QJEEM05Chfeb5: JEE Main 2005 Chemistry - Class 12 JEEM05Chfeb5 Solution: t 1/4 can be taken as the time taken for the concentration of a …

Question

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t_1/4 can be taken as the time taken for the concentration of a reactant to drop to

\frac{3}{4}

of its initial value. If the rate constant for a first order reaction is K, the t_1/4 can be written as

Accepted Answer

t_{1 / 4} = \frac{2.303}{K} \log \frac{1}{3 / 4}

= \frac{2.303}{K} \log \frac{4}{3}

= \frac{2.303}{K} (\log 4 - \log 3)

= \frac{2.303}{K} (2 \log^{2} - \log 3)

= \frac{2.303}{K} (2 \times 0.301 - 0.4771)

= \frac{0.29}{K}

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