CHAPTER 5 RESULTS SHOWING SCOPE AND QUALITY OF RESEARCH ON
8.3 DIFFICULTIES WITH CHEMICAL FORMULAE AND EQUATIONS
8.3.2 Difficulties with formulae and equations in acid-base reactions
From the theoretical framework (see Section 3.3) for the three historical models considered here, all acids contain hydrogen, and all Arrhenius acids are also Brønsted acids, but not vice versa. By contrast, Brønsted bases and Arrhenius (or operational model) bases are mutually exclusive classifications. This means that an Arrhenius base cannot be a Brønsted base, and neither can a Brønsted base be an Arrhenius base. It thus follows that a student with Difficulty R6 who uses the heuristic: All formulae with hydrogen indicate acids will not necessarily have a misplaced idea of what constitutes an acid in any of the models, although they treat formulae superficially. However, the conception R7: All formulae with OH indicate bases suggests not only a simplistic way of looking at formulae, but a circumscribed conception of a base, allowing only the Arrhenius model. Thus, it is proposed that R6 and R7 should be seen as two separate difficulties.
Students could fruitfully add examples to the categories illustrated in Figure 8.1 which follows.
This diagram shows that all of the Arrhenius acids such as HCl, H2SO4 and H3PO4 are also Brønsted acids, whereas bases which are common to both the Arrhenius and Brønsted models are seldom included in high school curricula (see Section 3.3.3.4). Furthermore there are some examples of that fall into acids and bases, these are amphoteric species.
Figure 8.1 Classification of examples of acids and bases
8.3.2.1 Difficulty R8: When an acid molecule dissociates it divides in two.
Furió-Más et al. (2007) investigated difficulties with dissociation of a diprotic acid through free- response questions, concerning the “complete ionic dissociation of H2SO4.”Here, the authors do not publish their acceptable answers but the particular pairs which they reported as incorrect include: H+ + SO4
2–, and H2
+ + SO4
2–. From these examples, Furió-Más et al. (2007) describe the student mental model as: When a molecule dissociates it divides in two. These authors have not made their frame of reference clear (one or two stages or ionization to account for HSO4
–
(see propositional knowledge below). Furthermore, they appear to accept only the dissociation model for creating ions. Consequently, the interim difficulty description cannot be framed with certainty – it requires further, carefully reported research – so I classify it as Level 2, Emergent.
Additional research needs less focused questions that do not restrict the students’ scientific models, in order to discover whether the difficulty is due to the word ‘dissociation’ which is relevant only to the Arrhenius model, or some other cause. In the interim, the difficulty maps to propositional knowledge including both theoretical models.
• An Arrhenius diprotic acid dissociates in two stages (10.2.1.2) given by the equations:
• H2SO4 HSO4– + H+ (10.2.1.2.1) and HSO4
– SO42– + H+ (10.2.1.2.2), giving the overall equation as: H2SO4 SO42– + 2H+ (10.2.1.2.3)
• A diprotic Brønsted acid ionizes in two stages (10.3.3) given by the equations:
• H2SO4 + H2O HSO4– + H3O+ (10.3.3.1) and HSO4
– + H2O SO42– + H3O+ (10.3.3.2)
8.3.2.2 Difficulty R9: The equation showing formulae for substances is suitable to explain neutralization reactions.
Drechsler and Schmidt (2005a) report an analysis of answers to school-leaving public examination multiple-choice questions where they found that instead of a net ionic equation,
“students preferred reaction equations that name salt and water as a product of an acid-base reaction”. Although not problematic among younger students, such conceptions which limit acid-base neutralization reactions to an operational model do not accommodate theoretical acid- base models, as could reasonably be expected of senior secondary students. Further research shows similar findings among students in Grades 10 and 11 (Ouertatani et al., 2007) and Grade 12 (Furió-Más et al., 2007), where the students apparently did not distinguish between the functions of the two types of equations, and preferred the apparently simpler one giving substances. Without further analysis, the difficulty can be described as: The equation showing formulae for substances is suitable to explain neutralization reactions. I only classify the
difficulty at Level 2 because, despite evidence from three independent studies, there is little in the research to explain why students focus only on the one type of equation. As to possible causes, Ouertatani et al. (2007) give no backing for their suggestion that students may not have sufficient understanding of ionic reactions. A second possible cause is suggested by the seemingly indiscriminate use in advanced school textbooks of the two types of equations, with no explanation for a particular choice, as shown by Oversby (2000a). The difference between an equation to describe a reaction in terms of reactants and products and one to explain why the reaction is classed as neutralization represents the essential difference between an operational model and theoretical models. Consequently I put forward the following propositional knowledge as appropriate for this difficulty:
• An equation with formulae describes the substances that are reactants and products (10.1)
• The formula equation for neutralization reactions has the form: acid + base salt + water (10.1.1)
• Equations with ionic reactants and/or products explain the reaction (10.2)
• Arrhenius model: neutralization is represented as: H+ + OH– H2O (10.2.1)
In this difficulty students appear to ignore a later model, a different way they misunderstand models is shown in the next difficulty.
