Question

$t_{1/2}$ for a first order reaction is $10\min$. Starting with $10M$, the rate after $20\min$ is

• A. $0.0693M{\min }^{-1}$
• B. $0.0693\times 5M{\min }^{-1}$
• C. $0.0693\times 2.5M{\min }^{-1}$
• D. $0.0693\times 10M{\min }^{-1}$

Answer 1

Answer: (C)

Given, $t_{1/2}=10\min$
$t=20\min$
$N_0=10M$
$\Rightarrow t=n{t}_{1/2}$
$20=n\times 10$
$\therefore n=2$
$\Rightarrow \frac{N}{N_0}={\left(\frac{1}{2}\right)}^n$
$\Rightarrow \frac{N}{10}={\left(\frac{1}{2}\right)}^2$
or $\frac{N}{10}=\frac{1}{4}$
$\therefore N=\frac{10}{4}=2.5M$
$\therefore$ Rate $=k[A]$
$=0.0693\times 2.5M{\min }^{-1}$