In the following question, a statement of assertion is given and a corresponding statement of reason is given just below it. Of the statements, mark the correct answer as –
Assertion (A): For the first order reaction, half-life period is expressed as ${(t)}_{1 / 2} = \frac{2.303}{k} \log 2.$
Reason (R ): The half-life time of a first order reaction is not always constant and it depends upon the initial concentration of reactants.

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If both A and R are true but R is not the correct explanation of A

Both A & R are false

If A is true but R is false

If both A and R are true and R is the correct explanation of A

answer is C.

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Detailed Solution

For a first order reaction $k = \frac{2.303}{t} \log \frac{a}{a - x}$
$(k) = \frac{2.303}{{(t)}_{1 / 2}} \log \frac{a}{a - a / 2} = \frac{2.303}{{(t)}_{1 / 2}} \log \frac{a}{a / 2} = \frac{2.303}{{(t)}_{1 / 2}} \log 2$
Therefore half-life period ${(t)}_{1 / 2} = \frac{2.303}{k} \log 2.$
Thus ${(t)}_{1 / 2}$ is independent of initial concentration of reactant for first order reaction.