Thanks.
Could you explain the contradiction that is occurring? I can't quite see it, you meant that the Kc value in part c is different to the one used in part e, I wrote the rounded value in part c. But then in part e, the unrounded value is used.
Two things always need to be true:
1. The equilibrium constant is unchanged (since there is no temperature change)
2. For every mol of C
2H
6 formed while equilibrating, there must be 1 mol of both C
2H
4 and H
2 consumed (stoichiometry), and vice versa.
If you try using the same equilibrium constant (as you have done) in part c. for part e. then you will end up with the change in [C
2H
4] being 0.004 M. This makes no sense
because you have interpreted the change in [C2H6] to be 0.020 M. So the stoichiometry is not consistent.
Alternatively, you can set everything to have the same change in concentration as it approaches equilibrium again (correct stoichiometry). So you can set [C
2H
4] to be 0.040
because you have interpreted the change in [C2H6] to be 0.020 M. But naturally here, if you try to calculate the equilibrium constant from these values, it will be different to that in part d.
So how do we make sure both the K
c value and stoichiometry is correct?
We simply cannot assume the change in [C2H6] is 0.020 M, i.e. we cannot assume the final [C2H6] is 0.18 M. You would let the final [C
2H
6] = (0.16 + x) M and final [C
2H
4] = (0.060 - x) M. You can then sub these values and [H
2] = 0.012 M (from the axis label) into the known K
c and solve for x to find all the final concentrations. This is the most rigorous approach.
The problem I have with the way the question is written is in part b.
you are meant to interpret some of the dotted lines to be exactly halfway between axis labels. But with part e.
you are not meant to! You are not at fault for interpreting the final [C
2H
6] to be 0.18 M because you have been conditioned by a previous part of the question to do so.