Question

Consider the reaction; $A\to B+C$. Initial concentration of $A$ is 1 M. 20 minutes time is required for completion of 20 percent reaction. If $\frac{d\left[B\right]}{dt}=k\left[A\right]$, then half life $\left(t_{1/2}\right)$ is:

• A. 55.44 min
• B. 50 min
• C. 62.13 min
• D. none of these

Answer 1

The correct option is C 62.13 min

Using integrated rate law expression.

$Kt=ln\frac{{\left[A\right]}_0}{{\left[A\right]}_t}$

$\Rightarrow 20k=ln\frac{{\left[A\right]}_0}{0.8{\left[A\right]}_t}$

$\Rightarrow k=\left(\frac{1}{20}\right)[ln10-3ln2]$

Now,

$t_{1/2}$ is given by $\frac{0.693}{k}$

$\Rightarrow t_{1/2}=\frac{0.693\times 20}{ln10-3ln2}=62.15min.$