On Friday's lecture, we discussed how the equilibrium constant K for a given reaction might change as we vary either the temperature or the pressure. From the Gibbs-Helmholtz equation, (∂(∆G/T)/∂T)P = – ∆H/T2 and that ∆G° = – RT lnK, it is straightforward to show that (∂(lnK)/∂T)P = ∆H°/RT2.
To see the effect of pressure, we look at the derivative (∂(∆G°)/∂P)T =∆V°. But, since the reference point ∆G° (1 bar) is independent of pressure, this derivative is zero and the dependence of K on P to be zero.
From these two results we conclude:
a) K is dependent only on temperature changes
b) this response is very sensitive (it is ln K that changes with T) and
c) the sign of the response is dictated by ∆H° (LeChatelier's principle in disguise)
Lastly, we began a formal discussion on phase diagrams/changes, our last chapter of the quarter, with the Ehrenfest classification of phase transitions. Some phase changes exhibit a discontinuity in the Sm vs T plot (as well as the Vm vs T plot). Since Sm is the first derivative of Gm, we call these first-order transitions. In other phase changes, the discontinuity does not arise until a plot of CP,m vs T; this is the second derivative of Gm so we call these second-order transitions. In general, an nth-order phase transition would have a discontinuity in the nth derivative of Gm, but only first and second-order are seen in practice. Though now outdated, the Ehrenfest classification is a useful way to think about the differences in the thermodynamics variables seen as systems undergo phase changes.
On Wednesday, phase diagrams and coexistence curves before hitting the Clausius-Clapeyron equation.