Question

Rate constant of a first order reaction is $0.0693{\text{min}}^{-1}$. If we start with $20{\text{mol L}}^{-1}$, it is reduced to $2.5{\text{mol L}}^{-1}$ in:
(Given $\log 2=0.3010$)

• A. $10\text{min}$
• B. $20\text{min}$
• C. $30\text{min}$
• D. $40\text{min}$

Answer 1

The correct option is C $30\text{min}$

Given,
$k=0.0693{\text{min}}^{-1}$
$\left[A_0\right]=20{\text{mol L}}^{-1}\left[A\right]=2.5{\text{mol L}}^{-1}$
For first order reaction, $kt=2.303\log \frac{\left[A_0\right]}{\left[A\right]}\Rightarrow t=\frac{2.303}{0.0693}\times \log \frac{20}{2.5}\Rightarrow t=30\text{min}$