filled"
(E1.296).
In the fourth interview, near the end of his course, Lovesh made a similar remark, but when probed was able to explain his point in terms of an electrostatic argument,
I: Erm, is that [focal figure 1, a sodium atom] a stable species, do you think?
L: Erm,
• • • (pause, c.3s)
L: no, because it hasn't got a, a full outer – electron shell, outer electron shell hasn't got eight electrons in.
I: So if it's not stable, what would tend to happen to that, do you think?
L: It will wanna donate the electron to another atom.
I: Right, when you say 'it wants to donate' it?
L: Erm.
•••
L: Well because that outer electron is less attracted to the nucleus, erm it is, it can easily be transferred, attracted by another atom.
L4.A067
In Jagdish's third interview she was able to consider the stability of a sodium atom to be relative to its surroundings: its valence electron would not be removed unless there was some nearby agent to apply sufficient force. H owever she continued to use anthropomorphic references, that the atom might want to form a lower energy level, and would give away its electron (J3.A345).As Jagdish had just been applying an electrostatic framework to answer questions I was interested to find out whether her subsequent use of anthropomorphic language was just a habit of speech or amounted to an active explanatory framework. I asked a question posed in similar anthropomorphic language, (i.e., 'were there things the atom wanted to do even more than form compounds?') to see how the response would be framed. Jagdish initially seemed to ignore the anthropomorphism, and answered in terms of forces (which might suggest her anthropomorphic use of language was indeed habitual), but then concluded with a further anthropomorphism, that the atom was "just happy on its own" (J3.A359).
I then attempted to test the extent to which Jagdish would continue to accept such language by presenting a range of alternative anthropomorphisms for her to accept or reject: did the atom desire, enjoy, get its kicks, reflect, consider, decide? As Jagdish appeared to accept all these alternatives (see appendix 34, §A34.3.2), a further attempt was made to find the extent to which these terms were being used as metaphor, by challenging their literal meaning: I asked Jagdish how the atom knew it wanted to form compounds: had it been told, or had it worked it out for itself? Her answer alluded to physical interactions, but also suggested that the atom can know, realise and want (J3.A385). Jagdish thought the sodium atom's realisation of the presence of a chlorine atom required close proximity, so the sodium would feel the chlorine (J3.A385). Despite this feeling Jagdish did not think a sodium atom would make a conscious decision to interact with another species: it just happened (J3.A432).
Later in the interview, the extent to which the atom had feelings was revisited. At first Jagdish seemed to find the anthropomorphism acceptable, but as stronger examples were suggested she seemed to start to have doubts. So she agreed that the atom desired to form a compound, although she did not think it got lonely (J3.A508). Whether the atom would get jealous "depends on how reactive that particular …atom is compared with the, other atom that has formed a compound" (J3.A508). She thought that an atom might feel envious, "if you can say that about an atom" (J3.A520). Jagdish did not think the atom would feel hate, and at this point decided the atom had no feelings (J3.A520).
Yet later still in the interview, Jagdish agreed with suggestions that an atom would prefer to have eight electrons; would want to have eight; and that it wanted to get another atom's electron (J3.B352). Once again Jagdish was quite comfortable with the use of anthropomorphic description, but when the sentience of the atom was queried she said that "it doesn't know" that it needs another electron (J3.B355). Instead of the anthropomorphic rationale Jagdish gave an alternative explanation in terms of energy levels (J3.B355), but then commented that being at a lower energy level was "what they all want" (J3.B361). Once again Jagdish had switched back to anthropomorphic language.
At the end of this interview Jagdish was discussing the hydrogen molecule and suggested that "all the atom wants to do is … it just wants to, neutralise the core charge" (J3.B437). This was the last episode in the interview, which therefore concluded with Jagdish referring to electrostatic factors, but in terms of an anthropomorphic framework of language. (This aspect of Jagdish's explanations is described in more detail in appendix 34, §A34.3.2).
During Kabul's fifth interview he referred to the delocalised electrons in a metal in an anthropomorphic way (wandering around), although he realised this and corrected himself – they only appeared to be wandering, but that was just the way it looked (K5.A206, see appendix 34, §A34.3.3).
Kabul also seemed aware of his use of anthropomorphism when discussing how orbitals could get hybridised if they wanted to (K5.A347). Kabul claimed that this use of "wants" was not literal, but "just theories … to make our life simpler" (although it was not clear whether the degree of metacognitive awareness Kabul had of his use of "they want" also extended to his use of "they need", see appendix 34, §A34.3.3), and he was satisfied with this level of description (K5.A361).
In his final interview, during the last term of his course, Kabul referred to stable species being happy, and again when this was queried he seemed to feel the description was appropriate. Later in the interview Kabul referred to how "an oxidising agent … tries to pull electrons away" from a sodium atom (K6.A243), which is "quite happy to give it away, because it comes more stable" (K6.A246), and how "an oxygen atom … has got six outer electrons … so they, each oxygen, has needs, … [for] 2 electrons to become more stable so you know they form the octet" (K6.A243). When Kabul's notion of atomic happiness was again challenged he was unable to explain what form this took. He at first suggested that the atom was aware, although not consciously so, rather "it just happens", as if by magic (indicated by the clicking of Kabul's fingers, K6.A259). Kabul then decided the atoms were "not really" aware, and reiterated that "it just happens" (K6.A268).
Later in the interview Kabul referred to how a dative bond would form between AlCl3 molecules "to obtain the octet state because octet state is usually stable" (K6.B128). The molecule knew it had not got an octet state as, "it's unstable, it's not aware, you know, physically, but, you know, it would prefer to have eight electrons" (K6.B135). Kabul thought that 'prefer' meant something "different" (K6.B135) for atoms than for people, but he was not able to explain this any further. (This aspect of Kabul's explanations is described in more detail in appendix 34, §A34.3.3).
So the cases of the individual colearners appear to be different in the degree of metacognitive awareness of their anthropomorphic language. Jagdish was comfortable with the most blatant anthropomorphisms (atoms enjoying and desiring and being jealous), but denied that atoms had feelings when asked directly. Kabul also seemed comfortable with language of this type but was aware that it was figurative, a way of making expression simpler. However, his awareness of the lack of literal meaning of expressions such as the 'the atom wants' did not make such terms problematic for him. He accepted these terms were "just theories", but perhaps for Kabul these theories that "made life simpler" had similar status to the theories of curriculum science, such as acid-base theory, redox, and kinetic theory. This issue is considered more in the discussion section (§12.4.4).
§11.4: Significance assigned to electronic history: the history conjecture
"it would seem a bit of an odd-ball, wouldn't it, to have somebody else's electron".
