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For a first order gas phase reaction : ...

For a first order gas phase reaction :
`" "A(g)rarr2B(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))/(3P_(0)-P_(t)))`

Text Solution

Verified by Experts

The correct Answer is:
B
`" "A(g)rarr2B(g)+C(g)`
`{:("Initial pressure:",P_(0),0,0),("Pressure at time t:",P_(0)-p,2p,p):}`
Total pressure at time `t=P_(0)-p+2p+p=P_(t)`
or, `P_(t)=P_(0)+2p`
`thereforeP_(t)-P_(0)=2p " or, "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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