More on chemical potential Chemical potential tells us even more than just about variation in G U+ pV- TS so for an infinitesimal change in u, we can write pdv-vap+ sdT+ Tas+ dG p-中p+Sd+7ds+(dp-Sa+uAhn+ eDna+…) P ∥+TS B-B and at constant volume and entropy dU an)s and if that' s not enough. what about H and A??? These too also depend upon the composition of a mixture! Chemical potential is IMPORTANT aH dA a) (b) n Dn
化学势 Chemical potential 纯物质G=n×Gm ang G O T P 化学势=摩尔 Gibbs能 理想气体的化学势 u o In P, standard state at p H=p°+R7h|2 P Pressure
化学势 Chemical Potential 理想气体的化学势 纯物质 G = n Gm m T P m G n nG = = , μ 化学势 = 摩尔Gibbs能
Thermodynamics of Mixing The simplest example of mixing: What is the Gibbs free energy if we take two pure ideal gases and mix them together? Consider gas a and gas B, both in separate containers at pressure p at temperature T The chemical potentials are at their "pure values"at this point. Gibbs energy is ∵ μA e矿4 RT In nUb+ RT In A B P We can simplify things by letting p denote the 3 pressure relative to p, writing + RT In pi+bLub+ RT In p
Gibbs Energy of Mixing After mixing, the partial pressures of the gases are pa and pB, where the total pressure is p= pA pB. The total Gibbs energy is then nAHA +RT In pa+nBluB+RT In pal The difference in Gibbs energies, Gr -Gi, is the Gibbs energy of mixing n,rt In +nRT II IX We use mole fractions, replacing ny with Xn IX nRT( In B Since the mole fractions are never greater than 1 the In terms are negative and Ami g<o This allows is to conclude that mixing processes are spontaneous, and gases mix spontaneously in 08 all proportions Molo fraction of A. x