Chapter 8 of Understanding Chemical Bonding: The development of A level students' understanding of the concept of chemical bonding
Alternative explanatory principles: the case of Tajinder
§8.0: The structure of the chapter
Tajinder was one of the colearners in the main cohort (1992-4) of chemistry students who participated in the study. Tajinder valued the experience of taking part in the research to such an extent that he requested additional sessions, and he was interviewed on over twenty occasions (see appendix 1, §A1.1), providing by far the most data of any of the colearners.
This chapter deals exclusively with Tajinder's case. It commences (§8.1) with a general overview of the case, and introduces the three explanatory principles that are considered to be central to Tajinder's thinking about chemical bonding. Then there is a consideration of Tajinder's understanding of the topic at the start of his course (§8.2), looking in particular at the octet rule explanatory principle that was the basis of his thinking about bonding at that time, and his understanding of forces. This provides the foundation for considering how Tajinder developed two new explanatory principles related to forces and energy during his course (§8.3).
Progression in Tajinder's understanding of chemical bonding is then discussed by considering the new conceptual tools he has acquired, and the increase in the range of phenomena he subsumes under his construct of chemical bonding (§8.4). It is argued in this section that Tajinder's progression was closely linked to his new explanatory principles, especially his coulombic forces explanatory principle (§8.4.3). However it is also pointed out that these supplemented rather than replaced his preexisting octet rule explanatory principle, which appeared to be deeply ingrained in his thinking (§8.4.4). So at the end of Tajinder's course he was working with three effectively distinct principles for explaining the same basic set of phenomena. Through the interviews Tajinder became aware of the pluralism in his thinking, and seemed quite happy to accept that his understanding of chemical bonding was based on a set of models, each of which he considered useful for some of the explanations he was required to give in chemistry (§8.4.5).
Tajinder's conscious awareness and acceptance of his pluralistic approach to explaining chemistry is seen as significant because of (i) the comments made about the fragmented nature of chemical knowledge in chapter 1 (§1.7.1); (ii) its relevance to the debate over the reality of students holding multiple frameworks considered in chapter 2 (§2.5.2); and (iii) its relevance to the question raised from a Piagetian perspective over whether adolescent students are capable of post-formal thinking (§2.2.1, although Tajinder was clearly an intelligent student and can not be taken as typical of 16-18 year olds).
The case study in this chapter is the result of many stages of analysis, and the interpretations presented are therefore many steps removed from the original data (as discussed in chapter 5, §5.3 and §5,4; see appendix 27 for an overview of the analysis and sample extracts from three intermediate stages in preparing the case study). It was suggested earlier that authenticity in interpretive research rested in part on the presentation of sufficient verbatim evidence to support the interpretations (§4.4.1, §4.4.5). Limitations of space, and considerations of readability, however lead to this chapter being a narrative digest of my findings (c.f. Pope and Denicolo's researcher's dilemma, §4.4.5). However, this chapter is supported by two appendices (appendices 28 and 29) which present many extracts from the original data base to support my findings.
Appendix 28 considers how Tajinder's progression in understanding chemical bonding may be linked to his acquiring and adopting an electrostatic explanatory scheme. That is, that Tajinder commenced A level chemistry explaining chemical bonding through his octet rule explanatory principle, but in order to make progress he had to learn to use an alternative basis for his explanations, the coulombic forces explanatory principle. It is proposed that to a great extent Tajinder's developing understanding of chemical bond may be seen as a transition from relying almost exclusively on the former, to increasingly using the latter when thinking about chemistry.
Appendix 29 provides evidence to support my findings that Tajinder never completely replaced his original octet rule explanatory principle with his new coulombic forces explanatory principle, and that he never integrated his ideas about systems evolving to minimum energy with the effects of electrostatic forces. This appendix then looks in detail at the pluralistic nature of Tajinder's explanations of chemical bonding.
Evidence from this case is also incorporated in the subsequent chapters in this section (chapter 9, 10 and 11), to help illustrate the general themes that were found to be common to several learners.
§8.1: An overview of Tajinder’s case in terms of alternative explanatory principles
From the wealth of detail available the following points give an overview of the case:
- at the start of the course Tajinder recognised three categories of chemical bonding (covalent, ionic and metallic).
- later in the course Tajinder was able to accept polar bonding as "in between" ionic and covalent – and then later still to explain this in terms of other concepts (electron density, electronegativity).
- during the course Tajinder came to accept other phenomena could be included under the general concept of chemical bond, i.e. hydrogen bonding, dative bonding, van der Waals' forces.
- Tajinder's definitions of chemical concepts became more sophisticated, for example the covalent bond was simply 'sharing' of electrons at the beginning of the course, but later became understood in terms of forces between the bonding electrons and the nuclei, and in terms of the overlap of atomic orbitals to form molecular orbitals.
- Tajinder acquired new concepts which related to bonding, such as electronegativity, orbitals, electron density, core charge, electron spin and energy levels.
During the period investigated Tajinder increased the number of 'tools' in his chemist's conceptual toolbox, the range of application of those tools, and his competence in using them.
