Question

Which of the following is the correct graph for a second order reaction?
Here,
$t_{\frac{1}{2}}$ is the half life period.
${\text{(Concentration)}}_i$ is the intial concentration of the reactant.

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

For a second order reaction:
$\frac{1}{\left[A\right]}=kt+\frac{1}{[A{]}_0}$

$[A{]}_0$ is the initial concentration
$\left[A\right]$ is the concentration at time t

At $t=t_{\frac{1}{2}},\left[A\right]=\frac{A_0}{2}$
Putting the values
$\frac{2}{[A{]}_0}=k{t}_{\frac{1}{2}}+\frac{1}{[A{]}_0}$

$t_{\frac{1}{2}}=\frac{1}{[A{]}_{0}k}$
Graph between $t_{\frac{1}{2}}$ and $\frac{1}{[A{]}_0}$ is a straight line with slope of $\frac{1}{k}$
Second order:

First order:
$t_{\frac{1}{2}}=\frac{\ln 2}{k}$


Zero order:
$t_{\frac{1}{2}}=\frac{[A{]}_0}{2k}$