Paminder, near the end of the first year of her A level course, P3.A428
Another aspect of learners' thinking identified in the interviews was the implicit suggestion that the history of an electron is significant. This could be seen as closely related to the notion of electrons belonging to atoms (discussed above, §11.1.4): for if electrons belong to particular atoms then it might be important to identify which atom an electron came from, and therefore belonged to.
The notion of molecular biography is obviously closely related to the theme of the previous section (§11.3), that is colearners tend to refer to chemical systems anthropomorphically. As was pointed out in chapter 3 (Benfey's analogy of molecular life-histories, §3.1.4), anthropomorphic and animistic references are not uncommon in scientific writing, and are not problematic when their metaphorical role is recognised (c.f. §11.3.3). This present section considers the significance that learners ascribe to such history when they do not recognise the limits of the analogy.
One consequence of the history conjecture is an assumption that when a bond breaks atoms get their own electrons back. The history conjecture may also lead to the ionic bond being defined in terms of the donation and acceptance of an electron between atoms, rather than an interaction between ions. This in term may support the 'misconception' that there are molecules in ionic materials (§3.2.6).
The assumption that an electron's history, or perhaps biography, is significant can not be explained in terms of electrons being seen as different to one another. In general the colearners in the study accepted all electrons were the same. An exception was Annie, who suggested in her first interview that electrons might "actually contain some of the element in the electron" (A1.138). She thought that the size and charge of the electrons would be different for the different elements (A1.144-150). However, such a view was not reflected by the other colearners, and their tacit assumptions about the importance of electronic history can not be explained in this way.
§11.4.1: Bond fission
When colearners discussed bond-breaking in contexts such as focal figure 3 (representing a molecule of tetrachloromethane) they sometimes specified that the electrons would return to the atoms from which they originated. According to curriculum science there is no reason to expect this, nor any mechanism to explain such a phenomenon. Notwithstanding curriculum science, learners in the study expected the electrons to return to the appropriate atom. Perhaps, as Paminder suggests in the motto above, the alternative seemed 'odd'. Atoms were said to take the electrons they had given in the first place, their own electrons, or the electrons which belonged to them (see appendix 35, §A35.1.1).
In some cases no rationale for these suggestions was offered beyond which electron belonged to, or originated in, which atom. So in Kabul's first interview he knew "there wasn't any difference" between electrons, but confirmed that they would go back to the 'right' atoms (K1.A270). Although he accepted that the "atom has no idea" which electron to take back, Kabul thought it would get the 'right' electron back (K1.A274). However, by the end of the first year of his course, Kabul had constructed an explanation for this phenomenon, based on electron spin, that was quite ingenious, although ultimately invalid (see appendix 35, §A35.1.2). The significant point here perhaps is that Kabul had become aware of, and concerned about, the lack of a physical reason to explain his belief, and rather than dismiss the notion that electrons return to their own atoms, he had developed a rationale to justify it. When he was persuaded that this argument did not work, Kabul was then prepared to accept that on bond breaking "either" electron would go to the chlorine atom (K4.383).
Several of the colearners explained why an atom would 'get its own electrons back' on bond fission in terms of there only being a force, or there being a greater force between a nucleus and its own electrons (see appendix 35, §A35.1.3). Again in these cases 'octet thinking' seems to take precedence over electrostatic ideas.
§11.4.2: Ionic bonding seen as electron transfer
In curriculum science terms ionic bonding is the force holding cations and anions in a lattice. However, in the research it was found that mention of ionic bonding to learners was most likely to elicit comments about electron transfer to form ions, in addition to, or in precedence to, or even in place of, consideration of the electrostatic forces between ions. Indeed, a great deal of evidence was collected in the research to support the view that at the start of an A level course the ionic bond is commonly identified with the electron transfer event conjectured to be required for ion formation (see appendix 35, §A35.2.1). For an example, in Noor's first interview for the research she explained ionic bonding in terms of an electron transfer event, where atoms attempted to satisfy the full shells explanatory principle, that is "ionic bonding is the transfer of electrons from one atom to another, and … the aim again is to try and get, erm, complete outer shell" (N1.A300). During her first term she depicted ionic bonding as an electron transfer event between isolated atoms,
Noor's diagram of ionic bonding, November, 1992
Noor may be seen to be making the assumption of initial atomicity (§11.1.1), and the data collected suggests that when asked to think about ions, many students do so by thinking first of atoms, and then considering ion formation from the atoms.
From the many similar statements (and diagrams) presented in the appendix (appendix 35) it may be inferred that the ionic bond was typically seen by the colearners as an electron transfer event between discrete atoms, to give ions with stable electronic configurations. The colearners' discussions of ionic bonding are consistent with the full shells explanatory principle, and are conceptualised in terms of discrete atoms (i.e. making an assumption of initial atomicity).
When students study ionic bonding at A level the main concept presented is that of a lattice of cations and anions bound by electrostatic forces. The colearners in the present study acquired this perspective to varying degrees. However, as was illustrated in chapter 10, the underlying electrostatic principles inherent in the curriculum science model were not always familiar to the colearners.
It was reported above (§11.4.1) that several colearners thought that in a covalent bond the individual electrons would be attracted more strongly by their 'own' atom. It was also found that Kabul only thought two ions could attract if there had been electron transfer between them, so that two counter ions in solution would not attract, as "attraction is only possible when a bond is formed" (K3.A056). For Kabul the close proximity of a positive ion and a negative ion was not sufficient for a bond to form between them (see appendix 35, §A35.2.2).
As the case study of Tajinder in chapter 8 demonstrates, learning the electrostatic explanation does not imply discarding the 'octet' rationale. Indeed there is evidence from the data collected that colearners often continued to see the ionic bond – at least primarily – in terms of electron transfer between discrete atoms, after they had been taught during their A level course that the bond was an electrostatic interaction between ions (see appendix 35, §A35.2.3). So ionic bonding continued to be defined as "complete transfer of, an electron, to another atom" (C3.646), when "one of the atoms loses its electrons and the other atom gains that electron" (K4.A512) and as "when one atom transfers electrons to another atom, completely, to form positive cation and negative anion" (L3.A025).
Among the colearners in the present study the ionic bond concept was often closely associated with, if not identified with, an electron transfer event, even after being taught at A level from the curriculum science perspective. Incidental data collected from induction exercises with other learners suggests that the definition of the ionic bond in terms of electron transfer – e.g. "ionic bonding is the transfer of electrons from one atom to another" – is common at the beginning of an A level course (see appendix 35, §A35.2.4). The focus in these definitions is with the needs (c.f. §11.3) of atoms to gain or lose electrons, and the bond is seen as (or intimately tied to) the resulting electron transfer events.
