Benzene diazonium chloride in aqueous solution decomposes according to the equation `C^(6)H^(5)N^(2)Cl rarr C_(6)H_(5)Cl+N_(2)` Starting with an initial concentration of `10 g L^(-1)`, the volume of `N_(2)` gas obtained at `50^(@)C` at different intervals of time was found to be as under :
`{:("t (min)":,6,12,18,24,30,oo),("Vol. of "N_(2) (ml):,19.3,32.6,41.3,46.5,50.4,58.3):}`
Show that the above reaction follows the first order kinetic. What is the value of the rate constant ?

Explanation

For a first order reaction
`k=(2.303)/(t)"log"([A_(0)])/([A])`
`k=(2.303)/(t)"log"(V_(oo))/(V_(oo)-V_(1))`
In the present case, `V_(oo) = 58.3 ml`.
The value of k at different time can be calculated as follows.