\(K\,\, = \,\,\frac{{2.303}}{t}\log \frac{{100}}{{0.1}}\) ............ \((2)\)
\((1) = (2)\)
\(\frac{{2.303}}{{32}}\,\log \,100 = \frac{{2.303}}{t}\log \frac{{100}}{{0.1}}\)
\(\frac{2}{{32}} = \frac{3}{t}\)
\(\Rightarrow t = 48\,\min.\)
$(R= 8.314\,JK^{-1} \,mol^{-1}$ and $\log 2=0.301)$