Question

4. Use the van der Waals gas law to derive a corrected equation for Gibbs free energy.

Answer 1

we know thant dG= VdP-SdT

at constan temperature, dT=0

dG= VdP                       (1)

for Vanderwaal gas of n=1 moles

the Equation is (P+a/V²)*(V-b)= RT

P= RT/V-b)- a/V², dP= (-RT/(V-b)²+ 2a/V³)dV

Hence Eq.1 becomes   dG= V{-RT/(V-b)²+2a/V³)dV

when the equation is integrated

deltaG= V₂*RT/(V₂-b) -V₁*RT/(V₁-b) +RT*ln{(V2-b)/(V1-b)} -2a*(1/V₂-1/V₁)

where V2 and V1 are volumes before and after expansion.