Question

The time required to decompose half of the substance for $n$th order reaction is inversely proportional to: ($a$ is initial concentration)

• A. $a^{n+1}$
• B. $a^{n-1}$
• C. $a^{n-2}$
• D. $a^n$

Answer 1

The correct option is B $a^{n-1}$

For $n^{th}$ order reaction
$-\frac{da}{dt}=k{a}^n-\frac{da}{a^n}=kdt-{\int }_{a_o}^{a_f}\frac{da}{a^n}=k{\int }_0^{t_f}dt\frac{1}{a^{n-1}}=\frac{1}{{a_o}^{n-1}}+(n-1)kt{t}_f\propto \frac{1}{{a_o}^{n-1}}$