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.


Answer:-

i. For the gas-phase reaction:

A(g) → B(g) + C(g)

Let the initial pressure of A be Pi, which decreases by x within time t.

ii. Pressure of reactant A at time t:

PA = Pi - x ....(1)

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

PB = PC = x

iii. The total pressure at time t is then:

P = Pi - x + x + x = Pi + x

Hence, x = P - Pi ...(2)

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

Thus:

PA = Pi - (P - Pi) = Pi - P + Pi = 2Pi - P

iv. The integrated rate law turns out to be:

k = 2.303/t log10([A]0/[A]t)

The concentration is now expressed in terms of pressures:

Thus, [A]0 = Pi and [A]t = PA = 2Pi - P

Substitution gives in the above equation:

k = 2.303/t log10(Pi / (2Pi - P)) ...(3)

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

chapter 6. CHEMICAL KINETICS class 12 chemistry textbook solution page 137