For the decomposition of azosiopropane to hexane and nitrogen at 543 k, the following data obtained.

Calculate the rate constant.

Explanation

`[CH_(3)]_(2)CHN =NCH[CH_(3)]_(2) [g] to N_(2) [g] +C_(6) H_(14)[g]`

Total pressure after time t,
`i.e., [P_(t)] =[P_(i)-P]+P+P=P_(i)+P`
`Or P=P_(t) -P_(i)`
`a=P_(i)[a-x]=P_(i)-P`on substituting the values of pi
`[a-x] =P_(i) -[P_(t)-P_(i)]`
`i.e., [a-x]=2P_(i)-P_(t)`
The decomposition reaction is of gaseous nature and the rate constant k can be calculate as :
`k=(2.303)/(t)log ""(a)/(a-x)`
subsitution of value of a and `(a-x)` given
`k=(2.303)/(t) log ""((P_(i))/(2P_(i)-P_(t)))`
i) Rate constant after `360 S=k_(1)`
`k_(1)=(2.303)/((360s))log ""(35atm)/((70-54)atm)`
`=(2.303)/( (360s))log ""(35)/(16)=(2.303)/((360s))log 2.1875`
`=(2.303xx0.33995)/((360s))=2.17xx10^(-3)s^(-1)`
ii) Rate constant after `720 s =k_(2)`
`k_(2) =(2.303)/((720s))log ""5 =(2.303 xx0.6990)/((720s))`
`=2.24xx10^(-3) s^(-1)`
Average rate constant `k=((2.17+2.24)xx10^(-3) s^(-1))/(2)`
`k=2.21 xx10^(-3)s^(-1)`