Answer:- 

A → product

The differential rate law for this reaction is given as:

rate = -d[A]/dt = k[A] ...(1)

where [A] is the concentration of the reactant at time t.

Rearranging Eq. (1), we get:

d[A]/[A] = -k dt ...(2)

Let [A]₀ be the initial concentration of the reactant A at time t = 0.

Suppose [A]_t is the concentration of A at time t.

Integrating equation (2) between the limits [A] = [A]₀ at t = 0 and [A] = [A]_t at t = t:

On integration, we obtain:

ln([A]_t/[A]₀) = -kt

or ln([A]_t/[A]₀) = -kt ...(3)

or k = 1/t ln([A]₀/[A]_t)

Converting ln to log₁₀, we can write:

k = 2.303/t log₁₀([A]₀/[A]_t) ...(4)

Equation (4) represents the integrated rate law for first-order reactions.