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 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.