Law of Mass Action

For a homogeneous phase chemical reaction at constant temperature and pressure, when the constituents are ideal gases, the chemical potential are given by the expressions of the type

(3.37)

where the Φ's are functions of temperature only.
Substituting in the equation of reaction equilibrium (Eq. (1.38))

v1(Φ1 + ln p + ln x1) + v2(Φ2 + ln p + ln x2) = v3(Φ3 + ln p + ln x3) + v4(Φ4 + ln p + ln x4)

(3.38)

On rearranging

v3 ln x3 + v4 ln x4 - v1 ln x1 - v2 ln x2 + (v3 + v4 - v1 - v2)ln p = -(v3Φ3 + v4Φ4 - v1Φ1 - v2Φ2)

(3.39)

∴

(3.40)

Denoting

ln K = -(v3Φ3 + v4Φ4 - v1Φ1 - v2Φ2)

(3.41)

where K, is known as the equilibrium constant, is a function of temperature only

(3.42)

This equation is called the law of mass action. K has the dimension of pressure raised to the (v₃+ v₄- v₁- v₂)th power. Here the x's is the values of mole fractions at equilibrium when the degree of reaction is ε_ε.
The law of mass action can also be written in this form

(3.43)

where the p's are the partial pressures.