For a first order reaction `A(g) rarr 2B(g) + C(g)` at constant volume and 300 K, the total pressure at the beginning (t=0) and at time t are `P_(o) and P_(t)`, respectively. Initially, only A is present with concentration `[A]_(0) and t_(1//3)` is the time required for the partial pressure of A to reach `1//3^(rd)` of its initial value. The correct option (s) is (are) :

Options

A.
B.
C.
D.

Answer

A, D

Explanation

`A(g) rarr 2B(g) + C(g)`
First order reaction
`A(g) rarr 2B(g) + C(g)`
`t=0" "[A]_(o)" "-" "-`
`t=t" "[A]_(o)-x" "2x" "x`
`[A_(o)]+2x" "alpha P_(t)`
`2x" "alpha" "(P_(t)-P_(o))`
`x" "alpha" "((P_(t)-P_(o)))/(2)`
In `(A_(o))/(A_(t)) = kt rArr" In " (A_(o))/(A_(o)-x) = kt`
`rArr" In "(P_(o))/(P_(o)-[(P_(t)-P_(o))/(2)])=kt rArr" In "(2P_(o))/(3P_(o)-P_(t))=kt rArr" In "2P_(o) -" In "(3P_(o) -P_(t))=kt`
`rArr" In "(underset(y)underset(darr)3P_(o)-Pt)=" In "underset(C)underset(darr)2P_(o)-underset("mx")underset(darr)(kt)" "`(so slope =-k (-ve))
`rArr" "t_(1//2) =(1)/(k) ln3, t_(1//3)` is independent of `[A]_(o)` , k is constant.