Question

Diazonium salt decomposes as
$C_6{H}_5{N}_2^{+}\to C_6{H}_{5}Cl+N_2$
At $0^{o}C$, the evolution of $N_2$ becomes two times faster when the initial concentration of the salt is doubled. Therefore, it is:

• A. A first order reaction
• B. A second order reaction
• C. Independent of the initial concentration of the salt
• D. A zero order reaction

Answer 1

The correct option is A A first order reaction

Given decomposition reaction is,
$C_6{H}_5{N}_2^{+}\to C_6{H}_{5}Cl+N_2$
Rate of the reaction is given by,
$r=\frac{d\left[C_6{H}_5{N}_2^{+}\right]}{dT}=\frac{d\left[N_2\right]}{\left[dT\right]}=k[x{]}^n...(i)$
Let, $x$ be the initial concentration of $C_6{H}_5{N}_2^{+}$ and let the reaction be $n^{\text{th}}$ order.
According to the question, at $0^{o}C$, the evolution of $N_2$ becomes two times faster when the initial concentration of the salt is doubled.
$2r=k[2x{]}^n...(ii)$
Now, $\frac{\left(ii\right)}{\left(i\right)}=2=2^n$
$\Rightarrow n=1$