All things bright & beautiful, all creatures great and small. Remember that hymn? We often talk about remembering the little things, well here’s a lesson in remembering the big things as well!
This post started life with an entirely different title. It was initially called, Should I ignore ‘-x’ in my ICE table? I started writing it a LONG time ago, and it had an entirely different thrust at that time. Then, the 2016 AP Chemistry statistics came into the public domain, and the national results for Q6 found their way on to my radar.
In short, 8% of kids failed to write anything meaningful at all for question 6 and they scored 0/4. Another 65% tried to answer the question and they scored 0/4 – yes, that’s 73% of the population scoring 0/4 on this question – staggering! 12% scored 1/4, and another 12% scored 2/4. Finally, 1% scored 3/4, and 1% scored 4/4. From a purely statistical viewpoint, this is a disastrous question.
Having said that, I actually think the question is fair! I know, it’s crazy that I should side with the CB/TDC on a matter such as this, but I think the fault could easily lie with teachers.
There are two separate issues here, one for part (a) and one for part (b).
Let’s split this into two ‘sections’. Part (a) first. I’ll deal with part (a) by circling back to the original thrust of this post and the addressing it’s connection to 2016, 6(a) at the end of the first section.
Should I ignore ‘-x’ in my ICE table? It’s a commonly asked question that has a pretty simple answer for AP chemistry, and that answer is usually ‘yes’.
What do we mean when we say ‘ignore -x’? What we are really asking is, ‘Is ‘x’ small enough to be considered negligible?’ For example, lets take a look at the dissociation of a solution of the weak acid, ethanoic acid, with a concentration 0.100 M of in water.
|Change||– x||+ x||+ x|
|Equilibrium||0.100 – x||0 + x||0 + x|
In this case the degree of dissociation of ethanoic acid is extremely small, so subtracting a very tiny number from 0.100 is considered to be approx. equal to 0.100, i.e., 0.100 – x ≈ 0.100. (You may have heard of the ‘5% rule’, but there really no need to apply this approximation in an AP context unless an AP question was written in such a way that insists upon it, and that’s a situation that I cannot imagine ever occurring).
In the calculation of Ka’s and Kb’s for weak acids and bases, the assumption of ‘x’ being negligible is both reasonable and indeed ‘necessary’, since the understanding is that quadratics will not be examined/need to be solved on the AP exam. Leaving ‘x’ in the problem causes the creation of difficult quadratic equation that means time is spent on math, and not on chemistry.
You can also safely make the ‘x is negligible’ assumption when dealing with common ion problems, i.e., that any ion concentration resulting from the dissociation of the ‘insoluble’ salt will be sufficiently small when compared to the ion concentration generated by a completely soluble salt, to make it meaningless. For example, take a look at the dissociation of the essentially ‘insoluble’ zinc hydroxide in water. With a Ksp of approx. 1 x 10-17, making x = 1.4 x 10-6.
|Change||+ x||+ 2x|
|Equilibrium||0 + x||0 + 2x|
So, if this equilibrium is established in a solution with a pH of 12, where the [OH–] = 1 x 10-2 (i.e., is a factor of 10,000 times bigger than that that comes from the zinc hydroxide), then
|Change||+ x||+ 2x|
|Equilibrium||0 + x||0 + 2x + 1 x 10-2|
and the ‘2x’ can be ignored, since it is completely negligible when compared to the 1 x 10-2.
In the both the case of Ka’s/Kb’s and Ksp calculations, I would strongly encourage students to make a very brief note of the fact that they are making such an assumption about the insignificance of x.
There have been AP questions in the past, where the degree of dissociation has been given, i.e., the ‘x’ value was quoted in the question. One such example s 2002B, 1. Under these circumstances, obviously one can (and should) include the ‘x’ value, but it may be that after the consideration of significant figures that one finds that it does not matter if one does include the x value or not.
So what the heck has all of this go to do with 2016, 6(a)? Well, it appears that a TON of students failed to understand that there is another circumstance when x can, and should, be basically ignored. That situation is the precise opposite of what I have written about above, i.e., it is when the equilibrium, rather than being skewed so far to the reactants side that x is infinitesimally small, it is skewed so far to the product side that x is so massive, that we effectively no longer have an equilibrium at all.
The clue was GIVEN in the question in 2016, 6 via the words, “Considering the value of K for the reaction“. The value was 7.7 x 107, i.e., MASSIVE! This means that effectively, the limiting reactant is reduced to concentration of zero, and the product concentration will be related to it (after consideration of the stoichiometric ratio). Essentially, there’s no equilibrium at ALL.
Lots of teachers will have talked about this, but it may be that tying it to the ‘x being so tiny so ignore it’ mantra, they can make the point more clearly.
Part (b) really has no relationship to the ‘x is big/small’ discussion above, but it offers teachers a really very important lesson – VERY.
I believe that part (b) is easy, IF you apply Q versus K. Prior to the new course beginning I was never a proponent of Q versus K, rather I was (and to some extent still am), a Le Châtelier guy. However, if one has been paying attention to the CB/TDC/CED, it was easy to predict that an ‘obscure’ question like this one was going to come up, and Q versus K would be the simplest answer.
The same thing happened last year when I heard a casual, off-the-cuff remark about microwaves. BOOM, there’s a question that referenced microwaves! Then there was a reference to non-uniform samples being used in PES plots. BOOM, there it is referenced in a MCQ.
The lesson here is simple. If you want to maximize your student’s scores, you’ve got to get a really good handle on what the CB/TDC is thinking whether you agree with it or not. Know thine enemy!