For the decomposition of azoisopropane to hexane and nitrogen at 54
K, the following data are obtained.

Calculate the rare constant.

Explanation

The decomposition of azoisopropane to hexane and nitrogen at
543 K is represented by the following equation.
`(CH_(3))_2 CHN=NCH(CH_(3))_(2(g))toN_(2(g))+C_(6)H_(14(g))`
`{:("At "t=0," "P_(0),0,0),("At "t=t,P_(0)-P,P,P):}`
After time, t, total pressure,
`P_(t)=(P_(0)-p)+p+p`
`rarr P_(t)=P_(0)+p`
`rArr p=P_(t)-P_(0)`
Therefore, `P_(0)-p=P_(0)-(P_(0)-P_(0))`
`=2P_(0)-P_(t)`
For a first order reaction,
`k =2.303/t"log"(P_(0))/(P_(0)-P)`
` =2.303/t"log"(P_(0))/(2P_(0)-P_(t))`
When `t =360 s_(1),`
` k=(2.303)/(720" s")"log" (35.0)/(2xx35.0-63.0)`
When t `720 s_(1)`
=`2.235xx10^(-3)s^(-1)`
Hence, the average value of rate constant is
`k=((2.175xx10^(-3))+(2.35xx10^(-3)))/2s^(-1)`
` 2.21xx10^(-3)s^(-1)`
Note: There is a slight variation in this answer and the one given in the NCERT textbook.