WBJEE · Chemistry · Chemical Kinetics

The kinetic study of a reaction like \(v A \rightarrow P\) at \(300 \mathrm{K}\) provides the following curve, where concentration is taken in mol \(\mathrm{dm}^{-3}\) and time in min.

Identify the correct order \((n)\) and rate constant \((k)\)

A \(n=0, k=4.0 \mathrm{mol} \mathrm{dm}^{-3} \mathrm{min}^{-1}\)
B \(n=1 / 2, k=2.0 \mathrm{mol}^{1 / 2} \mathrm{dm}^{-3 / 2} \mathrm{min}^{-1}\)
C \(n=1, k=80 \mathrm{min}^{-1}\)
D \(n=2, k=16.0 \mathrm{dm}^{3} \mathrm{mol}^{-1} \mathrm{min}^{-1}\)

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Answer & Solution

Correct Answer

(D) \(n=2, k=16.0 \mathrm{dm}^{3} \mathrm{mol}^{-1} \mathrm{min}^{-1}\)

Step-by-step Solution

Detailed explanation

From the given graph Slope \(=\frac{(\text { rate })^{1 / 2}}{[A]}=4\) \(\because\) rate \((r)=k[A]^{n}\) Where, \(k=\) rate constant \([A]=\) concentration at time \(t\) (in min). \(n=\) order. According to the graph \((n=2)\)…

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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The kinetic study of a reaction like \(v A \rightarrow P\) at \(300 \mathrm{K}\) provides the following curve, where concentration is taken in mol \(\mathrm{dm}^{-3}\) and time in min. Identify the correct order \((n)\) and rate constant \((k)\)

Step-by-step Solution

The kinetic study of a reaction like \(v A \rightarrow P\) at \(300 \mathrm{K}\) provides the following curve, where concentration is taken in mol \(\mathrm{dm}^{-3}\) and time in min.

Identify the correct order \((n)\) and rate constant \((k)\)