The brief outline above gives little indication of the extent to which bonding- related concepts became integrated in Tajinder's cognitive structure during his course. In the previous chapter it was suggested that many of Annie's comments in her interviews could be organised into two complexes of related ideas, each one based in a core explanatory principle that formed the starting point for much of her thinking. It will be argued here that Tajinder's utterances about chemical bonding can largely be understood as related to one of three such explanatory principles. I have labelled these three principles as the octet rule explanatory principle, the coulombic forces explanatory principle, and the minimum energy explanatory principle. These explanatory principles may be paraphrased as:
the octet rule explanatory principle
i) atoms are stable if they have full outer shells, and unstable otherwise;
ii) an atom that is unstable will want to become stable;
iii) the unstable atom will form bonds such that it seems to have a full outer shell, and thinks it has the right number of electrons.
the coulombic forces explanatory principle
i) there is always a force between two charged particles;
ii) similar charges repel, opposite charges attract;
iii)the magnitude of the force diminishes with increasing charge separation;
iv)forces acting on particles may be balanced at equilibrium.
the minimum energy explanatory principle
i) configurations of physical systems can be ascribed an energy level;
ii) lower energy is more stable than higher energy;
iii) physical systems will evolve towards lower energy configurations
In the following pages the findings from the case study are presented, and discussed.
§8.2: Tajinder’s knowledge of bonding at the start of the course
Tajinder was aware of three types of bonding at the start of his A level course. He included three categories of bonding in a concept map drawn during an introductory class (September, 1992). He later suggested the same categories when asked to name and draw the types of bonding he was familiar with (November, 1992).
He described these classes of bonding in the following terms:
• Transfer of electrons takes place in ionic bonding.
• In covalent bonding, electrons are shared.
• Metallic bonding takes place in metals. In this type of bondings [sic] the electrons are free to move around the area of the metal.
§8.2.1: An explanatory principle based on the octet rule
At the start of his A level course, then, Tajinder had already acquired a limited range of concepts related to chemical bonding. When first interviewed (interview T1, October, 1992) it became clear that to the extent that these concepts were connected in cognitive structure they were linked through an explanatory principle based on the octet rule.
The octet rule is a 'rule of thumb' that is fairly successful in elementary chemistry as few exceptions are met during most introductory courses. However, the rule does physical systems will evolve towards lower energy configurations. not have any genuine explanatory power, being merely a heuristic for discriminating stable and unstable structures at the atomic level. Despite its heuristic value, the octet rule does not suggest any mechanism by which noble gas electronic configurations arise, merely that such configurations tend to be stable.
During his first research interview Tajinder demonstrated that for him the octet rule had provided the basis for an explanatory principle. The explanatory principle that Tajinder used could be summarised:
i) atoms are stable if they have full outer shells, and unstable otherwise;
ii) an atom that is unstable will want to become stable;
iii) the unstable atom will form bonds such that it seems to have a full outer shell, and thinks it has the right number of electrons.
It will be noted that in the absence of any physical mechanism for bond formation, an anthropomorphic explanation is used – atoms are imbued with, or at least spoken of as if imbued with, consciousness and the ability to act on their thoughts. (This is a feature that was found to be common with other chemistry learners, as is demonstrated in chapter 11, §11.3).
§8.2.2: Tajinder’s application of the octet rule explanatory principle
The first interview showed how Tajinder used his octet rule explanatory principle to find a common basis to the three types of chemical bond he was familiar with.
So for Tajinder these classes of bond were explained as follows:
• Covalent bonding: In covalent bonding electrons are shared because of the number of electrons needed for an atom to be stable. For example, in hydrogen both atoms think [sic] they have two electrons. Although the electrons are shared each is perceived as belonging to the atom from which it originated, and if the bond is broken each atom will get its own electron back. (Ownership of electrons {§11.1.4} , and the tendency to see the history of an electron as significant {§11.4} were found to be common features of colearner thinking).
• Ionic bonding: This is where an atom loses its outermost electron to another atom which needs one electron in its outer shell to become stable. The sodium atom, for instance, is not stable and needs to lose an electron to have a full outer shell, so it loses it to a chlorine atom.
• Metallic bonding: An isolated sodium atom would become stable if it could lose an electron. In the context of metals electrons can leave atoms. Metallic bonding involves lots of free electrons which originate from the outer shells.
In each case the bond allows the atoms to have the stable electronic configuration.
§8.2.3: Limits to the range of convenience of the octet rule explanatory principle
Although the octet rule explanatory principle provided Tajinder with a basis for conceptualising his three categories of bonding according to a common principle, it also led to deductions that were inconsistent with aspects of curriculum science, and which would potentially impede his progress in A level chemistry. That is, it acted as a substantial learning impediment (§1.5.3).
Ionic bonds are distinguished from just forces: Although ionic bonding was defined in terms of the octet rule explanatory principle, Tajinder was not able to explain the integrity of the ionic lattice from this perspective. So in his scheme the ionic bond was the transfer of electrons between particular ion pairs, whereas the structure held together because of the positive and negatives. Tajinder supposed that ions were equally attracted to their neighbours, but not equally bonded. Each sodium ion could only be bonded to one chlorine ion; then no more bonds could be formed, as there were no more outer electrons available. (Tajinder's thinking about ionic bonding at this stage of the course included features that were also found in the data from other learners: construing the ionic bond as electron transfer (§11.2.2), limiting the number of ionic bonds according to valency (§11.5), and discriminating between two classes of interaction – bonds and just forces – between neighbouring counter ions in the ionic lattice (§11.7.1). These features are all considered in chapter 11.)
