Question

For a given reaction of the first order, it takes $15$ minutes for the concentration to drop from $0.8M$ to $0.4M$. The time required for the concentration to drop from $0.1M$ to $0.025M$ will be:

• A. $15$ minutes
• B. $60$ minutes
• C. $30$ minutes
• D. $7.5$ minutes

Answer 1

The correct option is C $30$ minutes

The reactant concentration drop from $0.8M$ to $0.4M$ i.e., $50$% takes place in $15$ minutes. So half life of the reaction is $15$ minutes.
Rate constant:
$k=\frac{0.693}{t_{\frac{1}{2}}}$

$k=\frac{0.693}{15}=0.0462{min}^{-1}$
Now the time taken for the concentration to drop from $0.1M$ to $0.025M$

$t=\frac{2.303}{k}\log \frac{0.1}{0.025}=\frac{2.303}{0.0462}\log \frac{0.1}{0.025}\approx 30min$

Hence, option (c) is correct.