Question

From different sets of data of $t_{1/2}$ at different initial concentrations say $a$ for a given reaction, the $[t_{1/2}\times a]$ is found to be constant. The order of reaction is:

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

Answer: (C)

$2$

For an $n^{th}$ order rate:
$\frac{1}{a^{n-1}}=\frac{1}{{a_0}^{n-1}}+(n-1)kt$
So,
For $n=2($second order)
$\frac{1}{a}=\frac{1}{a_0}+kt$
For $a=a_0/2\frac{2}{a_0}-\frac{1}{a_0}=k{t}_{1/2}{t}_{1/2}=\frac{2}{a_{0}k}$
$\therefore \left(t_{1/2}{a}_0\right)=\frac{2}{k}$ (constant).