Question

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

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

Answer 1

The correct option is B 32 minutes

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

The integrated rate law for a first order reaction is given by,

ln $\left[\frac{A_0}{A}\right]=kt$

where,

$A_0$ is the initial concentration
A is the final concentration

So at 10 minutes, $50\%$ of the reaction is complete.
So the concentration now will be,

100 – 50 = 50

$k=\frac{1}{t}ln\left[\frac{A_0}{A}\right]$
$att=16minutes\to k=\frac{1}{16}ln\frac{100}{50}=\frac{1}{16}ln2$ …(i)

At time $t_o$, $75\%$ of reaction is complete.

[A]=100-75=25

$\therefore k=\frac{1}{t_o}ln\frac{100}{25}=\frac{1}{t_o}ln4=\frac{2}{t_o}ln2$ …(ii)

Equating equations 1 and 2 as Rate constant is specific for a reaction at a given temperature,

$\frac{1}{16}ln2=\frac{2}{t_o}ln2\therefore t=32min.$