COMEDK · Chemistry · 19. Chemical Kinetics

The half- life of a first order reaction is ' \(p\) ' and its \(3 / 4^{\text {th }}\) life period is ' \(q\) '. \(p\) and \(q\) are related to each other by: [Given: \(\log 3=0.4771, \log 4=0.6040\) ]

A \(p=2 q\)
B \(2 p=q\)
C \(q=\dfrac{p}{4}\)
D \(\dfrac{p}{q}=3\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(2 p=q\)

Step-by-step Solution

Detailed explanation

For a first order reaction, the rate constant \(k\) is given by \(k = \dfrac{\ln 2}{p}\), where \(p\) is the half-life. The \(3/4^{\text{th}}\) life period \(q\) is the time taken for the concentration to reduce to \(1/4\) of its initial value. The integrated rate equation is…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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