Covalent bonds are not conceptualised in terms of forces: Although a hydrogen molecule contains charged particles, this is not considered the be like the ionic case – Tajinder's perception is that the charges just stop the molecule falling apart (whereas the bond is the sharing of electrons to give full outer shells).
Intermolecular attractions are not bonds: Tajinder thought there could be 'positive- negative attractions' between molecules, although not if they were neutral. He thought that perhaps there could be a force – but not a bond. (This was another feature which was also found with other learners, and is discussed in chapter 11, §11.7).
It is seen that Tajinder did have some ideas about the roles of charges and forces in (what we would call) chemical bonding. However, as Tajinder defines bonds in terms of his octet rule explanatory principle, he did not include these force ideas within the realm of his bonding concept.
§8.2.4: Tajinder’s thinking about forces at the start of his course
It was noted above that Tajinder did not consider chemical bonding was concerned with forces. When Tajinder was asked about physical situations where forces were acting (interview T2, February 1993) it was found that his ideas were not always consistent with the curriculum science interpretation.
Newton's laws of motion. Whereas Newton-2 (§3.1.3) would associate balanced forces with zero acceleration, Tajinder associated this with zero speed. Tajinder also demonstrated alternative conceptions about the forces involved in interactions between several bodies. From Newton-3 it is known that when two bodies interact they are subjected to forces of equal magnitude, but opposite direction (c.f. 3.1.3). However, when Tajinder was asked about the case of an object placed on the earth, he did not think the forces could be of the same magnitude.
Tajinder also had non-Newtonian alternative conceptions about the gravitational forces acting in a solar system. He believed that the earth attracted the moon (as it does) but explained they did not get any closer as the moon repelled the earth. Nor did his model follow an inverse-square law: a planet furthest from the sun would be attracted the most, while the planet nearest would be repel the sun the most.
Interactions between charges. Tajinder did suggest that a larger charge or smaller separation should lead to a larger force, but he also thought that if two charges interacted the smaller charge would experience the greater force, and implied that the mass of the charges affects the force (perhaps not clearly distinguishing the force with its effect). Notwithstanding these ideas about charges in abstract, Tajinder did not always follow these rules in applying the ideas to atomic situations: for example he thought all electrons in a silicon atom would be equally attracted to the nucleus (interview T2, February 1993). In the first interview (October 1992) he had referred to a positive-negative bond that attracts the electrons to the nucleus, as there was always attraction between positive and negative. However he was not sure if the nucleus was attracted to the electrons.
Equilibrium. Ultimately Tajinder would come to understand that chemical processes (e.g. bond formation) could be understood as the results of systems with unbalanced forces. The system would evolve to a new configuration where an equilibrium of forces was established. However initially Tajinder had difficulty with the concept of equilibrium. For example at one point in the first interview (October 1992) he suggested that the repulsions present in a hydrogen molecule were greater than the attractions. He also thought that two protons in a nucleus would experience repulsion, but not attraction – although they were held together by a force (T2, February 1993). At a later date Tajinder discusses van der Waals' forces between two neon atoms and suggested that the attraction of the nucleus for the electrons (of the adjacent atom) is greater than the repulsion between the electrons (T3, April 1993).
The conservation of force explanatory principle. It was clear from the early interviews that Tajinder did not seem to clearly distinguish the concept of force, from that of charge, or from that of energy. For example when Tajinder discussed the interaction between the nucleus and electrons in a sodium atom, he appeared to conceive this as one central attraction from the nucleus to all the electrons (T1, October 1992). When Tajinder wrote in an assessment (about ionisation energy) that when one electron is removed from a shell the shell is subsequently held more tightly (March 1993) he could have been thinking about the effect of reduced repulsion between electrons. However over time it became clear that Tajinder applied an explanatory principle that I have labelled conservation of force. For example in a discussion about ionisation energies Tajinder refers to "how much force the atom has" (T5.A064).
§8.2.5: Tajinder’s application of his conservation of force explanatory principle
Tajinder's conservation of force explanatory principle could be summarised:
• an atomic nucleus has a certain amount of force available, that depends upon the charge on the nucleus, and is shared between the electrons.
When comparing the ionisation energies of beryllium and magnesium Tajinder referred to various relevant factors, but then suggests that magnesium does not have as much attraction to the outermost electrons as there are more electrons to attract (T5, April 1993). On another occasion he refers to the attraction in a helium atom being spread out over two electrons (T6, May 1993). In a subsequent interview Tajinder gives a clearer exposition of this conception (T7, May 1993), when he compares the helium atom to the helium ion. His argument followed the lines:
In the ion the protons only have one electron to attract.
Slightly less energy is needed to remove the atom's electron, because there are two electrons for the nucleus to attract. The amount of force the nucleus can give out is spread over the number of electrons there are – as if you've got an extra electron, the nucleus can not just give out extra force.
Tajinder's notion of conservation of force led to appropriate predictions in some contexts. Successive ionisation energies within an electron shell do increase as the repulsion between electrons is reduced, and the radius of the species decreases. Tajinder explained the same phenomenon from the idea of conservation of force, that there were less electrons to share the nucleus' attraction, so each electron received a larger share of the force.
