What Does uo(g)=u1o(g) Imply in Chemical Potential Terms?

[zmike]

2 Phase Equilibria Confusion!?

I am having trouble with the derivation for the chemical potential of liquid component of a system.

We have a closed system with 2 components in their liquid and gas form

This is the line that doesn't make sense to me:
u^o_(g)=u1o(g)
Isn't this saying that total chem pot of the gas phase (of both components) is equal to the chem pot of 1 component?

the final equation is
u1(l)=u1*(l)+ RT ln[p1/P*]


u1 = chem pot of component 1
o = a standard condition
*= pure
u= chem pot

thanks so much

 

[Valerie Park]

No, the equation uo(g)=u1o(g) is saying that the chemical potential of component 1 in the gas phase is equal to the chemical potential of component 1 in the standard state. This equation is just stating the definition of a chemical potential. The final equation you have is the equation for the chemical potential of component 1 in the liquid phase. The equation is derived from the Gibbs free energy equations for a two component system and the assumption of ideal behavior. In the equation, u1(l) is the chemical potential of component 1 in the liquid phase, u1*(l) is the chemical potential of pure component 1 in the liquid phase, R is the gas constant, T is the temperature, p1 is the partial pressure of component 1, and P* is the total pressure of the system.