Question

For a first order reaction,

$\left(A\right)$ $\to$ products,

the concentration of $A$ changes from $0.1$M to $0.025$M in $40$ minutes. The rate of reaction when the concentration of $A$ is $0.01$ M is:

• A. $1.73\times {10}^{-4}$ mol $d{m}^{-3}mi{n}^{-1}$
• B. $1.73\times {10}^{-5}$ mol $d{m}^{-3}mi{n}^{-1}$
• C. $3.47\times {10}^{-4}$ mol $d{m}^{-3}mi{n}^{-1}$
• D. $3.47\times {10}^{-5}$ mol $d{m}^{-3}mi{n}^{-1}$

Answer 1

Answer: (C)

$3.47\times {10}^{-4}$ mol $d{m}^{-3}mi{n}^{-1}$

For $1^{st}$ order reaction,

rate constant, $R=\frac{2.303}{t}\log \frac{\left[A\right]}{[A{]}_t}$

$\therefore R=\frac{2.303}{40}\log \frac{0.1}{0.025}=\frac{0.693}{20}$

For $1^{st}$ order reaction,

rate=$K\left[A\right]=\frac{0.693}{20}\times 0.01$

$=3.47\times {10}^{-4}mold{m}^{-3}mi{n}^{-1}$

Hence, the correct option is $C$