It would have been interesting to have allowed Tajinder to follow through this logic as far into the course as possible, and see whether he spontaneously found the need to supplant this conception. However this would have been unethical (§4.3.2), so Tajinder was presented with the orthodox scientific views. Later in the same interview Tajinder referred to the electron in the Li2+ ion being subject to more attraction than an electron in the Li+ ion. Again his initial reasoning was that the effect of the nuclear charge was spread among the two electrons in the 1+ ion. When challenged he was able to form a new argument based on electron repulsion. In the end of year examination Tajinder wrote that "the Mg+ ion has a stronger pull on the second electron as the first has been removed" (June, 1993) – a comment that seems to be sensible from the conservation of force explanatory principle.
In his second year of the course Tajinder explained that a carbon atom would pull the bonding electrons in two carbon-hydrogen bonds less well than one, because its ability to pull electrons is being stretched (T13, November 1993). Again, rather than consider the additional repulsions, Tajinder seems to consider that the amount of pull available is limited.
§8.3: Tajinder’s adoption of new explanatory principles
During his course Tajinder supplemented his existing explanatory principles (the octet rule and conservation of force) with two additional principles more closely based on the curriculum science he was being taught.
§8.3.1: Acquiring an explanatory principle based on Coulombic electrostatics
At the start of his A level course Tajinder already thought that there was always attraction between positive and negative charges (T1, October 1992) – although in practice he did not always apply this principle.
Much of the classroom presentation of chemical ideas that Tajinder experienced was based around basic electrostatics, i.e. Coulomb's law. In qualitative terms these ideas may be expressed:
i) there is always a force between two charged particles;
ii) similar charges repel, opposite charges attract;
iii) the magnitude of the force diminishes with increasing charge separation;
iv) forces acting on particles may be balanced at equilibrium.
Tajinder's construction of a conceptual framework for understanding chemical bonding based on the electrostatic explanatory principle was hindered by his preexisting ideas which acted as substantial learning blocks (§1.5.3):
1: his own alternative conceptions of electrostatics, which meant that his interpretations of the interactions present between charges did not always match the orthodox curriculum science view;
2: Tajinder's use of the octet rule explanatory principle, which already 'explained' chemical bonding for him. (The limitations of this principle, discussed above, which are apparent from the viewpoint of curriculum science, would not be readily detected by someone defining and demarcating bonding phenomena from the perspective of the octet rule explanatory principle, c.f. §2.2.3).
For example when discussing metallic bonding quite early in his course, Tajinder stated that there was a force between the atoms joining them together (T2, February 1993). He described this as positive and negative forces. These were not the same thing – similar forces attract, whilst opposite forces repel. At this point Tajinder had not clearly distinguished charges from forces. Similarly in a concept map written as part of his revision for first year examinations Tajinder referred to the forces holding ions together as being "electrostatic forces, +ve and -ve" (June 1993).
As he proceeded in his studies Tajinder was able to explain the van der Waals' interactions between two adjacent atoms in terms of forces, but thought that the attractions would be larger than the repulsions (T3, April 1993). Shortly after this (T4, April 1993), Tajinder talked of the nucleus of one atom attracting the electrons of another – but suggested that there was a sort of force that holds the atoms together as well (T3, April 1993).
By the end of the first year Tajinder acquired a concept of hydrogen bonds in terms of attractions between ∂+ and ∂- ends of molecules. However, at one point during his second year he commented that he was not sure if Coulomb's law could be applied to hydrogen bonds, as Coulomb's law was really about electrons (T11, October 1993).
§8.3.2: Tajinder’s developing application of the coulombic forces explanatory principle
By the end of the first year of his course Tajinder was beginning to develop a conceptual framework for understanding bonding based on the coulombic forces explanatory principle. He explains metallic bonding in terms of the attraction between electrons and the positive ions, and refers to there being only electrostatic bonds present (T8, June 1993). He comments that all the bonds are equal in an ionic structure such as sodium chloride, and refers to forces due to oppositely charged ions. However these comments are mixed with others that are based on the octet rule explanatory principle. At this time covalent bonding is still understood in terms of sharing electrons to obtain stable electronic configurations.
Tajinder is able to apply electrostatic ideas in a number of contexts: for example that anions are larger than the parent atom as the gained electrons lead to additional repulsion between electrons (T4, April 1993). He appreciates how ionisation energy depends on core charge, and the nucleus-to-electron distance (T5, April 1993; T6, May 1993; T7, May 1993) and how the shapes of molecules could also be explained in terms of electrostatic repulsions (T9, June 1993; T23, May 1994).
Over his course Tajinder comes to apply electrostatic principles to the three categories of bonding he had at the start, and incorporate them in a complex of conceptions derived from the coulombic forces explanatory principle. He is able to explain covalent bonding in terms of the nucleus of one atom having a certain amount of attraction (c.f. §8.2.5) for another atom's electrons, and this force being what holds the molecule together (concept map on chemical bonding prepared as revision exercise, June 1993). He explains the process of bond formation as the core charges attracting electrons from the other atom into 'gaps' in their electronic configuration, so the atoms are attracted together to form a bond (T16, January 1994). Near the end of the course the bond in the hydrogen molecule is explained in terms the attraction of each nuclei for both electrons, balancing the repulsions present (T20, April 1994).
Tajinder came to understand the metallic bond as being formed when there is an attraction, a force, between one of the nuclei and the electrons on another atom: again an equilibrium is reached (T21, April 1994).
