Question

A first order reaction which is $30\%$ complete in 30 minutes has a half-life period of

• A. 24.2 min
• B. 58.2 min
• C. 102.2 min
• D. 120.2 min

Answer 1

The correct option is B 58.2 min

$A_t=A_0{e}^{-\lambda t}$

$\frac{A_t}{A_0}=e^{-\lambda t}$

$\frac{70}{100}=e^{-\lambda t_{0.3}}$

$ln\frac{70}{100}=-\lambda \ast 30$ ----eq.1

$\frac{50}{100}=e^{-\lambda t_{0.5}}$

$ln\frac{50}{100}=-\lambda t_{0.5}$ ----eq.2

eq.1 \ eq.2

$\frac{ln\left(0.7\right)}{ln\left(0.5\right)}=\frac{30}{t_{0.5}}$

$0.5146=\frac{30}{t_{0.5}}$

$t_{0.5}=\frac{30}{0.5146}\approx 58.2min$