Another ∆G° mystery

Written by Adrian
On February 27, 2016

We’ve lived through the nonsense of the inclusion of PES in the new AP Chemistry curriculum. Many think the exclusion of quantum numbers, stinks. Some people HATE the removal of colligative properties from the course. For me, these (and other things) provoke varying degrees of outrage that range from complete indifference to utter incredulity. Then we come to EU6D and LO 6.25 and another ∆G° mystery. Just what precisely is going though the mind of the TDC/CB with those?

Let’s clear one thing up immediately. The chemistry is simple. Very simple. Essentially it’s nothing more than the application of the equation that links ∆G° with K, i.e.,

∆G° = – R T ln K

In the good old days it used to be largely sufficient to plug numbers into that equation to calculate a value for the change in Gibb’s Free Energy or the equilibrium constant. Becasue of the math of the equation, kids would quickly see that when K > 1, a positive value for ln K would result, and in turn ∆G° would be negative. When K < 1 the opposite would be true of course, and if K happened to be equal to 1 then ln K =0 and in turn ∆G° = 0.

Delta G StandardAll of that tells us that the sign of ∆G° (positive, negative or even 0), can be used as an indicator of the ratio of products to reactants at equilibrium. Fine, no problem, simple and straightforward, so why complicate the issue with a specific reference to ‘thermal energy’ (RT), and its value of 2.4 kJmol-1? I’ve already asked about the mystery of the actual value of RT, but putting that aside for a moment, here’s the next question.

Is there a reason why the CED has isolated a WHOLE Enduring Understanding statement (EU6D) for that simple chemistry? Why couldn’t kids simply be asked about the application ∆G° = – RT ln K and an understanding that K > 1 mean products being favored at equilibrium and a negative ∆G° (and vice-versa)? What’s the point of the whole ‘thermal energy’/RT specific reference? I’ve only managed to come up with one thing, but I remain unconvinced that even it makes much sense.

It seems to me that the CED is saying that even when (for example), K = 2/1 = 2, or K =1/2 = 0.5, that this is still considered relatively close to products and reactants being ‘equally favored’ (or at least in the words of the CED, having ‘significant concentrations’) IN THE GRAND SCHEME OF THINGS. Even though K’s = 2 and 0.5 hardly seem ‘equally favored’ in terms of products and reactants, it could be literally millions of times smaller (or bigger), for example, with the massive Ka’s of a strong acids or the tiny Ka’s of weak ones. So is the whole point of the existence of EU6D really only a question of scale comparison? If so, it goes way beyond my examples of K = 2 and K = 0.5. Some AP teachers choose to use values of 0.001 and 1000 as examples of K’s where the products/reactants are not (in their words) strongly favored at all. Even though that makes perfect sense to me (since the range can be many factors of 10 bigger and smaller than even those), K’s such as 0.001 and 1000 produce a range of approx +17 to -17 for ∆G°, and NOT +2.4 to -2.4 that the CED references. The question becomes, what is considered a significant concentration? Very ambiguous.

As you can tell, I don’t get the point of a whole hoopla surrounding ∆G° = – RT ln K getting its own EU, but I think it is bound up in the obsession that the CB/TDC has regarding algorithmic calculations (and perhaps calculations in general). They just don’t want kids using equations to calculate numbers, and in the process of following that edubabble mantra, they’ve turned a simple relationship into a convoluted mess. We have seen this already on the new exam with removal of Nernst, coupled with persistent questioning surrounding non-standard cells. Sometimes it’s just BETTER to do a calculation and be done with it. This is what schools of education have got wrong. This is another example of that.

A concept such as the one tied up in EU6D can really only be sensibly tested with a formula and a bit of math. Becasue of the edubabble mantra of ‘no algorithmic calculations’, now it has to be artificially set up with the insertion of the largely meaningless  +/-2.4 kJmol-1 value, in order to allow it still be be tested (somewhat) quantitatively. Why not test it quantitatively, PROPERLY? It’s madness, but typical of education ‘research’.

As a result I feel that this probably won’t be tested on the free response section of the exam. Why not? Well, any kid could pick up their calculator, apply the formula, and probably – horror of horrors – answer the question by performing a calculation! The CB would HATE that! If on the other hand this is asked in a MCQ context, then we can go down the edubabble route of RT and 2.4.

One final observation. Of the six exams that have been produced by the College Board that relate to the new curriculum, there hasn’t been a single point devoted to LO 6.25. Perhaps, in the words of another AP chemistry teacher, “Maybe the question writers are scratching their heads on this one, too.

10 Comments

  1. Paul Cohen

    I have not yet been asked to write any questions on that L.O. We are often asked to address SPECIFIC L.O. in our MC questions. I have written questions for L.O. 5.13 though, and I believe that 6.25 permits many of the same questions, where thermodynamic feasibility is at issue. 6.25 allows us to bring in values of K greater than or less than one as well. I would have no trouble writing an MC for 6.25.

