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For a first order gas phase reaction : ...

For a first order gas phase reaction :
`A_((g)) to 2B_((g)) +C_((g))`
`P_(0)` be initial pressure of A and `P_(t)` the total pressure at time 't'. Integrated rate equation is :

A

`(2.303)/(t)log((P_(0))/(P_(0)-P_(t)))`

B

`(2.303)/(t)log((2P_(0))/(3P_(0)-P_(t)))`

C

`(2.303)/(t)log((P_(0))/(2P_(0)-P_(t)))`

D

`(2.303)/(t)log((2P_(0))/(2P_(0)-P_(t)))`

Text Solution

Verified by Experts

The correct Answer is:
B
Initial : `{:(A_((g)) ,to, 2B_((B)), +,C_((g))),(P_(0),,0,,0),(P_(0)-P,,2P,,P):}`
Total pressure at time (t) `=P_(0)-P+2P+P=P_(1)`
`rArr P_(t)=P_(0) +2P`
`P_(t)-P_(0) = 2P rArr P=(P_(t)-P_(0))/(2)`
`k=(2.303)/(t)log[(P_(0))/(P_(0)-P)]=(2.303)/(t)log[(P_(0))/(P_(0)((P_(t)-P_(0))/(2)))]`
`=(2.303)/(t)log[(2P_(0))/(2P_(0)-P_(t)+P_(0))]=(2.303)/(t) log[(2P_(0))/(3P_(0)-P_(t))]`
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