Similar features may be found in examples of the work from students near the end of their A level studies. For example the following definition of ionic bonding assumes discrete atoms as a starting point, focuses on electron transfer, and includes an explicit reference to full electron shells,
"Ionic – forms lattice of Cations and Anions where electrons are transferred attaining full outer shell of e-"
concept map, 2nd year student, May 1992
In a mock A level examination (March 1994), some of the students' explanations of the bonding in sodium chloride demonstrated the same features (see appendix 35, §A35.2.5). The same concerns were represented graphically by some candidates, for example:
"Sodium chloride – ionic bonding in this solid:-
Mock examination response, March 1994
As the Sodium has an electron in it's [sic] outer shell it can donate this electron to the chloride to form a stable ion with a full outer shell."
Some responses that did mention the electrostatic forces, still focused on electron transfer (see appendix 35, §A35.2.6).
Appendix 2 describes a simple pen-and-paper instrument (the truth about ionic bonding diagnostic instrument) used in the research to test whether some aspects of colearners' thinking elicited in this study were more widespread. The instrument was used to test a sample of 81 A level students who had not yet studied bonding at that level, and 128 who had (see appendix 2 for details). One of the statements presented in this instrument (item 24) was that:
"an ionic bond is when one atom donates an electron to another atom, so that they both have full outer shells"
Over four-fifths of those surveyed before being taught about bonding at A level agreed with this definition of the ionic bond, and over half of those who had been taught the topic at A level also thought the statement was true (see appendix 2, table A2.4). Although the sample used was quite small, and can not claim to be fully representative of A level chemistry students in general, this small scale survey does suggest that a molecular interpretation of ionic materials may be common.
§11.4.3: References to ionic molecules
According to curriculum science the concept of the molecule is not relevant to ionic materials, where there is an extended lattice of ions. However, in the present research it was found that the particular ions that were conjectured to have been involved in a specific electron transfer event were sometimes considered to be a molecule. A number of the colearners explicitly referred to molecules in sodium chloride (Annie, Brian, Jagdish, Kabul, Tajinder and Umar, see appendix 35, §A35.3.1).
Brian thought that in the sodium chloride lattice each ion was part of a molecule with each of its neighbouring counter ions (B2.40), but in general a molecule of sodium chloride was conceptualised in terms of an ion-pair within the lattice. Several colearners were able to nominate which ions in a diagram were meant to be in the same molecule. One colearner, Kabul, at one point suggested that there were ionic bonds within a molecule (i.e. ion-pair), but covalent bonds between the molecules (K2.A581) in potassium fluoride. Even at the end of her course Annie referred to a molecule of sodium chloride comprised of two atoms (A3.30).
So in this research study several of the colearners specifically referred to molecules in the context of ionic bonding. 'Incidental' data collected from other learners shows that the notion of ionic molecules is not restricted to the colearners interviewed for this research (see appendix 35, §A35.3.2).
Students may then see the dissolving of ionic materials in terms of the solvation of molecules (i.e. ion-pairs) rather than ions,
[Sodium chloride dissolves in water] "because the water breaks up the large salt crystall [sic] into tiny molecules of N aCl, I don't think that any atomic changes go on in this process."
Induction exercise, September 1994
References to sodium chloride molecules were identified in scripts for a mock A level examination, and in particular that the molecules were held together in the solid by van der Waals' forces (see appendix 35, §A35.3.3).
Appendix 2 describes a simple pen-and-paper instrument (the truth about ionic bonding diagnostic instrument) used in the research to test whether some aspects of colearners' thinking elicited in this study were more widespread. The instrument was used to test a sample of 81 A level students who had not yet studied bonding at that level, and 128 who had (see appendix 2 for details). Four of the thirty items in this instrument related to the presence of of molecules in focal figure 5:
focal figure 5
The four items were:
- 7. In the diagram each molecule of sodium chloride contains one sodiumion and one chloride ion.
- 13. There are exactly fifteen molecules of sodium chloride in the diagram
- 18. There is a bond between the ions in each molecule, but no bonds between the molecules.
- 29. There are no molecules shown in the diagram.
In each case a significant proportion of the responses supported the notion of molecules being present in the figure. Item 29, which denied the presence of molecules was considered 'false' by 59% of A level students who had not studied the topic at A level, and 46% who had. 50% of those who had not studied bonding at A level, and 46% of those that had, thought there were 15 molecules of sodium chloride in the diagram; and almost equal proportions 53%, and 52% respectively thought that the molecules contained one cation and one anion. Item 18, which suggested there were no bonds between the molecules, was supported by smaller proportions of respondents (36% of students who had not, and 22% of students who had, studied bonding at A level), but this item required students to accept the presence of molecules, and take a particular view of the interaction between them. Although the sample used was quite small, and can not claim to be fully representative of A level chemistry students in general, this small scale survey does suggest that a molecular interpretation of ionic materials may be common.
It would seem then that, on the basis of the evidence presented, the notion of ionic molecules, i.e. ion-pairs that are discrete units within an ionic lattice, may be widespread amongst A level chemistry students, even though it is not sensible from a curriculum science perspective.
§11.5: Electrovalency as the determinant of the number of ionic bonds formed: the valency conjecture
If – from the 'octet perspective' – the electron transfer event is seen as an integral part of the ionic bond, such that ionic bonds can only occur where there has been electron transfer, then the number of ionic bonds that an atom may form is determined by the number of electrons it will donate or accept in reaching an octet state, i.e. by the electrovalency. A number of the colearners in the study (Carol, Kabul, Lovesh, Noor, Paminder and Tajinder) demonstrated the tendency to think along these lines at the start of their A level course (see appendix 36). Carol suggested that an atom could form as many ionic bonds "as it wants, as long as it's got electrons to cover how many it does want" (C1.262). Tajinder reported that in sodium chloride "one chlorine is only bonded to one sodium, because a sodium atom can only lose one electron, so, therefore … it can only gain one bond" (T1.A446). In Paminder's first interview she reacted to a diagram showing sodium surrounded by four chloride ions (in a plane of the crystal structure) by demanding to know how that could be possible: "how can you have that when, there's only one electron in the sodium, to give to one chlorine, so how are these three, how are they attached to that?" (P1.A307).
Appendix 2 describes the truth about ionic bonding diagnostic instrument, that was written to provide a pencil-and-paper test for some of the alternative conceptions elicited during the interviews with colearners. The valency conjecture would limit sodium and chlorine to forming one ionic bond each as their ions have charge of magnitude one. Several items in the truth about ionic bonding diagnostic instrument related to this aspect of ionic bonding:-
- 2. Each chloride ion in the diagram is bonded to only one sodium ion.
- 4. A sodium atom can only form one ionic bond, because it only has one electron in its outer shell to donate.
- 10. Each sodium ion in the diagram is bonded to only one chloride ion.
- 14. In the diagram each chloride ion is bonded to more than one sodium ion.