Similarly, Tajinder is able to explain how in ionic bonding, there is an attraction between the ions – because one has a positive charge and one a negative charge – but they do not coalesce because there will be repulsions between nuclei, and between electrons, and the repulsions equal the attractions (T20, April 1994). At this point Tajinder considers that ionic bonding is an attraction between positive and negative ions, rather than a transfer of electrons (T23, May 1994).
§8.3.3: Tajinder’s application of the minimum energy explanatory principle
Tajinder acquired the idea of the lowest available energy level as an explanatory principle early in his course. This principle could be stated:
- i) configurations of physical systems can be ascribed energy levels;
- ii) lower energy is more stable than higher energy;
- iii)physical systems will evolve towards lower energy configurations.
Although a physical system evolving to minimum energy may be considered equivalent to the effect of forces acting on the system until an equilibrium is reached, Tajinder did not continue the study of physics past G.C.S.E. level, and he did not tend to perceive the notions of minimising energy, and the effect of electrostatic forces as directly related.
When Tajinder was interviewed at the start of the third term, having been introduced to the idea of seeing chemical processes in terms of energy levels in class, he explained that if you had two atoms, and they joined together, the energy would be low (T3, April 1993).
When considering the electronic configuration of beryllium Tajinder explained that this would be 2s2 rather than s1p1 as the latter would be a higher energy (T3, April 1993). However Tajinder also suggested that a px orbital must be at a lower energy level than the py orbital as the former was always filled first. Here Tajinder did not appreciate the arbitrary nature of labelling the degenerate orbitals.
As with the octet rule explanatory principle, Tajinder seemed to need to imbue the atoms concerned with human thoughts and desires – at least metaphorically – as a mechanism for achieving stability. For example in his last term of the course Tajinder explained that it required energy to promote an electron in a molecule, as when a molecule forms it wants to stay at the lowest energy (T21, April 1994).
Tajinder's adoption of the minimum energy explanatory principle was largely tied to the development of the concept of molecular orbital. The principle was applied to the covalent bond, where two hydrogen atoms form a bond, forming two molecular orbitals (bonding and antibonding); and in a metal where there are molecular orbitals formed from overlap of atomic orbitals – Tajinder suggested these molecular orbitals must be at lower energy otherwise the metal would not exist (T21, April 1994). Tajinder did not at first think this idea could be applied to an ionic material such as NaCl – but then decided that there were molecular orbitals, but they were so polarised that they did not show, as the [i.e. bonding] molecular orbital was all around the chlorine ion. This may be considered as a sophisticated observation. This explanatory principle was applied to polar bonds, such as in lithium iodide, tetrachloromethane, water and hydrogen fluoride. Tajinder thought there might be a scale, so the more covalent the species, the more dominant the molecular orbital, and the more ionic, the less dominant. (In curriculum science terms in the more ionic case the molecular orbital would be more similar to the atomic orbital). However Tajinder did not consider hydrogen bonding could fall within a molecular orbital explanation, as that was just an attraction (c.f. §11.7).
§8.4: Tajinder’s progression in understanding chemical bonding
By comparing Tajinder's understanding of chemical bonding at the end of his course, with his understanding when he started his A level studies (i.e. as described in §8.2) it is clear that his understanding has shown considerable progression – a good deal of learning has taken place. This may be demonstrated by considering the range of relevant tools he has acquired for his chemist's tool box (§1.7.2), and the increased range of application of his concept of 'chemical bonding'.
§8.4.1: Tajinder's acquisition of new conceptual tools related to 'bonding'
During his course Tajinder acquired new conceptual tools for thinking about chemical bonding and related themes.
Electronegativity: by the second term Tajinder had acquired a concept of electronegativity, as a tool for deciding the type of bonding – a high difference in electronegativity suggests ionic bonding, but a low difference suggests covalent (T2, February 1993). However this rule would suggest calcium chloride, which Tajinder thought was covalent, was ionic.
Orbitals: Tajinder had acquired the use of the term orbital within the first month of his course (the concept was used in his organic chemistry classes). However initially Tajinder thought that orbitals were spheres with electrons at opposite sides (T1, October 1992). The term was not clearly distinguished from his existing concept of shell, and he tended to use the two terms as if synonymous (c.f. §9.2.1). In a subsequent research session, where Tajinder undertook Kelly's repertory test, he used the construct "shows rough placement of electrons in orbitals" to describe figures that actually represented electrons in shells (November 1992).
However during his second term Tajinder was able to describe an orbital as an area [sic – i.e. volume] around the nucleus of an atom, where an electron is likely to appear, that is, where 95% of the time you could find the electrons (T2, February 1993). Tajinder was apparently confusing the orbital itself with the arbitrary boundary drawn in diagrams, an error which recurred (T5, April 1993; T6, May 1993, cf. §9.2.4). He knew there were four types of orbital: s, p, d and f. He was not clear how orbitals related to shells, but could say that if all the p-orbitals were full of electrons then this would show like a sphere shape of electrons smeared out, and he thought this [i.e. the sub-shell] was what was represented by the circles drawn in elementary work. He continued to confuse orbitals, shells and sub-shells for some time (T6, May 1993; T14, November 1993).
