Question

This time Arun got first order reaction to set up in Laboratory. He observed for 16 min and noticed that reaction is $50\%$ completed. How much time will it take for the reaction to $75\%$ complete?

• A. 24 min
• B. 32 min
• C. 28 min
• D. 48 min

Answer 1

The correct option is B 32 min

As concentration is expressed in percentage it is always easier to take initial concentration as 100.

or first order reaction ln $\left[\frac{A_0}{A}\right]=Kt$ where
$A_0$ is initial concentration
A is final concentration So at 10 min $50\%$ of reaction is complete so the concentration now will be 100 – 50 = 50
$K=\frac{1}{t}In\left[\frac{A_0}{A}\right]$
$at1=16min\to K=\frac{1}{16}ln\frac{100}{50}=\frac{1}{16}ln2$ …(i)
and at time t $75\%$ of reaction is complete
[A]=100-75=25
$\therefore K=\frac{1}{t}In\frac{100}{25}=\frac{1}{t}In4=\frac{2}{t}In2$ …(ii)
Equating equations 1 and 2 as Rate constant is specific for reaction.
$\frac{1}{16}In2=\frac{2}{t}In2\therefore t=32min.$