17. A chlorine atom can only form one ionic bond, because it can only accept one more electron into its outer shell. - 21. In the diagram each sodium ion is bonded to more than one chloride ion.
The instrument was used with a sample of 81 A level chemistry students yet to study bonding at A level, and 128 who had studied the topic at this level (see the details in appendix 2).
Items 2, 10, 14 and 21 concerned the number of bonds each ion had in the lattice. The proportion of respondents supporting the view that each ion only had one bond varied in the range 37% to 46% for the four items amongst those yet to study bonding at A level, and in the range 14% – 28% for those who had. These four items did not specify the type of bond being discussed, and although from a curriculum science perspective the bonds would all be ionic, learners would not necessarily share this assumption.
Items 4 and 17 specifically referred to ionic bonds, and for these items a majority of respondents agreed with the valency conjecture viewpoint:
| item number | item statement | support for valency conjecture before teaching | support for valency conjecture after teaching |
| 4 | A sodium atom can only form one ionic bond, because it only has one electron in its outer shell to donate. | 57% selected TRUE | 60% selected TRUE |
| 17 | A chlorine atom can only form one ionic bond, because it can only accept one more electron into its outer shell. | 60% selected TRUE | 58% selected TRUE |
The sampling method was 'convenience sampling' (see appendix 2), and this survey can not be claimed as representative of the wider population of A level chemistry students. Also, there was no matching of the two samples of students before and after teaching, and therefore the close matching of the responses before and after teaching can not be considered too significant.
Notwithstanding such caveats, this finding suggests that the notion that the number of ionic bonds is restricted by electrovalency may be one that is not readily 'corrected' by teaching. A more rigorous survey would be needed to confirm this. This point is considered in the discussion in chapter 12 (§12.6). The data presented certainly demonstrates that several colearners held a valency conjecture that clearly impeded their learning of the taught model of ionic bonding, and the small scale survey carried out with the diagnostic instrument suggests this may be a widespread feature of chemistry students' thinking.
§11.6: Dichotomous classification of bonding
"bonds can be either covalent or ionic"
Induction exercise, September 1991
The full shells explanatory principle readily accommodates covalent and ionic bonding, but this research suggest that learners cannot easily use it to explain other classes of bonding. Therefore for a learner applying the full shells explanatory principle anything that is recognised as bonding may well be classified in terms of the dichotomy ionic-covalent.
§11.6.1: Learner’s dichotomies
It would seem from the research being reported here that typically learners commenced A level with distinct models of covalent and ionic bonding, and criteria to distinguish the two cases. The interview study suggests that the colearners were only likely to have any detailed knowledge of two types of bonding when they enrolled on an A level course (see appendix 37, §A37.1.1), and this is supported by evidence collected from other students setting out on A level chemistry (see appendix 37, §A37.1.2). Some students may well be aware of metallic bonding when they commence their A level studies, but this category does not readily fit with the full shells explanatory principle for explaining bonding (§11.6.6). So in the following classification of bonding, covalent and ionic bonding are explained in terms of the familiar notions of electron sharing, electron transfer and stable electron shells, whilst the metallic bond is just explained as a tautology,
"The types of bonding are:
Induction exercise, September 1995
• IONIC; the donation of electrons. e.g. If one atom has one electron in its outer shell, and another has 7, the first atom may donate an electron to the second in order for both of them to become stable.
• COVALENT; is the sharing of electrons in order for atoms to become stable. e.g. 2 atoms with 7 electrons in their outer shells each, may each share one electron from another in order to become chemically stable
• METALLIC; atoms in metals bond tightly together to form a strong substance"
It would seem from the data collected that it is common for students commencing A level to classify bonds into two categories, using simple criteria:
| covalent | ionic |
| electrons are shared | electrons are transferred |
| between non-metal atoms | from metal to non-metal atoms |
As with all aspects of this study the data collected from the individual colearners reflected their unique cognitive structures. Paminder used the dichotomy covalent- ionic near the beginning of her course, but she did not seem to have explicit criteria (such as whether the elements involved were metal or non-metals) for determining bond type. Although Paminder would assign bonds to one of the two categories, it was not possible to elicit her criteria, although she seemed to feel the classifications were not arbitrary (see appendix 37, §A37.1.3).
Carol also used the covalent-ionic dichotomy to classify bonds, but whereas for most of the colearners discussed above these two categories were of equal standing, Carol construed ionic bonds to be in some way a lesser category (see appendix 37, §A37.1.4). Indeed in order to interpret her comments coherently it became necessary to conjecture that Carol used the word 'bond' in two distinct ways, to stand for a covalent – and one might almost say a 'proper' to her mind -bond, or for just an attractive force.
The tendency of learners to distinguish between chemical bonds and just forces will be considered later in the chapter (§11.7), but Carol was unusual in seeming to class ionic bonds as just forces. However, if Carol did not tend to ascribe ionic bonds the same full bond status as covalent bonds, she still gave ionic bonds a higher status than other forms of bonding (see appendix 37, §A37.1.5).
§11.6.2: Learners’ classification of polar bonds
"well, ionic I suppose. Well, no, covalent I think"
Carol's classification of the polar bond in hydrogen fluoride (C2.432)
In general then, when learners commence an A level course they have two categories of bond, covalent and ionic, which are distinguished by such criteria as overlap being represented, or the classification of the elements involved as metals and non-metals. These two categories may be explained in terms of the full shells explanatory principle, and may be described by most learners as sharing of electrons and transfer of electrons respectively. Early in the A level chemistry course students will be taught about the electronegativity scale (in place of the simple metal/non- metal classification), and that most bonds show some degree of polarity rather than being simply covalent or ionic.
As would be expected, before learners had the category of polar bond available, they tended to classify polar bonds as covalent or ionic (see appendix 38, §A38.1.1). Interestingly alternative figures representing hydrogen chloride molecules were construed differently by Kabul when he undertook the construct repertory test (November 1992). One triad element was construed as having covalent bonding, and not being an ionic compound, where the other representation of the same molecule was construed as being an ionic compound, and not having covalent bonding (see appendix 38, §A38.1.2).
In the interviews the assignment of a bond as covalent or ionic was sometimes tested by asking the colearner to then compare bonds: asking if two bonds that had both been classed as, say, covalent (when one might be more precisely described as polar) were the same type of bond. When this technique was undertaken with Kabul (in relation to a species where he had described carbon-carbon, carbon- hydrogen and carbon–oxygen bonds as covalent), it did not seem to have occurred to him that covalent bonds could be different, and he seemed to find the question somewhat meaningless (see appendix 38, §A38.1.3).
