Q29 / 160 · AP EAMCET 2021 (23 Aug Shift 2) · Chemistry
Which among the following represents the expression for $\left(\frac{3}{4}\right)^{\text {th }}$ life of $1^{\text {st }}$ order reaction?
- A$\frac{k}{2.303} \log \left(\frac{4}{3}\right)$
- B$\frac{2.303}{k} \log \left(\frac{3}{4}\right)$
- Correct answerC$\frac{2.303}{k} \log (4)$
- D$\frac{2.303}{k} \log (3)$
Solution
For first order reaction,
$t=\frac{2.303}{k} \log \frac{a}{a-x}$
if $t=t_{3 / 4}$ and $x=\frac{3}{4} a$
Then, $t_{3 / 4}=\frac{2.303}{k} \log \frac{a}{a-\frac{3 a}{4}}$
$\Rightarrow \quad t_{3 / 4}=\frac{2.303}{k} \log 4$
Hence, the correct answer is option: 'C'.