Question

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

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

Answer 1

Answer: (B)

58.2 min

Answer 2

For first order reaction $t=\frac{1}{K} \log \frac{a}{a-x}$ $\frac{t_{30 \%}}{t_{50 \%}}= \frac{\frac{1}{K} \times 2.303 \times \log \frac{100}{100-30}}{\frac{1}{K} \times 2.303 \times \log \frac{100}{100-50}}$ $\frac{30}{t_{1 / 2}}=\frac{\log \frac{10}{7}}{\log 2}$ $\frac{30}{t_{1 / 2}}=\frac{0.1549}{0.3010}$ $t_{1 / 2}=\frac{0.3010 \times 30}{0.1549}=58.2\, min$