    Reply
    • Adrian

      I could write plenty of Q’s for LO 6.25 too, but don’t you feel the introduction of the whole ‘thermal energy’ thing unnecessarily convoluted?

      Reply
      • Paul Cohen

        I have never used the phrase “Thermal energy” in 50 years of teaching chemistry! The entire 6 D 1b is a waste of space. However, it is not at all useful when writing questions, and I wouldn’t worry about it. John Milligan – they avoid referring to Nernst by simply stating its implications non-quantitatively. i.e. ” An decrease in the value of “Q” increases the value of E…” The exact statement is ” Deviations from standard conditions that will take the cell further from equilibrium than Q = 1 will increase the magnitude of the cell potential relative to Eo.” A badly written approach to a fairly simple concept.

        Just remember, that they also omit the calculation of delta G under non-standard conditions, which I think is an even worse omission!

        Reply
        • John Milligan

          I remember doing all of those calculations in my high school chemistry class 30 years ago. The AP test then included them. I pains me in more than one way to see how the HS chemistry program is being degraded.

          Reply
        • Adrian

          I have never used the phrase “Thermal energy” in 50 years of teaching chemistry!

          A badly written approach to a fairly simple concept.

          Just remember, that they also omit the calculation of delta G under non-standard conditions, which I think is an even worse omission!

          They broke AP Chemistry!

          Reply
  2. Russ Kohnken

    I was surprised by the thermal energy thing too, particularly since I don’t remember seeing reference to it in textbooks. So thank you for giving it some thought to try to create some context for it.

    Reply
  3. John Milligan

    Adrian,

    This is completely the opposite of what I teach my college level students. It’s more along the lines of what you pointed out deltaG 1 and vice versa. As to your example of K =2 or K = 0.5 it still points out that the products/reactants are favoured, just not “strongly” favoured.

    When dealing with the edubabbleists at the college level, I often feel like Dr. Evil: “Why must I be surrounded by fricking idiots!”

    It really isn’t a difficult concept to get and to be honest, at the college level, it seems that half of my students can’t do the calculation anyway.

    BTW, how does the CB deal with non-standard cells without referring to the Nernst equation?

    Reply
    • Adrian

      BTW, how does the CB deal with non-standard cells without referring to the Nernst equation?

      Short answer, ‘tortuously’! In reality with the use of ‘Q’ but with NO reference to Nernst or calculations, or with the use of the term ‘driving forces’ being less/more.

      Reply
  4. Neema Salimi

    In grad school, we were expected to be familiar with the shortcut equation dG = -1.4 log K, which assumes 37C and is in units kcal/mol. So we would know very quickly that a 4 kcal/mol reaction was ~K=10^3 and K=10^9 was roughly 14 kcal/mol. This happened all the time (e.g. “that drug is a nanomolar binder, so it’s 14 kcal/mol”).

    The other aspect was Boltzmann population distributions. Fluctuations on the order of a couple kT (or RT) are common, and knowing RT=0.6 kcal/mol at 37C was useful in that way.

    Obviously I don’t know the ins and outs of the AP Chemistry curriculum, so their particular interest in this is lost on me.

    On the “what levels matter part,” those teachers saying that a K of 1000 or 0.001 aren’t significant; well, yes and no. In terms of thermal fluctuations, those are huge (7 kT). You aren’t going to get that skewed of a distribution of anything from randomness. In terms of reactions with far larger K’s, then, yeah, they’re small.

    Here’s the other thing. Standard state energies are one thing, and real life is another. Biologists learn standard state energies for some well-known reactions, but standard state in biology is the most meaningless thing ever. The only things close to molar concentration are a few ions, and everything else is relatively large and tightly packed, so who knows what the effective concentrations are?

    So to your point, it’s a interesting thing for the CB to bring up without more guidance as to what they want you to actually teach the children. Dihedral rotations in organic molecules? Probably not.

    For biologists (at least for biochemists/biophysicists, like 15% of the total), this energy stuff matters a lot. Most of the conformational changes and chemical reactions in cells have relatively small dG’s, and this is likely out of necessity for reactions to run both directions. Hope this added some.

    Reply
    • Adrian

      Thanks, interesting stuff. Despite the title of this post, for my money there really is no mystery as to why this (irrelevant to AP chemistry) stuff has been included in the new curriculum. It came from the edubabble that says we need cross-curricular connections. Now, I’ll save the details of that rant for another time, but we DON’T need any such thing at this time and this level, but what this educational nonsense does, is force irrelevant and ridiculously inappropriate material into the curriculum to the point that it looks bizarre. This is a classic example of such.

      BTW, for a second I thought that 37oC was going to solve this problem, but of course it doesn’t!

      Reply

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