# Deriving Gibb's Free energy

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1. Nov 21, 2014

### ChristineMarie

1. The problem statement, all variables and given/known data
Derive an equation for the change in free energy, ΔGmixing, when ideal gases with the same temperature and pressure, are mixed.

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

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

2. Nov 21, 2014

### Staff: Mentor

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

Last edited: Nov 21, 2014