In the present research it was found that there was a strong tendency for learners to often ignore the category of polar bond, and to continue to divide bonds into covalent and ionic. There are many examples in the data collected of colearners who had been taught about electronegativity and polar bonding, labelling a bond as covalent or ionic, when from the curriculum science perspective it would be appropriate to use the category of polar (see appendix 38, §A38.1.4).
focal figure 14
Boron fluoride is an example of a substance where bonding would be expected to be polar according to curriculum science. Focal figure 14 represented a molecule of boron trifluoride as a resonance between canonical forms (where the individual bonds were shown as covalent or ionic in the individual canonical forms, but where the resonance implies the actual bonds are intermediate). Some of the colearners still used a dichotomous classification, suggesting that there were covalent and ionic bonds between boron and hydrogen in the same species (see appendix 38, §A38.1.5).
In the 1994 College mock A level examinations, 31 students answered a question about bonding. When asked to explain the bonding in phosphorus (V) chloride, there were 7 (23%) references to the ionic bonding in the solid state. The phosphorus-chlorine bonds in the molecule (in the vapour phase, or in the [PCl4]+ and [PCl6]– ions in the solid) are polar, but not one of the candidates mentioned this. 25 (81%) referred to covalent bonds. Where more details of this 'covalent' bonding was given, 10 students (32% of those answering the question) specifically referred to electrons being 'shared', i.e. the full shell explanatory principle description of the bond. (Two students referred to stable electronic configurations, and two
mentioned the 'expanded octet'. Only one student mentioned the electrostatic
nucleus-electron interaction. There were no references to molecular orbitals.) The
following example is from a student who illustrated the type of bonding construed in PCl5:
"Phosphorus (V) chloride is covalent bonding, in which one electron is supplied by each atom."
(Mock examination response, March 1994.)
So even in an examination context it would seem learners do not tend to readily bring to mind the category of polar bonding. However, it might be suggested that learners are applying the covalent-ionic dichotomy as a first approximation to bond type. Indeed it is quite normal (although perhaps not rigorous) in chemistry to refer to the same bond as covalent or polar according to the context as seems appropriate (c.f. the discussion of the chemist's toolbox in chapter 1, §1.7.2). We might therefore interpret classifications such as those discussed above as meaning that a bond was 'essentially covalent' or 'effectively ionic'. This could explain most of the dichotomous classifications discussed above (although not the assignment of both covalent and ionic bonding to boron trifluoride). Yet there were occasions during
the research where colearners were clearly not sure of the nature of a bond, but would still tend to prefer the covalent-ionic categories, and would not suggest 'polar', or 'something in between' (see appendix 38, §A38.1.6).
It was also found that explicit reference to electronegativity or bond polarity might nonetheless be accompanied by a dichotomous classification of bond type. At the end of Annie's course she thought the bonding in focal figure 8 was probably ionic. Despite discussing there being a "pole" in the "molecule", she thought that a metal and non-metal normally combined that way (see appendix 38, §A38.1.7). So Annie's more established learning appears to take precedence when she has to classify the bond type. The data collected in this research includes a range of other examples of colearners demonstrating they were able to talk of electronegativity differences and polarity in bonds, but then going on to classify polar bonds dichotomously – even when the bond polarity is particularly relevant to the context of the dialogue (see appendix 38, §A38.1.8).
Hydrogen bonding can only occur where the intramolecular bond is sufficiently polar. However, it was found that even where colearners explicitly recognised the presence of hydrogen bonding, and explained that this implied a bond between hydrogen and a more electronegative element, they might still label the intramolecular bond as covalent (see appendix 38, §A38.1.9).
One of the consequences of polar bonding is the possibility that bond fission may be heterolytic rather than homolytic (although this is not consistent with a view that on bond fission each atom 'gets its own electrons back', as discussed earlier, §11.4.1). When this possibility was put to Kabul it seemed to be so counter-intuitive that he was nonplused (see appendix 38, §A38.1.10).
It is of interest that the tendency to label bonds as covalent and ionic can co-exist with an ability to explain how the nature of a bond depends on the difference in electronegativity. So a student may classify a bond in a way inconsistent with their own explanation of how they classify bonds (see appendix 38, §A38.1.11).
Where the concept of bond polarity is used in classifying a bond, it may be used as a moderator to the primary classes of covalent and ionic. So for Debra the polarity of the bond was a secondary effect, which moderated the covalent bond (see appendix 38, §A38.1.12). Similarly during his course Kabul described polar bonds as similar to and like covalent bonds, and suggested that polar bonds was a sub-class of covalent bonds (see appendix 38, §A38.1.13). In the same way when Tajinder started to use the descriptor 'polar' for bonds, this did not mean he no longer classed them as covalent (see appendix 38, §A38.1.14). There was evidence in the study that other colearners also used the 'polar' label less as a category in its own right, but more as a moderator for the covalent and ionic categories (see appendix 38, §A38.1.15), including Carol who seemed to conceptualise polar bonds as covalent but "trying to be ionic" or "ionic but trying to be covalent" (c.f.§11.3).
§11.6.3: Learners’ classification of dative bonds
Dative bonding is:
"When an atom donates both electrons to a covalent bond"
Concept map, first year student, June 1994
Dative bonds involve the interaction between a poorly shielded positive core on one species, and electron density – often a non-bonded ('lone') pair of electrons – on another. In an example such as the aluminium chloride dimer, the electrons in the dative bond bridge between species of different electronegativity: in this example the chlorine core has a +7 charge and the aluminium a +3 charge, so the electron density will be greater near the ('donor') chlorine end of the bond. This dative bond is a polar bond.
However in this research it was found that dative bonds were often considered by colearners to be covalent rather than polar. This is considered to be significant, as from an electrostatic viewpoint the dative bond is clearly polar. However, the covalent category follows from the full shells explanatory principle description of electron sharing, where polar bonding does not readily make sense from such a perspective.
Sometimes in the interviews the colearners simply described dative bonds as covalent (see appendix 38, §A38.2.1). On other occasions dative bonds were presented as similar to covalent bonds (see appendix 38, §A38.2.2). In Kabul's explanation of the dative bond in aluminium chloride he refers to what he calls the "G.C.S.E. format", which says that "in order to attain a stable state you must have eight electrons", and suggests that "one of the chlorine atoms seems to donate two electrons, and form a dative bond, which is just similar to covalent bond once it's formed" (K4.B414). This comment could reflect something that has been emphasised by a teacher or text – that is that it does not matter where the electrons came from, their origin does not effect the bond. This would be a useful teaching point in terms of the 'history conjecture' (§11.4), but if it is put in terms of 'the dative bond being like any other covalent bond' it may lead to an epistemological learning impediment (§1.5.5) by encouraging the dichotomous classification of bonds.
