Question

For a first order reaction \(A → B\), the rate constant, \(k = 5.5×10^{–14}s^{–1}\). The time required for 67% completion of reaction is \(x×10^{–1}\) times the half life of reaction. The value of \(x\) is _____. (Nearest integer)

Answer 1

Correct Answer: 16

\(∵ kt = ln \frac {A_0}{A}\)

\(\frac {ln2}{t_{\frac 12}}\) \(t\)_67% \(=ln\frac {A_0}{0.33A_0}\)
\(\frac {log\ 2}{t_{\frac 12}}\)\(t\)_67% = \(log \frac {1}{0.33}\)
\(t\)_67% \(= 1.566 t_{\frac 12}\)
\(x = 15.66\)
Nearest Integer \(= 16\)

So, the answer is \(16\).