Chemical Kinetics and Nuclear ChemistryHard

Question

Which of the following represents the expression for 3/4th the life of a first-order reaction?

Options

A.$\frac{k}{2.303}\log\frac{4}{3}$
B.$\frac{2.303}{k}\log\frac{4}{3}$
C.$\frac{2.303}{k}\log 4$
D.$\frac{2.303}{k}\log 3$

Solution

When $t = t_{3/4}\lbrack A\rbrack = \left\lbrack A_{0} \right\rbrack - \frac{3}{4}\left\lbrack A_{0} \right\rbrack = \frac{\left\lbrack A_{0} \right\rbrack}{4}$

Now, $t_{3/4} = \frac{1}{K}.\ln\frac{\left\lbrack A_{0} \right\rbrack}{\left( \frac{\left\lbrack A_{0} \right\rbrack}{4} \right)} = \frac{\ln 4}{K} = \frac{2.303}{K}.\log 4$

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