Consider a first order gas phase decomposition reaction given below:
`A(g) to 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

Options

A. `k=(2.303)/(t)log.(p_(i))/(p_(i)-x)`
B. `k=(2.303)/(t)log.(p_(i))/(2p_(i)-p_(t))`
C. `k=(2.303)/(t)log.(p_(i))/(2p_(i)+p_(t))`
D. `k=(2.303)/(t)log.(p_(i))/(p_(i)+x)`

Answer

B

Explanation

`{:(,,A(g),,to,,B(g),,+,,C(g)),("Initially",,"pi",,,,0,,,,0),("Attime t",,"Pi"-x,,,,x,,,,x):} `
`p_(t)=p_(i)-x+x+x=p_(i)+x`
For first order reaction `x=p_(t)-p_(i)`
`k=(2.303)/(t)log.(p_(i))/(p_(i)-x)`
`=(2.303)/(t)log.(p_(i))/(p_(i)-(p_(t)-p_(i)))=(2.303)/(t)log.(p_(i))/(2p_(i)-p_(t))`