Another variant for describing the dative bond was to construe it as a type of covalent bond (see appendix 38, §A38.2.3). It would seem that there is little substantial difference between learners seeing a dative bond as covalent, as a type of covalent bond, or like covalent. Whichever of these descriptions is used, the inherent polar nature of the dative bond is ignored. From the curriculum science perspective, the dative bond is a special case of the polar bond, and colearners' dichotomous classification of dative bonds is a special case of the tendency for polar bonds to be seen as either covalent or ionic, or as slight modifications of these archetypes.
§11.6.4: Learners’ classification of metallic bonds
"suppose you have, say for example, sodium, right? Sodium's like made up, suppose you have metal, a sheet of sodium metal, yeah, that consists of metallic bonding, that means like it's made of, like, the metal sodium, and it's just like bonded like between itself, it's not ionic, and it's not covalent either, it's like, it's hard to explain this. It's just like that metal's bonding there, I mean you don't have something like chlorine mixed with it, and, do you get me? {laughs} "
Paminder 'explaining' the metallic bond, P2.A195
The full shells explanatory principle can not be used to explain the metallic bond in terms of a simple pithy description such as sharing or transferring electrons (as in the covalent and ionic cases respectively). In the present study it was found that colearners generally did not know about metallic bonding when they started their course, and any previous learning exhibited tended to be at the level of 'metallic bonding occurs in metals'. Appropriate progression during an A level course would lead to an understanding of metallic bonding in terms of electrostatic interactions between atomic cores and delocalised electrons, and of overlap of atomic orbitals to give molecular orbitals. Data collected during the research suggest that prior to demonstrating this level of understanding colearners' explanations of metallic bonding tended to fall into four general categories:
- there is no bonding in metals;
- there is some form of bonding in metals, but not proper bonding;
- metals have covalent and/or ionic bonding;
- metals have metallic bonding, which is a sea of electrons.
Some of the colearners displayed several of these interpretations at various stages in their course. For example each of these positions, and others, were elicited from Annie as she attempted to make sense of metallic bonding (see appendix 39, §A39.1.1).
From a curriculum science perspective Annie's first suggestion that metals did not have any bonding seems inconsistent with the obvious structural integrity of common and familiar metals such as iron and copper. However Annie felt bonding was not needed, and similar ideas were elicited from Jagdish and Noor (see appendix 39, §A39.1.2). Noor did not think the bonding in a metal was covalent or ionic, and she did not know of any other class of chemical bond. So although she thought there had to be something holding the metal together, she concluded it could not be chemical bonding.
The apparent (i.e., from the octet perspective) paradox that metals held together, but chemical bonds were either covalent or ionic, led to colearners either making apparently arbitrary decisions that the bonding would be covalent (Carol, Kabul, Mike) or ionic (Paminder) or – when colearners had some knowledge of the delocalised electrons and the cations – attempts to rationalise how the bonding was like covalent (Kabul), or like ionic (Edward), or some combination of the two (Debra), (see appendix 39, §A39.1.3). This tendency was reflected in some of the incidental data collected from other chemistry students (see appendix 39, §A39.1.4).
As colearners progressed through their A level course they became more familiar with the notion of the metallic bond, but there was considerable evidence that incorporating curriculum science models of this type of bond into cognitive structure could be a slow process. One colearner (Carol) was reluctant to admit a discrete metallic category of bond, even when she (a) recognised the need for bonding in metals, (b) was familiar with the term 'metallic bonding', and (c) identified it as positive ions in a sea of electrons (see appendix 39, §A39.1.5).
Another colearner, Kabul, actually seemed to 'coin' the term 'metallic bonding' spontaneously before he had formal been introduced to it. When he then read up on the topic he learnt that "iron forms a hexagon around it's shell" (i.e. that it was hexagonal close packed), which he interpreted as "it has got six electrons in its outermost [sic] shell" which were bonded to surrounding iron atoms. Based on this he went on to hypothesise that other metals would form different shapes such as decagons, pentagons and triangles (see appendix 39, §A39.1.6). This finding was idiosyncratic, but is interesting for two reasons. Firstly, Kabul built an alternative model of metal structures based on something he had read in a textbook, and his knowledge of the 'hexagonal' structure of iron could be considered as acting as an epistemological learning impediment (§1.5.5). Secondly, the assumption that the number of bonds equated with the number of valence shell electrons – in principle at least, actually Kabul misidentified which electrons were in the outer shell – is very similar to the valency conjecture commonly found with ionic bonding (§11.5). That is a notion of valency from covalent bonding was misapplied in a context where it was not valid.
Although colearners readily took up the idea of a sea of electrons, there was evidence that this was sometimes little more that rote learning of a new expression. For example, in Lovesh's first term he drew the types of chemical bond he was aware of. His diagram of metallic bonding gave little clue about the nature of the bonding, beyond the labelling of an interstitial space as "see [sic] of electrons".
Lovesh's diagram for metallic bonding, November 1992
Umar was actually familiar with the term 'sea of electrons' from his school course. Despite this when he was probed he described covalent and ionic bonds in pure metals and alloys respectively (see appendix 39, §A39.1.7). Other colearners also had difficulty making sense of the sea of electrons model , and some extended the sea metaphor to have the conduction electrons swim or floating about in the sea (see appendix 39, §A39.1.8).
In the 1994 College mock A level examination, of the 31 students answering the question on bonding, 23 (74%) referred to metallic bonding when explaining the bonding in copper, and an equal number mentioned the sea of electrons. Some students referred to the sea of electrons without giving any clear indication of what this metaphor is meant to imply, being satisfied to provide simple descriptions (see appendix 39, §A39.1.9). Certainly several of the students' diagrams of metallic bonding in copper seemed to show an imbalance of charge (see appendix 39, §A39.1.10), such as the following example:
"Copper. This has mettalic [sic] bonding. In Mettalic bonding the atoms are held together in a "sea" of electrons which acts like a glue."
Mock examination response, March 1994
Two of the students taking the examination extended the sea metaphor to suggest that the cations were like islands in the sea, and there were also references to the electrons drifting, and to the cations being suspended and floating in the sea (see appendix 39, §A39.1.11).
In the interview study there was some suggestion that the sea of electrons description of the metallic bond – although limited in itself – could act as a suitable image for developing an electrostatic model of the bond. However, the evidence from the mock examination presented above suggests that even if these A level examination candidates had acquired an electrostatic model of the bond, a significant number were content to give examination responses in terms of the sea image alone. This is an issue that will be considered in my final chapter (§12.4.3). The following proposition from a concept map (drawn up as an end-of-first-year revision exercise) suggests that even when an electrostatic model of the bond is taken up, this may supplement – rather than develop – the sea metaphor,
"Metallic bonding is only occrent [sic] in metals and is the attraction between the +ve charge of the metal ions and the -ve charge of the electrons. It also has a sea of electrons which flow around the structure."
