I'm in year 12 of school doing A2 chemistry learning about entropy and its relationship to reversible equilibria. I learned about the following three ideas from my course book (verbatim), for a reaction at equilibrium:
- $\Delta S_{\text{total}} = 0$
- $\Delta S_{\text{total}}$[forward reaction] = $\Delta S_{\text{total}}$[backward reaction].
- $\Delta S_{\text{total}} = R\ln K$, where $R$ is the gas constant and $K$ is either $K_c$ or $K_p$.
I'm confused about points 1 and 3 and would like to know if my understanding of 2 is correct.
For point 2, does it imply that at equilibrium the total entropy change from both the forward and backward reactions are zero, but if the forward reaction is say $\Delta S_{\text{sys}} + \Delta S_{\text{surr}} = 22 + (-22)$, then the backward reaction has to be $\Delta S_{\text{sys}} + \Delta S_{\text{surr}} = (-22) + 22$ (as opposed to something like $(-60) + 60$ which is also zero but the individual magnitudes are different)?
For points 1 and 3, if they're both agreed to be true then $\Delta S_{\text{total}} = 0=R\ln K \implies K = 1$, no matter the reaction. This result is just absurd because it's implying all reversible reactions have a position of equilibrium close to the middle. What exactly is going wrong? Later on in the book, there is another contradiction where it provides the following reaction at equilibrium: $$\ce{SO2(g) + 1/2O2(g) <=> SO3(g)}\quad\Delta S^\circ_{\text{total}}=238.3 JK^{-1}mol^{-1}$$ How come the total entropy change is nonzero during equilibrium? My guess is that it has something to with the fact that this entropy change is standard whereas the one in point 1 is not. Similarly, I think the entropy change in point 3 should also be standard. If that's the case, what exactly is the difference between $\Delta S_{\text{total}}$ and $\Delta S^\circ_{\text{total}}$?
Note, I don't know what Gibbs free energy is but from the expression I've seen online, it seems to be equal to $-T\Delta S_{\text{total}}$ so I'd appreciate if the explanations of my questions are in terms of entropy changes.
Edit: the book is Edexcel IAL Chemistry Student Book 2 (ISBN 13: 9781292244723), page 72 as requested in the comments.