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)

30

Answer 2

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