Question

The rate of a first order reaction is $0.04 mol \, l^{-1} \, s^{-1}$ at 10 seconds and $0.03 \, mol \, l^{-1} \, s^{-1}$ 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

Answer: (D)

24.1 s

Answer 2

$K = \frac{2.303}{10} \log \frac{0.04}{0.03}$ $K = \frac{2.303}{10} \log \frac{4}{3}$ $K = \frac{2.303 \times0.123}{10}$ $K = 0.0285 t_{1/2} = \frac{0.693}{K}$ $t_{1/2} = \frac{0.693}{0.0285} = 24.1s.$