Question

$75\%$ of a first-order reaction is completed in 30 minutes. What is the time required for $93.75\%$ of the reaction (in minutes) to be completed?

• A. 45
• B. 120
• C. 90
• D. 60

Answer 1

The correct option is D 60

As we know that, for a first order reaction Half-Life ($t_{1/2}$) is independent of concentration of reactant.

$⟹t_{1/2}$ is constant for a first order reaction.

Let us consider a first order reaction :

$A\to B$

Let $\left[A_0\right]$ be the initial concentration of reactant and $t_{1/2}$ = $x$ min.

When reaction is 50% completed, then [A] left will be $\frac{\left[A_0\right]}{2}$

When reaction is 75% completed, then [A] left will be $\frac{\left[A_0\right]}{4}$

When reaction is 93.75% completed, then [A] left will be $\frac{\left[A_0\right]}{16}$

time taken for [A] to become $\frac{\left[A_0\right]}{2}$ from $\left[A_0\right]$ is $x$ min

Time taken for [A] to become $\frac{\left[A_0\right]}{4}$ from $\frac{\left[A_0\right]}{2}$ is $x$ min

Time taken for [A] to become $\frac{\left[A_0\right]}{8}$ from $\frac{\left[A_0\right]}{4}$ is $x$ min

Time taken for [A] to become $\frac{\left[A_0\right]}{16}$ from $\frac{\left[A_0\right]}{8}$ is $x$ min

We are also given that time taken for 75% completion of reaction is 30 min.

$⟹2x=30$

$⟹t_{1/2}$ for the reaction is $15min$

$\therefore$ time taken for 93.75\% completion of reaction is 4$x$ min

Hence, time taken for 93.75% completion of reaction is $60$ min.

Hence, Option "D" is correct answer.