Thermodynamic Derivation of Law of Mass Action

Thermodynamic Derivation of Law of Mass Action

Thermodynamic Derivation of Law of Mass Action


Thermodynamic Derivation of Law of Mass Action

We know that-
dF  =  VdP − SdT
At constant T-
dF  =  VdP
or, dF  =  (RT/P)dP      (As PV = RT for one mole)
On integrating the above equation-
∫dF = RT∫dP/P
F = Fo + RT lnP
or, F = Fo + RT lna
Since, PV = nRT
So, P = (n/V)RT = CRT
P ∝ c and also a ∝ c
so, P ∝ a
So, we can use a in place of P
Let us consider a general reversible reaction-
aA   +   bB    ⇌   cC   +   dD
If aA and aB are the activities of A and B at the start of the reaction and aC and aD are the activities of C and D respectively at temperature T then the free energies per mole of A, B, C and D are-
FA = FoA + RTlnaA
FB = FoB + RTlnaB
FC = FoC + RTlnaC
FD = FoD + RTlnaD
When FoA, FoB, FoC and FoD are the standard free energies at unit activity. Hence, the free energy change for the reaction becomes-
ΔF = ΣΔFProduct − ΣΔFReactant
or, ΔF = (cFC + dFD) − (aFA + bFB)
or, ΔF = (cFoC + RTlnaC + dFoD + RTlnaD) − (aFoA + RTlnaA + bFoB + RTlnaB)
or, ΔF = [(cFoC + dFoD) − (aFoA + bFoB)] + [(RTlnaC + RTlnaD) − (RTlnaA + RTlnaB)]
Thermodynamic Derivation of Law of Mass Action

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