Question

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 pᵢ. After lapse of time 't' total pressure of the system
increased by x units and became 'pₜ'. The rate constant k for
the reaction is given as ........... .
(a) k = 2.303/t log pᵢ/pᵢ - x
(b) k = 2.303/t log pᵢ/2pᵢ - pₜ
(c) k = 2.303/t log pᵢ/2pᵢ + pₜ
(d) k = 2.303/t log pᵢ/pᵢ + x

Answer 1

The rate constant k for the reaction is given as :

• The initial pressure of the system before decomposition of

A was pᵢ

• After lapse of time 't' total pressure of the system decreased by x units and became 'pₜ'

• Total pressure, pₜ = pa + pb + pc

pa, pb and pc are the partial pressure of A, B and C, respectively.

• If x atm be the decrease in pressure of A at time t, the increase in pressure of B and C will also be x atm each.

• pₜ = ( pi - x ) + x + x = pi + x

x = ( pₜ - pi )

where, pa = pi - x = pi + ( pt - pi )

= 2pi - pt

• k = (2.303/t)[log(pi/pA)]

= (2.303/t)×log(pi/2pi - pt)