NEET 2019 · ChemistryIntegrated ratePrevious Year Question

If the rate constant for a first order reaction is $k$ , the time $t$ required for the completion of 99% of the reaction is given by:

Answer: (C) $t = \frac{4.606}{k}$ . \textbf{Answer:} (C) $t = \frac{4.606}{k}$ \textbf{Solution:} For a first order reaction: $t = \frac{2.303}{k} lo g \frac{[ A ] _{0}}{[ A ]}$ For 99% completion, $[A] = 1%$ of $[A]_{0}$ , so $\frac{[ A ] _{0}}{[ A ]} = 100$ .

A. $t = \frac{0.693}{k}$
B. $t = \frac{6.909}{k}$
C. $t = \frac{4.606}{k}$ ✓
D. $t = \frac{2.303}{k}$

Correct Answer

Solution & Explanation

\textbf{Answer:} (C) $t = \frac{4.606}{k}$ \textbf{Solution:} For a first order reaction: $t = \frac{2.303}{k} lo g \frac{[ A ] _{0}}{[ A ]}$ For 99% completion, $[A] = 1%$ of $[A]_{0}$ , so $\frac{[ A ] _{0}}{[ A ]} = 100$ . $t = \frac{2.303}{k} lo g (100) = \frac{2.303}{k} \times 2 = \frac{4.606}{k}$

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If the rate constant for a first order reaction is k, the time t required for the completion of 99% of the reaction is given by:

Solution & Explanation

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If the rate constant for a first order reaction is $k$ , the time $t$ required for the completion of 99% of the reaction is given by: