A 1st order reversible reaction of the type is composed of the reactions:

The rate law is:

Substitute [*B*] = [*A _{0}*] – [

*A*], where [

*A*] is the initial concentration of

_{0}*A*, in the above equation and rearranging, we have.

Let

Eq16 becomes . Differentiating eq17 with respect to [*A*], we have , and differentiating this expression with respect to time, we have , which is equivalent to

Let *x* = *x _{0 }*when

*t*=0 and integrate the above expression. We have

Substitute eq17 in eq18, noting that the 2nd term on RHS of eq18 refers to concentrations at *t* = 0, where [*A*] = [*A _{0}*],

which rearranges to

When *t* = 0, eq19 becomes [*A*] = [*A _{0}*]. As

*t*→ ∞,

Since ,

Therefore, the equilibrium constant for the reaction is:

This is the link between chemical kinetics and thermodynamics.