Benzenediazonium chloride dissociates as
`C_(6)H_(5)N_(2)^(+)Cl^(-)rarrC_(6)H_(5)Cl+N_(2)`
At `0^(@)C` , if the concentration of diazonium salt is doubled , the rate of evolution of `N_(2)` is also doubled. Find the order of the reaction.

Explanation

If the order of the reaction is n , then rate
`=-(d[C_(6)H_(5)N_(2)^(+)Cl^(-)])/(dt)=(d[N_(2)])/(dt)=k[C_(6)H_(5)N_(2)^(+)Cl^(-)]^(n)`
Let the initial concentration of `C_(6)H_(5)N_(2)^(+)Cl^(-)=x "mol .L"^(-1)`
So , initial rate of `N_(2)` formation `=(d[N_(2)])/g =kx^(n)" "...[1]`
As doubling the concentration of diazonium salt, the rate of evolution of `N_(2)` get doubled . So ,
`2xx(d[N_(2)])/(dt)=kxx(2x)^(n)=kxx2^(n)x^(n) " "...(2)`
Dividing equation [2] by [1] , we get ,
`2=2^(n) " or, "n=1`
Thus , order of the reaction = 1.