Question

The rate constant of a first order reaction is $ 0.0693\,{{\min }^{-1}}. $ What is the time (in minutes) required for reducing an initial concentration of $ \text{20}\,\text{mol}\,{{\text{L}}^{-1}} $ to $ \text{2}\text{.5}\,\text{mol}\,{{\text{L}}^{-1}} $ ?

• A. 40
• B. 30
• C. 20
• D. 10

Answer 1

Answer: (B)

Given, $ k=0.0693{{\min }^{-1}} $ $ t=? $ $ a=20\,mol\,{{L}^{-1}} $ $ a-x=2.5\,mol\,{{L}^{-1}} $ $ k=\frac{2.303}{t}\log \frac{a}{a-x} $ $ t=\frac{2.303}{k}\log \frac{20}{2.5} $ $ t=\frac{2.303}{0.0693}\log 8 $ $ =33.23\times 0.9030\,\min $ $ =30\min $