At this stage Tajinder did not appreciate that the atomic orbitals interact to form molecular orbitals in bonding. He classified figures representing molecular orbitals as 'show[ing] s and p orbitals' (Kelly's construct repertory test, November 1992), and thought it was possible to draw molecules of oxygen and methane showing the s and p orbitals (T2, February 1993, c.f. §9.3.2).
In his third term Tajinder described an orbital as just the probability of finding the electron in a certain area [sic], and was aware that two electrons could go in the same orbital, but he would confuse orbital lobes with the orbitals themselves (T3, April 1993). Tajinder was not sure if covalent bonds could be counted as orbitals (T4, April 1993). He thought that electrons were restricted in where they can be in space, because they are in orbitals (T5, April 1993).
Electron density: Tajinder seemed to accept a notion of electron density readily, and was able to discuss the overall electron density of electron configurations (T3, April 1993). He could apply this idea to atoms such as neon – where the p electrons form a sphere when smeared out – and fluorine – which has not got a spherical electron density overall, because it is missing an electron and the others cannot move over to make up for this (T5, April 1993).
Core charge: By the third term Tajinder was able to use the concept of core charge – being the charge in the nucleus minus shielding electrons – and could generally work out core charges (T3, April 1993). Sometimes when using the concept of core charge in an explanation he would forget that this means he has already allowed for the effect of core electrons, and would introduce the effect of these electrons into his argument (T4, April 1993; T6, May 1993). He was sometimes uncertain when he should use his new tool of core charge, and when to use the more familiar idea of nuclear charge (T5, April 1993).
Electron spin: When Tajinder first used the term spin-pairing he did not seem to have any notion of what is implied, beyond there being two electrons in one orbital (T3, April 1993, c.f. §9.2.6). He seemed unclear whether spin is a property of electrons or of orbitals (T5, April 1993). At this time he commented that electron spin does not really mean anything, because the electron does not spin as it is part wave. Rather, he thought that electrons are said to spin in opposite directions to explain how two electrons can be in the same orbital without a very large repulsion. (This comment, perhaps a slightly distorted version of a comment presented to the group during class, seems to suggest that Tajinder was quite open to science being incomplete, and a human construction).
Energy levels: Tajinder acquired the use of the concept of energy levels during the first year of the course, although he initially referred to them as shells or orbitals (T5, April 1993, c.f. 9.2.3).
§8.4.2: Tajinder develops new categories of chemical bond
At the beginning of the course Tajinder only had three categories of chemical bond: covalent, metallic and ionic. He accepted that there might be forces between adjacent molecules, but a this was not considered to be chemical bonding – which was understood in terms of the octet rule explanatory principle. The construction of a complex of ideas derived from the alternative coulombic forces explanatory principle allowed Tajinder to include new forms of interaction as chemical bonds:
Van der Waals' forces. Tajinder came to understand van der Waals' forces in terms of electrostatic attractions, forces from one nucleus to the electrons of another atom (T3, April 1993). He understood that this was possible even when atoms were neutral and symmetrical, as the sphere described an overall picture over time, and (at any one instant) there were 'electron lumps'. Tajinder explained that as the electrons move around there would always be the possibility of little gaps (T11, October 1993). He thought that the electrons could be all down one side of the molecule for an instant (T9, June 1993).
Hydrogen bonding. At the beginning of his course Tajinder did not have a concept of hydrogen bonding, but by the end of the first year he was able to describe this as a certain type of attraction between ∂+ and ∂-, and so a type of bond (T8, June 1993). Tajinder included this as a category of bonding (which took place between hydrogen and a non-metal) on a concept map produced at this time (concept map on chemical bonding, prepared as a revision exercise, June 1993).
Polar bonding. At the start of the course Tajinder would class bonding in compounds as ionic or covalent (c.f. §11.6.2). The carbon-chlorine bond was considered to be in the same class as the hydrogen-hydrogen bond, i.e. covalent (T1, October 1992). Tajinder used water as an exemplar for covalent bonding when he was asked to draw the types of bonding with which he was familiar (November, 1992). By the second term Tajinder was talking of differences in electronegativity being used to determine bond type, but in terms of a dichotomy: a low difference meant covalent, a large difference polar (T2, February 1993).
When interviewed at the end of the first year and asked to list the types of bond he knew about Tajinder did not include polar (T8, June 1993). However later in the same session he did refer to electrons in the carbon-hydrogen bond being pulled more toward the carbon, and Tajinder referred to the bond in methane as covalent and polar. He then reported that bonding in compounds was normally polar, which was something in between ionic and covalent. This view (that polar bonds were the most common, and were to be understood as something in between ionic and covalent) was reiterated in a concept map Tajinder drew about this time (concept map on chemical bonding, prepared as a revision exercise, June 1993). At this point Tajinder's concept of the polar bond did not seem to be built on sound electrostatic principles: the comment that the polar bond involved a type of attraction between the ∂+ and ∂- ends of a bond suggested some confusion between cause and effect (T8, June 1993).
Often when Tajinder referred to polar bonding he would simply explain this in terms of electronegativity difference causing the electrons to be nearer one end of the bond (T9, June 1993). However sometimes Tajinder would take the explanation further, explaining for example that an iodine atom would attract electrons more than a lithium atom (T9, June 1993), and that bonding electrons are attracted more to oxygen than hydrogen in water, as oxygen has a larger pull on them (T11, October 1993). In discussing the carbon-chlorine bond Tajinder took the argument one further step towards basic principles – chlorine pulls the electrons more because it has a core charge of +7, so the electron density is pulled in until the electrons reach a point where they cannot go any further because of the repulsions from the chlorine [non-bonded] electrons, and the attraction of the carbon nucleus (T17, February 1994).
