Question

For the second order reaction, concentration $\left(x\right)$ of the product at time $t$ starting with initial concentration $\left[A_o\right]$ is:

• A. $\frac{kt[A_o{]}^2}{1+kt\left[A_o\right]}$
• B. $\frac{k+[A_o{]}^2}{1+kt}$
• C. $\frac{1+kt[A_o{]}^2}{k+[A_o{]}^2}$
• D. None of these

Answer 1

The correct option is A $\frac{kt[A_o{]}^2}{1+kt\left[A_o\right]}$

A reaction said to be a second-order when the overall order is $2$. The rate of second-order reaction may be proportional to one concentration squared.

$R=k[A{]}^2$

For rate proportional to single concentration squared, the time dependence of concentration is given by

$\frac{1}{\left[A\right]}=\frac{1}{A_0}+kt\Rightarrow \left[A\right]=\frac{\left[A_0\right]}{1+kt\left[A_0\right]}$

Therefore, concentration of product after time $t=\left[A_0\right]-\left[A\right]=\left[A_0\right]-\frac{\left[A_0\right]}{1+kt\left[A_0\right]}=\frac{kt[A_0{]}^2}{1+kt\left[A_0\right]}$.