COMEDK · Chemistry · 19. Chemical Kinetics

A first order reaction proceeds to \(90 \%\) completion. What will be the approximate time taken for \(90 \%\) completion in relation to \(t_{1 / 2}\) of the reaction?

A 5.66 times of \(\mathrm{t}_{1 / 2}\)
B 5.02 times of \(\mathrm{t}_{1 / 2}\)
C 4.54 times of \(\mathrm{t}_{1 / 2}\)
D 3.32 times of \(\mathrm{t}_{1 / 2}\)

Verified Solution

Answer & Solution

Correct Answer

(D) 3.32 times of \(\mathrm{t}_{1 / 2}\)

Step-by-step Solution

Detailed explanation

For a first order reaction, the rate constant \(k\) is given by \(k = \dfrac{2.303}{t} \log \left( \dfrac{[A]_0}{[A]_t} \right)\). For \(90 \%\) completion, \([A]_t = [A]_0 - 0.90[A]_0 = 0.10[A]_0\). Substituting this into the rate equation,…

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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