Let us consider a homogeneous phase having arbitrary amounts of the constituents, A₁, A₂, A₃ and A₄, capable of undergoing the reaction

(3.26)

The phase is at uniform temperature T  and pressure p. The Gibbs function of the mixture is

G = µ1n1 + µ2n2 + µ3n3+ µ4n4

(3.27)

where the n's are the number of moles of the constituents at ant moment, and the µ's are the chemical potentials. Let us imagine that the reaction is allowed to take place at constant T and p. The degree of reaction changes by an infinitesimal amount from ε to ε + dε. The change in the Gibbs function is

dGT.p= Σµkdnk = µ1dn1 + µ2dn2 + µ3dn3 + µ4dn4

(3.28)

The equations of constraint in differential form are

(3.29)

(3.30)

(3.31)

(3.32)

On substitution of  Eqs. (3.29-3.32) in  Eq. (3.28),

(3.33)

From Eq. (1.35), following interpretations can be made,

(1) When the reaction proceeds spontaneously to the right, dε is positive, and since dG_T.p<0

(v1µ1 + v2µ2) > (v3µ3 + v4µ4)

(3.34)

(2) When the reaction proceeds spontaneously to the left, dε is negative

(v1µ1 + v2µ2) < (v3µ3 + v4µ4)

(3.35)

i.e.,Σv_kµ_k is positive.
(3) At equilibrium, the Gibbs function will be minimum, hence

v1µ1 + v2µ2 = v3µ3 + v4µ4

(3.36)

which is called the equation of reaction equilibrium. Therefore, it is the value of Σv_kµ_k which causes or forces the spontaneous reaction and is called the “chemical affinity”.