Q. 54.0( 1 Vote )

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.

B.

C.

D.

Answer :

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 pa is the partial pressure of element A.


pi is the initial pressure of element A.


Let pt be the total pressure , pt =pa + pb + pc


Where, pa ,pb ,pc are partial pressure of A,B,C respectively


At t=0 pa=pi , pb =0, pc =0


At t=t pa=pi-x, pb=x , pc=x ,so pt= pi-x + x +x pt=pi + x ………(pt=pa+pb+pc)


Know at t=t , pt = pi+x x=pt-pi


At t =t , pa=pi-(pt-pi) pa=2pi-pt


Putting these values in Equation 1 we get,


K=


Thus Option (ii) is correct.

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