AP EAMCET · Chemistry · Chemical Kinetics
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 \(\frac{2.303}{k} \log \left(\frac{3}{4}\right)\)
- C \(\frac{2.303}{k} \log (4)\)
- D \(\frac{2.303}{k} \log (3)\)
Answer & Solution
Correct Answer
(C) \(\frac{2.303}{k} \log (4)\)
Step-by-step Solution
Detailed explanation
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, \(t_{3 / 4}=\frac{2.303}{k} \log \frac{a}{a-\frac{3 a}{4}}\) \(\Rightarrow \quad t_{3 / 4}=\frac{2.303}{k} \log 4\)
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