It has been quite a while since I’ve posted anything, and I apologize to all the tens of readers I have out there. I admit, I’ve been somewhat lazy, but I’ve tried to make sure that everything else I have to do got done. I guess this blog is lower priority.

We have been hitting a variety of topics in class, from chemical equilibrium to phase equilibrium, and a few places in between. What do they all have to do with one another? Quite simply, ΔG. And the good news is, that won’t go away for a while!

In my last post, I mentioned that under conditions of constant temperature and pressure, ΔG is the criterion for spontaneity. But what does that mean? It certainly doesn’t have anything to do with rates, since that’s kinetics. In thermodynamics, we’ve learned that spontaneous processes are irreversible, and tend to maximize the total entropy (ΔStot > 0) and (at constant T & P) minimize the Gibbs free energy: ΔG < 0.

One question you might rightly ask, is how does the Gibbs free energy depend on pressure and temperature. We saw that

dG = VdP - SdT

which shows how G = G(T,P). If the quantities are molar, this becomes:

d\overline{G} = \overline{V}dP - \overline{S}dT = d\mu

where μ is the chemical potential. The temperature dependence of μ is just

\left(\frac{\partial \mu}{\partial T}\right)_{P} = -\overline{S}

The pressure dependence was found to be

\mu = \mu^{\circ} + RT\ln{\frac{P}{P^{\circ}}}

where the ° symbolizes standard thermodynamic conditions. These two relationships can go a very long way. Some examples include chemical equilibrium, phase equilibrium, and colligative properties of solutions. In the world of biology, chemical potential gradients are what drive ion channels and many other processes.