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

### 3. Answer the following in brief.

xii. Derive the integrated rate law for the first order reaction, A(g) →B(g) + C(g) in terms of pressure.

**i.** For the gas-phase reaction:

`A`_{(g)} → B_{(g)} + C_{(g)}

Let the initial pressure of A be P_{i}, which decreases by x within time t.

**ii.** Pressure of reactant A at time t:

P_{A} = P_{i} - x ....(1)

The pressures of the products B and C at time t:

P_{B} = P_{C} = x

**iii.** The total pressure at time t is then:

P = P_{i} - x + x + x = P_{i} + x

Hence, x = P - P_{i} ...(2)

The pressure of A at time t is obtained by substituting Eq. (1) into Eq. (2).

Thus:

P_{A} = P_{i} - (P - P_{i}) = P_{i} - P + P_{i} = 2P_{i} - P

**iv.** The integrated rate law turns out to be:

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

The concentration is now expressed in terms of pressures:

Thus, [A]_{0} = P_{i} and [A]_{t} = P_{A} = 2P_{i} - P

Substitution gives in the above equation:

k = 2.303/t log_{10}(P_{i} / (2P_{i} - P)) ...(3)

Here, P is the total pressure of the reaction mixture at time t.