Question

Gaseous reaction, $A\to B+C$ follows first-order kinetics. The concentration of $A$ changes from 1 M to 0.25 M in 138.6 minutes. When the concentration of $A$ is 0.1 M, the rate of reaction will be:

• A. $2\times {10}^{-3}Mmi{n}^{-1}$
• B. ${10}^{-3}Mmi{n}^{-1}$
• C. ${10}^{-2}Mmi{n}^{-1}$
• D. $5\times {10}^{-4}Mmi{n}^{-1}$

Answer 1

The correct option is B ${10}^{-3}Mmi{n}^{-1}$

Half-life of a first-order reaction is constant.

In 138.6 min, concentration reduced to $\frac{1}{4}$ of the original.

$\therefore$ Half life of reaction = $\frac{138.6}{2}=69.3$ min

$\frac{0.693}{K}=t_{1/2}$

$\Rightarrow K=\frac{0.693}{69.3}={10}^{-2}{min}^{-1}$

$rate=K\left[A\right]$

= ${10}^{-2}\times {10}^{-1}M{min}^{-1}$

$\Rightarrow {10}^{-3}M{min}^{-1}$