我们需要考虑，混合体的化学势。
Where I'm going to have to worry about the chemical potentials of mixtures.
我们需要写出，物质a的化学势。
And we're going to have to write chemical potential for a species, a, let's say, which is in solution.
那么μ，构型的化学势，就是。
So mu, the chemical potential for these configurations, dA/dN is just dA/dN. With T and V constant.
减去一点反应物的，化学势。
Subtract a little bit of chemical potential from the reactants.
水的化学势受到，其他成分的强烈影响。
And so the chemical potential of the water is strongly affected by all the other constituents.
结果导致，化学势的降低。
And that's what's resulting in the decrease in chemical potential.
此时两边的化学势，相等。
And at that point the chemical potentials of both sides are going to be the same.
现在我们有这样一个方程，从化学势开始。
So now we have this equation, where we started out with the chemical potentials.
所以我们要研究化学势。
等于对于理想气体一巴时的,化学势加上。
That it's equal to the chemical potential RTlogp at one bar for an ideal gas plus RT log p.
都是化学势相等出发。
如果我们计算出化学势，它就是N分之一乘以A
So if we work out the chemical potential, it's just one over N times A.
然后按照所有，纯净物的标准化学势展开混合。
And then we expand it out in terms of the standard chemical potentials for everything being pure.
我们知道吉布斯自由能，等于化学势之和，对吗？
And I know the Gibbs free energy is just the sum of the chemical potentials, right?
用纯化学势，乘以它们的浓度，代替这些化学势。
And instead of these chemical potentials, you would write them in terms of the pure chemical potentials times their concentrations.
到达某个程度时化学势，会由于压强的改变而平衡。
And at some point the chemical potentials will equalize because of the change in pressure.
对这些化学势的任何一个，我把它写成压强的函数。
So for each one of these chemical potentials, I'm going to write it in terms of the pressure.
当我们考虑依数效应时，我们从化学势的角度出发。
When we get to the colligative properties, we'll attack it from the point of chemical potentials.
我们知道了怎样从化学势，得到分压，就写在这儿。
But we know now how to go from chemical potentials to partial pressures. It's written right here.
因为每一个组分在所有相中的化学势,都必须相等。
Every single component has to have its chemical potential its chemical potential equal throughout the phases.
从对化学势，在简单理想，混合里的行为的理解开始。
Just from starting from our understanding of what the chemical potential does even in a simple ideal mixture.
乘以化学势。
处于气态的A的化学势等于，处于液态的A的化学势。
Chemical potentials of a, in the gas phase has to be the same as the chemical potential of a in the liquid phase.
换句话说，化学势之差等于，这个差值随着压强的变化。
In other words, the difference in the chemical potential is, this changes as a function of pressure.
所以混合态是的化学势,永远小于,纯态物质的化学势。
Therefore the chemical potential in the mixture is always less than the chemical potential inside the pure material.
吉布斯自由能和化学势的变化，一切都，由这个子系统决定。
Changes in Gibbs free energy, changes in the chemical potential. Everything will be related to this partition function. This subsystem.
在平衡态固相和液相的化学势相等，固相和气相一样。
And turning the crank at equilibrium, being equal between the solid phase and the liquid phase.
这告诉我们的是，我们只有化学势，每个分子的亥姆霍兹自由能。
What this is telling us is that we just have a chemical potential, of Helmholtz free energy per molecule.
也就是，从中我们将证明，混合物的化学势，永远比纯净物的低。
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.
所以那意味着,溶液中的化学势,总是低于,纯液体中的化学势。
So what that means is that the chemical potential in the solution is always lower than the chemical potential of the pure liquid.
应用推荐