**chapter 6. CHEMICAL KINETICS class 12 chemistry textbook solution**

### 3. Answer the following in brief.

x. Derive the integrated rate law for first order reaction.

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:

_{0}^[A]

_{t}(d[A]/[A]) = -k∫0^t dt

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 log_{10}, we can write:

k = 2.303/t log_{10}([A]_{0}/[A]_{t}) ...(4)

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