Consider a first order gas phase decomposition reaction given below :

A(g) → B(g) + C(g)

The initial pressure of the system before decomposition of A was p_i. After lapse of time ‘t’, total pressure of the system increased by x units and became ‘p_t’ The rate constant k for the reaction is given as _________.

Given,

For first-order reaction for a gaseous reaction at a constant temperature the concentration is replaced by the partial pressure of reactants and products.

Where p_a is the partial pressure of element A.

p_i is the initial pressure of element A.

Let p_t be the total pressure , p_t =p_a + p_b + p_c

Where, p_a ,p_b ,p_c are partial pressure of A,B,C respectively

At t=0 p_a=p_i , p_b =0, p_c =0

At t=t p_a=p_i-x, p_b=x , p_c=x ,so p_t= p_i-x + x +x p_t=p_i + x ………(p_t=p_a+p_b+p_c)

Know at t=t , p_t = p_i+x x=p_t-p_i

At t =t , p_a=p_i-(p_t-p_i) p_a=2p_i-p_t

Putting these values in Equation 1 we get,

K=

Thus Option (ii) is correct.