chemical potential

Especially when you're talking about something like a chemical potential, which is really nothing but the Gibbs free energy.

Therefore the chemical potential in the mixture is always less than the chemical potential inside the pure material.

Subtract a little bit of chemical potential from the reactants.

And on the gas phase side, mu A, it's going to be the same thing as the chemical potential of the pure A.

So of course, the free energy in either case is just the sum of the number of moles of each times the chemical potential of each.

Right, it's just a number of moles times the chemical potential in each case.

Chemical potentials of A, in the gas phase has to be the same as the chemical potential of A in the liquid phase.

Whenever we derive anything connected to phasetransitions, we usually always start with the fact that the chemical potential changes.

OK, so in equilibrium now, when we talk about equilibrium in solution, we still have to, still going to be the chemical potential.

Just from starting from our understanding of what the chemical potential does even in a simple ideal mixture.

Because it's in equilibrium, the chemical potential of that particular component has to be the same in all the phases.

Every single component has to have its chemical potential its chemical potential equal throughout the phases.

So what that means is that the chemical potential in the solution is always lower than the chemical potential of the pure liquid.

There for, to define chemical potential for a droplet is unreasonable either in conception or in method.

Which is that, from what we're going to prove, is that the chemical potential in the mixture is always less than for the pure substance.

So it's going to be the chemical potential of the pure material.

at the same pressure the chemical potential of the water's lower inside the cell or inside the enclosure with the membrane.

Well, that's just the chemical potential of A, in the pure state, at temperature T and pressure pT.

By the way, it's convenient because it looks just like the chemical potential in a mixture of ideal gases.

Furthermore, the chemical potential approaches an infinite negative value as pressure approaches zero.

In this situation, the chemical potential difference in the two solutions generates a voltage over each membrane.

Changes in Gibbs free energy, changes in the chemical potential. Everything will be related to this partition function. This subsystem.

These log partial pressures all come from expanding out the chemical potential as mu naught plus RT log p.

We learned that the pressure dependence of the Gibbs free energy gives you the pressure dependence for the chemical potential.

Nothing new here, this is just our expression for the chemical potential in the gas, with reference to a standard potential.

And that would change what the reference potential is chemical potential is.

A So, we can write for A, mu A of the liquid at some temperature and pressure must equal chemical potential A That's the partial pressure.

Now, the chemical potential, as we saw, was the Gibbs free energy.

So that's a very simple expression for the chemical potential of A.

Another method for proving the three thermodynamical partial derivatives equaling chemical potential is given.

Is equal to the chemical potential of the pure system, same temperature under pressure is p sub a on that side.

The chemical potential has to be equal outside and inside the container.

But as the pressure rises, now the chemical potential changes and goes up.

And that's what's resulting in the decrease in chemical potential.

A We're done because on that side here I have mu A, the chemical potential of A in the mixture, temperature T, pressure p total.

And that's going to change what the chemical potential of a species is.

The chemical potential of h-ZBNNR appears a maximum at a certain width.

Now, what do we know about the chemical potential in both parts?

That it's equal to the chemical potential RTlogp at one bar for an ideal gas plus RT log p.

So here's the chemical potential at point beta.

So we're going to reference this to some standard state chemical potential.

But really, it's a chemical potential idea.

We know a lot about the chemical potential of something in the gas phase.

And so the chemical potential of the water is strongly affected by all the other constituents.

So if we work out the chemical potential, it's just one over N times A.

And now we know how to calculate the chemical potential in the gas phase.

In other words, the difference in the chemical potential is, this changes as a function of pressure.

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