Question

Which among the following is wrong for 1^st order reaction?
(A) ${t_{99.9\% }} = \frac{5}{2}{t_{99.9\% }}$
(B) ${t_{99.9\% }} = 10{t_{\frac{1}{2}}}$
(C) ${t_{99.9\% }} = 3{t_{90\% }}$
(D) ${t_{96.875\% }} = 5{t_{\frac{1}{2}}}$

Answer 1

Hint: Before doing this question we have to know that what is first order reaction so first order reaction is a reaction in which the rate of reaction only depends on the concentration of 1 molecule, this is called a first order reaction. By using this type we can solve the above given question easily.

Complete Step by Step Solution:
As we get detail about 1st order reaction above we get to know we take some further details about all reactions,
As we all know that when any reaction completes $90\% $ of it its half time will be $\frac{{10}}{3}{t_{\frac{1}{2}}}$.
As similarly in above options we get there most of the reaction are completing between $95$ to $99.99\% $ for which we know that when any reaction completes $99.99\% $ then its half time will be $10{t_{\frac{1}{2}}}$ .
As in above given option there is one option who did not satisfies the rules of first order reaction, which is,
${t_{99.9\% }} = \frac{5}{2}{t_{99.9\% }}$
So, the wrong option for first order reaction is ${t_{99.9\% }} = \frac{5}{2}{t_{99.9\% }}$ .
Hence, the correct option is (A).

Note: As doing first order reaction questions there are many types of other things which we have to understand. The major formula which is used to calculate many types of numerical question of first order reaction is $k = \frac{{2.303}}{t}\log \left( {\frac{a}{{a - x}}} \right)$. When we have to calculate the half time of the first order reaction we also used the following formula as the most ${t_{\frac{1}{2}}} = \frac{{0.693}}{k}$ .As per using the formulas we can easily solve many types of first order reaction questions.