8.3.2.3 Difficulty R10: The general Brønsted reaction scheme shows neutralization.
The idea that students may superimpose parts of one acid-base model onto another, imagining that they model the same aspect is suggested in two reports. The student conceptions are best explained in terms of numbered equations representing the acid-base reaction, as shown in Figure 3.1 from the Theoretical Framework (see flip-out page 47). Firstly, Hand and Treagust (1988) report as a misconception found among Grade 10 students in Australia: “Neutralisation is the breakdown of an acid or something changing from an acid”. Such a student could have Brønsted’s reaction scheme in mind – thinking that equation 3.8 depicted an acid breaking down and that this was neutralization. Then Ross and Munby (1991) report a connection found on a student’s concept map: a base is the product of neutralization. Such a student could imagine that either of equations 3.8 and 3.9 concerning the Brønsted model showed neutralization. Use of either of these equations suggests that students are superimposing the general reaction scheme of the Brønsted model onto a neutralization reaction; that is, they are using the model inappropriately. These students should have rather applied equations in the form 3.1, 3.4 or 3.10 to aqueous neutralization. There is evidence to support my speculations, as follows.
Drechsler and Schmidt (2005b) give qualitative data from interviews showing that students did believe that the operational equation (1) and a Brønsted representation (4) both contained the same information. Indeed, both do have acid + base as reactants, which could confuse students, especially if they do not distinguish the acid-base models. For example, a student was confronted with the two equations:
HCl + NaOH NaCl + H2O and acid1 + base2 base1 + acid2
The student indicated the products and concluded: “salt and water are formed... there should be an acid and a base as well...perhaps you can identify NaCl as an acid...” From the same report, another student used NaOH instead of the ion OH– as the proton acceptor. To accommodate this notion the student tried to write an equation with NaH2O as the product. Drechsler and Schmidt categorize this difficulty as being due to students not understanding the appropriate contexts for each model, which is not a clear description. Instead, a clearer description could be obtained by mapping the difficulty to corresponding propositional knowledge statements, which in this case were:
• The Brønsted general reaction scheme applies to many different types of reaction. (7.3.3)
• Brønsted model, neutralization reactions can be represented as: H3O+ + OH– H2O + H2O (10.3.2.1)
Reversing these propositional statements then leads to the difficulty description: The general Brønsted reaction scheme shows neutralization. This difficulty, suspected in two other contexts, is thus partially established through a further triangulated study (Drechsler & Schmidt, 2005b).
Accordingly, it is classified at Level 3+. The difficulty is likely to be found among other student populations because Furió-Más et al. (2005) found evidence for this difficulty in 17% of the textbooks they analysed and 55% of teachers they surveyed indicated it was acceptable to explain neutralization using the Brønsted model. It follows that formal instruction could be the source of the difficulty. Further confirmation is also needed through studies in other chemical contexts.
8.3.2.4 Summary of difficulties with chemical symbolism
Difficulties with chemical symbolism show two categories of difficulties. Firstly students treat formulae in a simplistic way (R6, R7 and R8). The second category shows students do not understand the role of particular equations in different acid-base models. Both these categories indicate little understanding of the underlying chemical structure giving rise to acid or base properties and the formation of appropriate mental models to explain the behaviour. This is also implicated in the difficulties discussed in the next section.
8.4 DIFFICULTIES WITH SYMBOLIC AND MATHEMATICAL