Dative bonds. Near the end of his first year Tajinder described a diagram of an aluminium chloride dimer as "completely wrong" as it showed chlorine with two bonds (T9, June 1993). Rather he thought (in accordance with octet rule explanatory principle) that a chlorine atom already had seven electrons in its outer shell, so it only needed one more, so it would only form one bond. However he was then able to discuss how there would be an attraction between molecules, although this would be electrostatic attraction, and not bonds. He suggested that there was a gap in the electron density cloud around aluminium, and as chlorine had full density the [aluminium] nucleus pulls electrons from the chlorine. This effect, he thought, was like a force (c.f. §11.7.4).
§8.4.3: Tajinder’s developing understanding of chemical bonding is related to his acquisition of new explanatory principles
At the start of his A level chemistry course then, Tajinder's thinking about chemical bonding was largely derived from his octet rule explanatory principle. This explanatory principle was of limited utility in understanding chemical bonding to the depth required at A level.
By the end of his course he had acquired two other explanatory principles which could be used to explain chemical bonds: the coulombic forces explanatory principle, and the minimum energy explanatory principle.
Tajinder used his coulombic forces explanatory principle to derive a complex of ideas to enable him to explain bond formation in terms of the nuclei of one atom attracting electrons of another, so that the atoms come together. Ionic, covalent, metallic, polar, hydrogen, dative bonds and van der Waals forces could be explained as due to electrostatic forces between the component species. A bond was seen as an attraction between two species (T12, October 1993), as something that keeps atoms held together, a force (T14, November 1993). Solvation was understood as the formation of bonds (T19, April 1994), albeit not fixed bonds, but ones constantly breaking and forming (T22, May 1994).
Tajinder's minimum energy explanatory principle was closely associated with the formation of molecular orbitals. This explanatory principle did not become as well integrated into existing cognitive structure during the course as the coulombic forces explanatory principle. For example (for Tajinder) hydrogen bonds did not fall within its range of convenience (T21.D224).
The importance of Tajinder's new explanatory principles in his developing understanding of chemical bonding is considered in more depth in appendix 28.
§8.4.4: Stability of the octet rule explanatory principle
So even when Tajinder had begun to construct a new explanatory conceptual scheme for understanding chemical bonding based around the coulombic forces explanatory principle, he still tended to apply his octet rule explanatory principle in some contexts. At the start of his third term he states that all elements try to gain noble gas configurations to become stable (T4, April 1993). At the end of the first year of A level work he talks about the covalent bond between two hydrogen atoms in terms of the two atoms being held together because they do not want to be unstable, so they share electrons to think they have noble gas configurations (T8, June 1993). He defines covalent bonding as "sharing of electrons", "the amount of electrons being shared depends upon the amount of electrons needed to become a noble gas configuration" (concept map on chemical bonding prepared as a revision exercise, June 1993).
When, during the third term, Tajinder undertook Kelly's construct repertory test, a number of constructs related to the octet rule explanatory principle were amongst those elicited (May 1993). These constructs were:
- need an extra electron to have full outer shell
- not have noble gas configuration
- shows noble gas configuration
- does not have full outer shell
Even in the second year of his A level course Tajinder would use the octet rule explanatory principle when discussing bonding. For example he talked of a sodium atom which would lose an electron to form an ionic bond – it wanted to become stable, an octet, a full outer shell (T17, February 1994, see appendix 29, §A29.2). On other occasions Tajinder talked of oxygen atoms that want an octet state to become stable; and that share electrons because they want to gain two electrons to have a full outer shell (T16, January 1994, see appendix 29, §A29.1); of hydrogen and chlorine atoms that wanted to gain a noble gas configuration (T11, October 1993, see appendix 28, §A28.2.1); and of carbon wanting to gain a full outer shell, and sharing electrons so it thinks it has eight (T10, October 1993). According to Tajinder a group 1 element wants to lose an electron to become stable, and iodine wants to gain an electron (T12, October 1993). Tajinder thought stability was to do with the arrangement of electrons around the nucleus, and was inversely related to reactivity. So francium and cæsium were not stable as they want to react, whereas fluorine was reactive – it needed an extra electron to gain a full shell (T10, October 1993). When it was pointed out to Tajinder that fluorine gas was not stable (i.e. was reactive) despite a full outer shell, he accepted that the outer shell criterion was not a good guide to stability. Despite this acknowledgement, later in the interview, Tajinder explained the formation of a dative bond between two aluminium chloride molecules in terms of the aluminium thinking it was stable, as it thought it had eight outer electrons. The polar bond is particularly important when considering the development of Tajinder's understanding of chemical bonding. Tajinder did not initially have such a category. Then it was considered simply as being in between ionic and covalent. Later it was understood in terms of the attraction of the two core charges for the bonding electrons. However even after Tajinder had discussed the bond in these terms, he would later talk of the unequal share of electrons in a carbon-chlorine bond being due to chlorine's greater desire for electrons. He also said that chlorine had more pull on the electrons in a hydrogen-chlorine bond, whereas hydrogen did not really mind (T18, March 1994, see appendix 29, §A29.3).
