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Half life period of a first order reaction is \( 10 \mathrm{~min} \). Starting with initial concentration \( 12 \mathrm{M} \), the
rate after \( 20 \mathrm{~min} \) is

A \( 0.0693 M \min ^{-1} \)
B \( 0.693 \times 3 M \min ^{-1} \)
C \( 0.0693 \times 3 M \min ^{-1} \)
D \( 0.0693 \times 4 M \min ^{-1} \)

Verified Solution

Answer & Solution

Correct Answer

(C) \( 0.0693 \times 3 M \min ^{-1} \)

Step-by-step Solution

Detailed explanation

For first order reaction,
Half -life is \( t \frac{1}{2}=10 \mathrm{~min} \)
\[
k=\frac{0.693}{10}=0.0693 \mathrm{~min}^{-1}
\]
As \( t_{\frac{1}{2}} \) is \( 10 \mathrm{~min} \), so, after \( 20 \mathrm{~min} \) or two half-life the conc. will be \( 3 \mathrm{M} \).
\( 12 M{t_{1 / 2}} \) Hence, the rate \( =0.0693 \times 3 M \mathrm{~min}^{-1} \)

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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Half life period of a first order reaction is \( 10 \mathrm{~min} \). Starting with initial concentration \( 12 \mathrm{M} \), therate after \( 20 \mathrm{~min} \) is

Step-by-step Solution

Half life period of a first order reaction is \( 10 \mathrm{~min} \). Starting with initial concentration \( 12 \mathrm{M} \), the
rate after \( 20 \mathrm{~min} \) is