Concept map, first year student, June 1994
§11.6.5: Learners’ classifications of intermolecular bonds
If learners commence A level with a bonding typology limited to covalent-ionic, then they do not have appropriate categories to deal with inter-molecular bonds.
focal figure 11
focal figure 17
One response to being shown diagrams such as focal figures 11 and 17 was to deny that there was any intermolecular bonding present in the substances represented (see appendix 39, §A39.2.1). Where the colearner recognised that something must be holding the molecules together, this would be considered as an attraction or force, but not a chemical bond (see §11.7).
However, sometimes colearners did identify intermolecular bonding, but – as with the metallic case above – in terms of the familiar categories of covalent and ionic bonding (see appendix 39, §A39.2.2).
Although colearners were generally unaware of hydrogen bonding at the start of their A level courses, there were a number of examples in the interviews of the term 'hydrogen bond' having been acquired, without an appreciation of the intended meaning (see appendix 39, §A39.2.3). In her second interview Debra suggested that the intramolecular bonding in hydrogen fluoride was hydrogen bonding (D2.343). Similarly, Paminder's construed diagrams representing methane or hydrogen as containing hydrogen bonds. After some questioning it was found that for Paminder hydrogen bonding was where hydrogen was bonding to something: "because, if you think about it, you know, 'hydrogen bonding', that's like, you know, 'what is hydrogen bonding to?' It's kind of that sense" (P2.A309). Paminder had apparently met the term hydrogen bond in the context of D.N.A. in biology, and seemed to have just adopted what seemed a likely meaning, i.e. a bond to hydrogen. It seems that references in her biology lessons had led to an epistemological learning impediment. Similarly, Umar seemed to have made the same 'intelligent guess' at what was meant by the term: "if 7's bonded to another atom" (U2.B034).
The meanings adopted by colearners Debra, Paminder and Umar were reflected in two responses to induction exercises taken by students commencing A level studies.
One student defined the hydrogen bond as if it was a covalent bond involving hydrogen,
"Hydrogen bond is when a hydrogen shares the same electrons with another element"
Induction exercise, September 1995
Another drew a diagram of the 'hydrogen bond', within what was apparently a water molecule,
Induction exercise, September 1995
It would seem that possible consequences of learners commencing A level with a limited typology of chemical bonds include,
- not recognising the presence of intermolecular bonding;
- classifying intermolecular bonds as ionic or covalent;
- interpreting the term 'hydrogen bond' within the covalent-ionic classification, as a type of covalent bond that involves hydrogen.
§11.7: The 'just forces' conjecture: distinguishing between bonds, and 'just forces'
It was shown above that intermolecular bonds may be misclassified as ionic or covalent by some learners (see appendix 39, §A39.2.2). Carol, Debra and Paminder all proposed ionic bonds in contexts where there were no ions shown. Kabul suggested extended covalent bonding in iodine without consideration of valency restrictions. These misclassifications may be seen as an attempt to categorise examples of bonding a learner meets, within a limited typology. An alternative strategy would be to discount phenomena that do not fit the covalent-ionic scheme as something other than bonding. Some forms of interaction that are accepted as examples of chemical bonding within curriculum science may be labelled as 'just forces' by a student who understands bonding in terms of the full shells explanatory principle. For example interactions such as hydrogen bonding that do not lead to new octet configurations may not be considered to qualify as bonds. When considering ionic materials, application of the valency conjecture may limit the number of bonds an ion is seen to form, and application of the history conjecture will allow a specific interaction to be identified as the ionic bond. The other interactions between counter ions may be considered to be just forces. §11.7.1: Ionic bonds as just forces. As reported above (§11.5), it was found that at the start of their A level course the colearners interviewed tended to suggest that in an ionic structure, such as sodium chloride, the number of bonds an ion could form was limited by its valency: so for example a sodium ion could only be bonded to one chloride ion. The colearners usually recognised that other ions would also adhere, but this was not considered to count as bonding. Rather the other ion-ion interactions were attractions, or forces (see appendix 40, §A40.1.1). Sometimes it was claimed that the interactions that were just forces were weaker than the force due to the ionic bond: so for example, Kabul distinguishes 'strong attractions' where electron transfer has taken place with 'weak attractions' with the other ions, and for Paminder an ion is most strongly attracted to "the one it forms a bond with", because "that's where it's transferred the electrons".
Similar views to those elicited from these colearners have been expressed in responses to course tests undertaken by other A level students (see appendix 40, §A40.1.2).
Appendix 2 describes a simple pen-and-paper instrument (the truth about ionic bonding diagnostic instrument) used in the research to test whether some aspects of colearners' thinking elicited in this study were more widespread. One of the aspects investigated was the notion that in an ionic material the interactions between counter ions that had not exchanged electrons were not bonds, but rather just forces: the just forces conjecture . The instrument was used to test a sample of 81 A level students who had not yet studied bonding at that level, and 128 who had (see appendix 2 for details). Five of the thirty items in this instrument related to the application of the just forces conjecture to focal figure 5.
focal figure 5
The five items were:
- 6. In the diagram a chloride ion is attracted to one sodium ion by a bond and is attracted to other sodium ions just by forces.
- 9. A positive ion will be bonded to any neighbouring negative ions.
- 22. In the diagram a sodium ion is attracted to one chloride ion by a bond and is attracted to other chloride ions just by forces.
- 25. A negative ion will be bonded to any neighbouring positive ions.
- 26. There are exactly fifteen ionic bonds in the diagram.
From a curriculum science perspective the two statements that a positive ion will be bonded to any neighbouring negative ions, and a negative ion will be bonded to any neighbouring positive ions are clearly correct, yet these propositions were thought to be false by 32% and 32.5% respectively of those A level students who had yet to study bonding. The statements were judged to be false by 27% and 30% respectively of the students who had studied bonding as an A level topic.
The most explicit statements of the just forces conjecture were supported by a considerable proportion of the students responding to the instrument. The statement that in the diagram a chloride ion is attracted to one sodium ion by a bond and is attracted to other sodium ions just by forces was judged 'true' by 41% of the A level students who had not yet studied bonding as an A level topic, and 35% of those who had. The complementary statement that in the diagram a sodium ion is attracted to one chloride ion by a bond and is attracted to other chloride ions just by forces received even stronger support, with 53% and 45% selecting 'true' of the A level students who had not yet studied bonding as an A level topic, and of those who had, respectively.
Focal figure 5 shows 30 ions, which from the full shell explanatory principle would be perceived as fifteen bonded ion-pairs. The consequent statement that there are exactly fifteen ionic bonds in the diagram was thought to be true by 44% and 30% of the A level students who had not yet studied bonding as an A level topic, and of those who had, respectively. (If an ionic bond is taken as a bond between two adjacent oppositely charged ions, then focal figure 5 actually features 49 ionic bonds.)
