Gibbs-Helmholtz Equation

Gibbs-Helmholtz Equation

Gibbs-Helmholtz equation is used to determine the change in Gibbs energy of a system as a function of temperature at fixed pressure.
When a system undergoes a reversible change, the change in free energy with temperature and pressure is given by-
dF = VdP − SdT -----(equation-1)
at constant pressure, dP = 0
so, (equation-1) becomes-
dF = − SdT
[dF/dT]_p = −S
∴ −ΔS = −(S₁ − S₂)
or, −ΔS = (dF₂/dT)_p −(dF₁/dT)_p
or, −ΔS = [(F₂ − F₁)/dT]_p
or, −ΔS = [d(ΔF)/dT]_p -----(equation-2)
we know that ΔF = ΔH − TΔS -----(equation-3)
so putting the value of ΔS from equation-2 in equation-3 we get-

The above equation is called Gibbs-Helmholtz Equation. and is applicable to all process which takes place at constant pressure.

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