The last time I taught equilibrium to my Year 13s, I had a number of bright, inquisitive students who got frustrated with the idea that for an equilibrium between A + B (see below) increasing the concentration of A would shift the position of equilibrium to the right but Kc would be unaffected. I tried showing small models with duplo blocks but to no avail. Eventually reaching an impasse I resorted to the position of “please just trust me for the moment, we can’t get too bogged down on this one!”

After the rest of the class had left I had some more time to think and figured some kind of probability-based model would be appropriate. Meanwhile my Year 11s have been finding equilibrium uncharacteristically hard this year – they’ve really been over-thinking it (something I’d be applauding if it hadn’t have been such a sticking point!)

So I decided a pre-emptive strike was warranted with year 13 this time. I walked in with at least 80 dice (nicked from the radioactive dice draw in physics) and the intention of setting up an equilibrium dice game very similar to that proposed in Equilibrium Principles: A Game for Students – J. Chem. Educ., 1999, 76 (4), p 502 DOI: 10.1021/ed076p502

$A \leftrightharpoons B$

$K_{c} = \frac{[B]}{[A]}$

The idea is that a set of students start with a pile of dice. On one side of the room the dice represent the reactants “A” and on the other side, the products “B”. A limited number of outcomes lead to a reaction. In my case we had about 60 dice to begin with. The students on one side of the room tossed them, separated out the ones that read 2 or 4 and passed them over to the B team. The next throw both teams went but B only “reacted” when they rolled a 3. If I’m totally honest I’m not sure how carefully they did it but as you can see below we quickly reached an initial equilibrium of sorts.

By throw 5 I was satisfied we had enough data to work with and used an average figure for the last couple of throws to calculate a value for Kc. Statistically, Kc should have been 2 (as the forward reaction was twice as likely as the reverse) but the value was actually about 1.5. The dice in fairness weren’t great and there were a number of other mitigating factors.

I asked the students to predict what would happen when we increased the concentration of A. Of course they all dutifully replied that the position of equilibrium would shift right to oppose the change. When I asked them to consider the effect on Kc, they unanimously agreed that Kc should increase because a higher value of Kc means there is “more product at equilibrium … there is a larger number on top of the expression” … fair enough

The point is of course that we have changed the total number of particles in the system too. Although the numerator will increase, so will the denominator.

You can see where I threw an extra 20 dice into the system for throw number six. The equilibrium immediately shifts right and settles at a higher concentration of B (of course we also have a slightly higher concentration of A!)

Numerically this example came out with a value of Kc of about 1.6. Although a bit higher, the students got the idea and could accept that this was within the realms of natural variation. Mission accomplished.

We taught our modules in a slightly different order this year so the students were both able to see how changing temperature would be like increasing the number of positive outcomes on the dice in one direction and to make the connection with free energy.

$\Delta G = \Delta H - T\Delta S$

As we increase the temperature we will make one direction more feasible (a phrase my students found quite amusing) and the other less feasible but the total number of particles will remain the same. Some might even make a connection with

$\Delta G = -RTlnK$

and of course this connection is touched on in the transition resource I did over here.

I thought that was the end of it but as it happens, a number of them got hung up on pressure: failing to see the connection between concentration in liquids and pressure in gases. It would be useful if there were a quick way of running through multiple scenarios like this on a very basic scale. I just popped over to the Phet site to see if they had anything appropriate and sure enough they had something close but not exactly what I’m after.

Anyway the dice model worked really well – we can only improve next time. If you have some bright kids who like looking at this kind of stuff, there is an activity in the RSC Gifted and Talented resource where they can draw links between the rate law and the equilibrium law which is worth them having a look at. It’s in the 16+ section of the resources available here (Sheets 31SW and 31DA – also many questions linking entropy and equilibrium earlier in that zip file)