§8.4.5: Tajinder’s pluralist approach to explaining chemical bonding
During his course Tajinder constructed new ways of explaining chemical bonding, without completely putting aside his preexisting explanatory principle. The evidence from this case study demonstrates that Tajinder's progression did not involve a sudden switch between explanatory principles, but a gradual tendency to use his octet rule explanatory principle less as he developed explanations based on the alternative foundations of Coulombic forces, and minimising energy.
For example at the end of his first year of A level study Tajinder explained his ideas about ionic bonds (T8, June 1993, see appendix 28, §A28.1.1). He referred to the forces due to the oppositely charged ions, and thought that all bonds in sodium chloride were equal, whereas he had previously suggested ions were equally attracted to their neighbours, but not equally bonded (T1, October 1992). However he started his explanation of ionic bonding in terms of the needs of atoms to gain or lose electrons to reach noble gas configurations. He still thought that as sodium can only lose one electron, it could only form one bond. Thus Tajinder had come to a paradox – a sodium atom can only form one bond, but actually has six equal bonds. He attempted to reconcile this contradiction with the suggestion that there was one bond, but it moved around. Tajinder suggested that the donated electron moved around, but he also thought the electron cannot leave the anion – another paradox.
Tajinder was asked to consider precipitation (double decomposition) processes. It was thought that this would be a context where the inadequacy of the electron transfer definition of ionic bonds would be clear. For example if a solution of barium nitrate was mixed with a solution of sodium sulphate, a precipitate of barium sulphate would be formed. (This example was chosen because Tajinder thought barium sulphate would be ionic, whereas he was unsure of the bonding in silver nitrate which had been the first example mooted). It might be considered that the ionic bonds in the barium sulphate 'obviously' could not be understood in terms of electron transfer from barium to sulphate, as these species already existed as ions before mixing. However Tajinder saw things differently. As – from his octet rule explanatory principle – the formation of ionic barium sulphate had to involve electron transfer from barium to sulphate, the reacting species were assumed to be solvated barium atoms and neutral sulphate 'molecules'. It was only when this view was probed that Tajinder accepted that the reactant solutions would not have had time to return the electrons on mixing. Tajinder's scheme involved:
barium nitrate solution – contains ions due to electron transfer from barium to nitrate
and
sodium sulphate solution – contains ions due to electron transfer from sodium to sulphate
which on mixing gives
a solution containing neutral barium and neutral sulphate
which react to form a precipitate of barium sulphate
which is ionic due to electron transfer from barium to sulphate
leaving sodium nitrate ion-pairs in solution
According to Tajinder, this reaction occurred because barium had wanted to lose two electrons to get a noble gas configuration, and had given them to the sulphate. He did not explain why the barium had reclaimed electrons from the nitrate anions. (This is discussed further in appendix 28, §A28.1.2).
Another example is from early in Tajinder's third term when he was interviewed about the electronic configurations of atoms. He thought that the inert gases have stable electronic configurations because of the electrons in the orbitals; that is, the atoms want to fill up electrons on each orbital to be stable (T3, April 1993). The second electron in a shell went into an s-orbital, not a p-orbital because it wants to become like a noble gas configuration, to become stable. It did not want to have the electron in the p-orbital. However Tajinder also gave the alternative explanation that the s1p1 configuration's energy level would be higher. Tajinder also referred to spin-pairing in this context, although he did not seem to be clear how this idea was relevant. Here stability was associated with low energy, and noble gas configurations, and both principles were seen anthropomorphically.
In his end-of-year examination Tajinder explained why he thought neon had the highest molar first ionisation energy of the elements in period 2 (June 1993). His explanation contained ideas derived from both the coulombic forces explanatory principle and the octet rule explanatory principle: neon has the highest core charge, has a full outer shell, and has no desire to have its electrons removed, as it already has noble gas configuration. His discussion of metallic bonding in the same examination included ideas of sodium and magnesium atoms having to lose one and two electrons (respectively), and also the electrostatic forces being stronger in the case of magnesium.
During an interview in the second year Tajinder was asked why hydrogen and chlorine react (T11, October 1993, see appendix 28, §A28.2.1). He suggested that more energy is given out during the reaction than taken in. However later in the interview he suggested the atoms want to obtain a noble gas configuration, or stable outer shells. When his attention was drawn to diagrams of the hydrogen and chlorine molecules in the reactants (with the atoms already having noble gas electronic configurations) Tajinder used an anthropomorphic version of the electronegativity concept: that chlorine wanted more of the electrons to itself, where hydrogen – being electropositive – wanted to get rid of electrons.
Tajinder's tendency to operate with a mixture of ideas based on different – and apparently incongruent – explanatory principles, is discussed in more detail in appendix 29. For example, in a single interview, (T16), Tajinder was able to 'explain' the bond in molecular oxygen in terms of atoms wanting octets, lowering the energy state of the system, and in terms of the electrostatic charges between nuclei and electrons (§A29.1). Tajinder tended to draw freely upon ideas from his three different explanatory schemes in various contexts, such as the reason for a bond forming between hydrogen atoms, the polarity of carbon-chlorine bonds, bonding in metals, the reaction between sodium and chlorine (§A29.2); organic reaction mechanisms (§A29.3); and the types of bond in ice (§A29.4).
