Question

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

Calculate the rare constant.

Answer 1

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.