Question

For a first order reaction, calculate the ratio between the time taken to complete $99.9\%$ of the reaction and the time taken to complete half of the reaction.

• A. 10 : 1
• B. 1 : 10
• C. 100 : 1
• D. 1 : 100

Answer 1

The correct option is A 10 : 1

The rate constant for first order reaction is given by
$k=\frac{2.303}{t}log\frac{a}{a-x}$
For $99.9\%$ completion of reaction
$t_{99.9\%}=\frac{2.303}{k}log\frac{100}{100-99.9}$ ...(i)
For $50\%$ completion of reaction
$t_{50\%}=\frac{2.303}{k}log\frac{100}{50}$ ...(ii)
On dividing equation (i) by (ii)
$t_{99.9\%}=10\times t_{\frac{1}{2}}$