Question

The half life period of a first order chemical reaction is $6.93$ minutes. The time required for the completion of $99$% of the chemical reaction will be: $(\log 2=0.301)$

• A. $230.3$ minutes
• B. $23.03$ minutes
• C. $46.06$ minutes
• D. $460.6$ minutes

Answer 1

The correct option is C $46.06$ minutes

We know that $99.9\%$ completion implies $0.001A_0$ of reactant remains.
$k=\frac{0.693}{t_{1/2}}=\frac{0.693}{6.93}=0.1{min}^{-1}So,\ln \left(\frac{A_0}{0.001A_0}\right)=0.1t\frac{\ln \left(100\right)}{0.1}=t=46.06minutes$