Molar Free Energy of an Ideal Gas at Temperature T and Pressure P

[ChristineMarie]

Homework Statement

Derive an equation for the change in free energy, ΔGmixing, when ideal gases with the same temperature and pressure, are mixed.

Homework Equations

ΔGmixing = nRT∑(xi)ln(xi)
(∂/∂T(G/T))p = -H/(TxT)

The Attempt at a Solution

Pi = xiPi*
μi = Gi,m
μ = (∂G/∂n) at constant T and P
μ = (∂[nGm]/∂n) = Gm

 

[Chestermiller]

Homework Statement

Derive an equation for the change in free energy, ΔGmixing, when ideal gases with the same temperature and pressure, are mixed.

Homework Equations

ΔGmixing = nRT∑(xi)ln(xi)
(∂/∂T(G/T))p = -H/(TxT)

The Attempt at a Solution

Pi = xiPi*
μi = Gi,m
μ = (∂G/∂n) at constant T and P
μ = (∂[nGm]/∂n) = Gm

If $\mu^0(T)$ represents the molar free energy of an ideal gas at temperature T and 1 atm, what is the molar free energy of a pure (unmixed) ideal gas at temperature T and pressure P (P in atm)?

Chet