Consider a first order gas phase decompostion reaction gives below
`A(g) to B(g) to C(g)`
The initial pressure of the system before decomposition of A `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) -p_(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))/(2p_(i) -x)`

Answer

B

Explanation

Initially At time t
`underset(p_(i)-x)underset(p_(i))(A (g) ) to underset(x)underset(0)(B (g)) to underset(x)underset(0)(C(g))`
`p_(t) = p_(i) - 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))`