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In a homogenous reaction A rarr B+C+D th...

In a homogenous reaction `A rarr B+C+D` the initial pressure was `P_(0)` and after time t it was P. Expression for rate constant k in terms of `P_(0)`, P and t will be

A

`k=(2.303)/(t)log.(2P_(0))/(3P_(0)-P)`

B

`k=(2.303)/(t)log.(2P_(0))/(P_(0)-p)`

C

`k=(2.303)/(t)log.(3P_(0)-P)/(2P_(0))`

D

`k=(2.303)/(t)log.(2P_(0))/(3P_(0)-2P)`

Text Solution

Verified by Experts

The correct Answer is:
A
`{:(,A,rarr,B,+,C,+,D),("Initial",a,,0,,0,,0),("After time t" ,a-x,,x,,x,,x):}`
It is given that `a=p_(0)" …(i)"`
`a-x+x+x+x=P`
`or a+2x=P" …(ii)"`
From (i),
`p_(0)+2x=P or x=(p-p_(0))/(2)`
From rate equation
`k=(2.303)/(t)log.(a)/(a-x)`
`=(2.303)/(t)log.(p_(0))/(p_(0)-((p-p_(0))/(2)))=(2.303)/(t)log.(2p_(0))/(3p_(0)-p)`
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