Question

The time taken for $10$% completion of a first order reaction is $20$ min. Then, for $19$% completion, the reaction will take:

• A. $40$ min
• B. $60$ min
• C. $30$ min
• D. $50$ min

Answer 1

The correct option is A $40$ min

When the reaction is 10% completed,
$k=\frac{2.303}{20}\log \frac{100}{100-10}$ ...(i)
When the reaction is 19% completed,
$k=\frac{2.303}{t}\log \frac{100}{100-19}$ ...(ii)
From equation (i) and (ii),
$\Rightarrow \frac{2.303}{20}\log \frac{100}{90}=\frac{2.303}{t}\log \frac{100}{81}$
$\Rightarrow \frac{1}{20}\times 0.04575=\frac{1}{t}\times 0.09151$
$\therefore t=40$ min.