It would seem then that, on the basis of the evidence presented, the notion of two types of attractive interactions in an ionic lattice, i.e. ionic bonds and just forces, may be widespread amongst A level chemistry students, even though it is not sensible from a curriculum science perspective.
At certain points during the research interviews, the ionic category of bond was itself excluded from chemical bonding by some colearners. In some cases, such as Kabul and Lovesh, this seems to be an alternative position taken up when the colearner was no longer able to accept the just forces conjecture. However, in some cases this view was adopted early in the interviews, rather than as a 'fall-back' position (see appendix 40, §A40.1.3). So for Annie at the start of her course, bonding was represented by "circles that overlap" and Annie did not think there was bonding in focal figure 5 where "they don't actually overlap or anything", rather "it would probably get held together by just forces". At one stage in her course Carol suggested ions would "not bond, but go together 'cause they're opposite charges". Kabul passed through a similar phase when he apparently did not construe the tenuous ionic bond, that was "between everywhere", as being as much of a bond as the covalent bond where there was "electron sharing" (these and other examples are discussed in the appendix).
§11.7.2: Metallic bonds as just forces
"The metallic bond is the bond formed between metal ions themselves. Metal atoms, sometimes have free electrons in their conduction bands that are free and have enough energy to leave the metal atoms. These leave the metal atoms, i.e. they become ions. These ions, are then positively charged, because they have lost electrons. Therefore the positively charged ions, are attracted to the electrons, therefore the metal forms this kind of lattice solid, with their own electrons that they have lost. This is called the metallic bond. Ionic and covalent bonds, are formed with other atoms or groups of different atoms, where atoms lose or gain electrons, or share them, where as [sic] metallic bonding is not the sharing or loss or gain of electrons. It is just a lose association with metal ions, and electrons they have lost, where this helps to hold the solid metal lattice together."
Colearner Quorat: Test response, December 1992
Earlier in this chapter it was suggested that some colearners were unable to understand metallic bonding in terms of the full shells explanatory principle (§11.2.3), and dealt with this by various strategies. One approach was to consider that metals did not contain bonds as such, but just forces holding them together (see appendix 40, §A40.2.1), and in Noor's case this was judged to be a very weak attraction.
At the start of her course Jagdish did not think there was any bonding in iron, although the atoms "do stick together", so "there must be" force between the iron atoms. Jagdish looked the topic up in her texts, but considered the books unhelpful.
Jagdish appeared to have some form of 'mental block' over the idea of bonding in a metal. She reported that if two different metals were melted down, mixed and left to solidify, she thought that metallic bonding would form, and she felt she understood that. She also thought it must be "the same thing if I just had like two different containers of iron and melted together, and put them together into one container": but despite this she could not understand "what bonding is holding the iron atoms together". Jagdish referred to molecules in the metal to explain what was happening, but this seemed to be a purely heuristic device ("helpful when you … talk about, what are bondings inside the iron that are holding it together, but not [when you are asked] what is an iron molecule?").
§11.7.3: Polar bonds as just forces
Another category of bond that some colearners had difficulty in explaining in terms of the full shells explanatory principle was the polar bond. Although this was often simply considered to be covalent, or ionic, or some modification of one of these types (see §11.6.2), there were examples of colearners excluding polar bonds from full bonding status (see appendix 40, §A40.3.1). So for Carol the interactions in a hydrogen fluoride molecule were not covalent or ionic, but rather "something to do with electronegativity".
§11.7.4: Dative bonds as just forces
focal figure 15
focal figure 16
A particular type of polar bond which some colearners found difficult to classify was the dative bond (as discussed earlier in this chapter, §11.2.4, §11.6.3). In Quorat's first interview for the research she described focal figure 16 as "aluminium chloride" with "six covalent bonds" and "just attraction" (Q1.B412). In Tajinder's first interview he dismissed focal figure 15 as "wrong" because it showed chlorine with two bonds and aluminium with four (T1.C119). However he accepted focal figure 16, which he also interpreted as having "six" "covalent" bonds. He thought the the arrows were meant to represent the "force of attraction", rather than a bond (T1.C134).
§11.7.5: Hydrogen bonds as just forces
Hydrogen bonding, unlike polar and dative bonds, can not be construed in terms of forming full shells, and thus was prone to be being excluded as a type of bonding by colearners operating from that criterion (see appendix 40, §A40.4.1). So hydrogen bonding was described as a type of "intermolecular force" (Jagdish), or "intermolecular attraction" (Lovesh); and, as Tajinder suggested, the hydrogen bond is "not actually a bond, but it's a force".
§11.7.6: Solvent-solute bonds as just forces
The interactions between solute and solvent molecules in a solution are important, as unless they are large enough solvation will not occur (as the energy has to be provided to overcome interactions between the solute ions/molecules for example). Deviations from Raoult's law are often explained in terms of the relative strengths of the bonds between the various species present, where it is assumed that the interaction between solvent and solute particles is a type of bond. However, these types of interaction are not explained by the full shells explanatory principle, and are not 'bonds' from such a criterion.
In the present research it was found that colearners would not consider these types of interactions as bonds, rather they were just an attraction (see appendix 40, §A40.5.1).
§11.7.7: Van der Waals bonds as just forces
"they're just forces aren't they?"
Carol at the end of her course (C3.4)
"it's actually a type of force, it's not actually a chemical bonding"
Tajinder (T8.A289)
Like hydrogen bonds, van der Waals forces do not involve the formation of octets, and thus may not be considered as bonds where learners define bonds in terms of the full shells explanatory principle. So in a molecular solid the molecules are not held together by chemical bonds but by just the forces (see appendix 40, §A40.6.1). As Annie said at the end of her course, "it's not bonding. But there's sort of van der Waals' forces", and Tajinder thought it was "not actually bonding" rather "the positive-negative attraction". Kabul also made the distinction between forces and bonds when he explained that van der Waals' forces were "neither ionic, or covalent, you know. Just an attraction and repulsion between atoms." He thought that solids held together by these van der Waals' forces had low melting temperatures "because there are weak forces (no bonds) between individual molecules".
So at various times during the interviews undertaken for this research colearners excluded the following types of interaction from being chemical bonds:
- ionic bonds – either in total, or those not seen as due to electron transfer;
- polar bonds, including dative bonds;
- metallic bonds;
- hydrogen bonds and other types of permanent dipole-dipole and ion- dipole interactions;
- van der Waals forces.
In each case the type of interaction concerned was recognised as a force between different atomic or molecular species, but as just forces, not chemical bonding. In most of these cases this classification may be interpreted as a consequence of defining chemical bonding in terms of the full shells explanatory principle, and being unable to construe the interactions as bonds by this criterion.
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