Question

The half life period of a first order chemical reaction is 6.93 minutes. The time required for the completion of 99% of the chemical reaction will be:[log 2 =0.301]
(A) 230.3 minutes
(B) 23.03 minutes
(C) 46.06 minutes
(D) 460.6 minutes

Answer 1

Hint: Determine the value of decay constant for the given value of half-life. Now we can substitute the value in the equation given below:
$t=\dfrac{2.303}{\lambda }\log \dfrac{a}{a-x}$
Where, t is time taken for the specified amount of decay
$\lambda $ is decay constant
a is initial concentration of reactant or radioisotope
x is the concentration of reactant or radioisotope that has decayed or disintegrated.

Complete step-by-step answer:
We will find the value of decay constant, $\lambda $.
$\lambda =\dfrac{0.693}{{{t}_{half\ life}}}$ = $\dfrac{0.693}{6.93}$ = 0.1/min
Let us now find the time taken for 99% of reactions to be completed.
$\lambda $ = 0.1 /min
a = 100
x = 99
Substituting these values in the above equation we get,
$t=\dfrac{2.303}{\lambda }\log \dfrac{a}{a-x}$
$t=\dfrac{2.303}{0.1}\log \dfrac{100}{100-99}$
t = 46.06 min

Therefore, the correct answer is option (C).

Additional information: Most of first order reactions are radioactive decay reactions. They are used to convert unstable nuclei to a stable nucleus. The energy released during this process is harnessed as well. Radioactive decay also known as radioactive disintegration or nuclear disintegration is the process by which an unstable atomic nucleus loses energy in the form of radiation to gain stability. Any material containing unstable nuclei is considered radioactive.

Note: In case, you are not able to determine the order of the reaction, take a look at the unit of decay constant. The unit of decay constant is different for every order of reaction. The unit of decay constant for first order reaction is ${{\min }^{-1}}$.