Chemistry - Chemical Kinetics Question with Solution | TestHub

For a first order reaction, the time required is given by the integrated rate equation:

$t=\frac{2.303}{k}\log \left(\frac{[A{]}_0}{[A{]}_t}\right)$

Given:

$k=0.02303{\text{ hours}}^{-1}$

$[A{]}_0=100\%$

$[A{]}_t=20\%$

Substituting the values into the equation:

$t=\frac{2.303}{0.02303}\log \left(\frac{100}{20}\right)$

$t=100\log (5)$

Using $\log (5)\approx 0.699$:

$t=100\times 0.699=69.9\approx 70\text{ hours}$

Answer: 70 hour