Question

The rate of a first-order reaction is $0.04mo{l}^{–1}{s}^{–1}$ at 10 seconds and 0.03 $mo{l}^{–1}{s}^{–1}$ at 20 seconds after initiation of the reaction. The half-life period of the reaction is

• A. 34.1 s
• B. 44.1 s
• C. 54.1 s
• D. 24.1 s

Answer 1

The correct option is D

24.1 s

$K=\frac{2.303}{10}\times log\frac{0.04}{0.03}$

$=\frac{2.303\times 0.124}{10}(t_{\frac{1}{2}}=\frac{0.693}{k})$

$\therefore t_{\frac{1}{2}}=\frac{2.303\times 0.301\times 10}{2.303\times 0.124}$

$=24.27s$

$\therefore t_{\frac{1}{2}}\approx 24.1\text{seconds}$