Question

In a first order reaction, the concentration of the reactant decreases from $0.8$ $M$ to $0.4$ $M$ in $15$ minutes. The time taken for the concentration to change from $0.1$ $M$ to $0.025$ $M$ is:

• A. $30$ min
• B. $15$ min
• C. $7.5$ min
• D. $60$ min

Answer 1

Answer: (A)

$30$ min

$-\ln \left(\frac{0.4}{0.8}\right)=kt$

$k=\frac{0.693}{15}{min}^{-1}$

Then,

$-\ln \left(\frac{0.025}{0.1}\right)=kt$

$t=\frac{\ln \left(4\right)}{0.693/15}=30mins$