Question

The half-life of the reaction $X\to Y$, following first-order kinetics, when the initial concentration of $X$ is $0.01$ mol L${}^{-1}$ and the initial rate is $0.00352$ mol L${}^{-1}$ min${}^{-1}$ will be :

• A. $19.60min$
• B. $1.969min$
• C. $7.75min$
• D. $77.5min$

Answer 1

Answer: (B)

$1.969min$

For a first order reaction,

$\frac{dx}{dt}=k\left[X\right]$

$0.00352=k\times 0.01$

$\Rightarrow k=0.352$

$t_{1/2}=\frac{0.693}{k}=\frac{0.693}{0.352}=1.969min$

Hence, the correct answer is option $\text{B}$.