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Azoisopropane decomposes acording to the...

Azoisopropane decomposes acording to the reaction:
`(CH_(3))_(2)CHN = NCH(CH_(3))_(2)(g) overset(250-290^(@)C)rarr N_(2)(g) + C_(6)H_(14)(g)`
It is found to be a first order reaction. If the initial pressure is `P_(0)` and pressure of the mixture at time `t` is `(P_(t))`, then the rate constant `(k)` would be

A

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

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
A
`{:(,(CH_(3))_(2)CH=NCH(CH_(3))_(2), rarr, N_(2) +, C_(6)H_(14)), (t=0,P_(0),,0,0),(t=t,P_(0)-x,,x,x):}`
`P_(t) = P_(0) - x + x + x = P_(0) + x`
`x = (P_(t)-P_(0))`
`(a-x) = (P_(0)-x) = P_(0) - (P_(t) - P_(0))`
`= 2P_(0) - P_(t)`
`k = (2.303)/(t) log.(a)/(a-x)`
`= (2.303)/(t) log.((P_(0)))/((2P_(0) - P_(t)))`
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