For the decomposition of azoisopropane to hexane and nitrogen at 543 K , the following data are obtained.
`{:(t(s),P("mm Hg")),(0,35.0),(360,54.0),(720,63.0):}`
Calculate the rate constant.

Explanation

`(CH_(3))_(2)CHN=NCH(CH_(3))_(2)(g)rarrN_(2)(g)+C_(6)H_(14)(g)`
`{:("Initial pressure",p_(0),0,0),("After time t",p_(0)-p,p,p):}`
Total pressure after time `t,P_(t)=(P_(0)-p)+p+p=P_(0)+p`
or, `p=P_(t)-P_(0)`
Now, `alphapropP_(0) and (a-x)propP_(0)-p`
`thereforea-xpropP_(0)-(P_(t)-P_(0)) " or, "(a-x)prop2P_(0)-p_(t)`
As the reaction is of the first order,
`k=(2.303)/(t)log.(a)/(a-x)=(2.303)/(t)log.(P_(0))/(P_(0)-P_(t))`
When t = 360s,
`k=(2.303)/(360)log.(35.0)/(2xx35.0-54.0)=2.174xx10^(-3)s^(-1)`
`=(2.303)/(360)log.(35)/(16)=(2.303)/(360)(0.3399)`
`=2.174xx10^(-3)s^(-1)`
When t = 720s,
`k=(2.303)/(720)log.(35.0)/(2xx35.0-63.0)=2.236xx10^(-3)s^(-1)`
` therefore` Average value of k
`=(2.174+2.236)/(2)xx10^(-3)=2.205xx10^(-3)s^(-1)`