Question

The time required for a first order reaction to complete $90$% is ${}^{\prime }{t}^{\prime }$. What is the time required to complete $99$% of the same reaction:

• A. $2t$
• B. $3t$
• C. $t$
• D. $4t$

Answer 1

The correct option is A $2t$

For the first order reaction :

$t=\frac{2.303}{k}log(\frac{\left(initialconcentration\right)}{\left(finalconcentration\right)}$

Let $t_1$ be the time required for 90% completion and $t_2$ be the time required for 99% completion.

So, $\frac{t_1}{t_2}=\frac{log\frac{100}{10}}{log\frac{100}{1}}$

$\Rightarrow \frac{t_1}{t_2}=\frac{1}{2}$

$\Rightarrow t_2=2t_1$

The time required for a first-order reaction to complete 90% is ${}^{\prime }{t}^{\prime }$. So, the time required to complete 99% of the same reaction is $2t$.