Question

First order reaction completes $20\%$ in $5$ min. How much time it will take for $60\%$ completion?

• A. $26.5$ min
• B. $20.5$ min
• C. $19.5$ min
• D. $18$ min

Answer 1

The correct option is B $20.5$ min

In 5 minutes, the reaction is 20% complete.

$[A{]}_0=100$ and $\left[A\right]=100-20=80$

$k=\frac{2.303}{t}lo{g}_{10}\frac{[A{]}_0}{\left[A\right]}$

$k=\frac{2.303}{5min}lo{g}_{10}\frac{100}{80}$

$k=0.0446mi{n}^{-1}$

Now, the reaction is 60% complete.

$[A{]}_0=100$ and $\left[A\right]=100-60=40$

$t=\frac{2.303}{k}lo{g}_{10}\frac{[A{]}_0}{\left[A\right]}$

$t=\frac{2.303}{0.0446mi{n}^{-1}}lo{g}_{10}\frac{100}{40}$

$t=20.5min$