KCET · Chemistry · Chemical Kinetics

For a reaction, \(A+2 B \rightarrow\) Products, when concentration of \(B\) alone is increased half-life remains the same. If concentration of \(A\) alone is doubled, rate remains the same. The unit of rate constant for the reaction is

A \(\mathrm{s}^{-1}\)
B \(\mathrm{L} \mathrm{mol}^{-1} \mathrm{~s}^{-1}\)
C \(\mathrm{mol} \mathrm{L}^{-1} \mathrm{~s}^{-1}\)
D \(\mathrm{atm}^{-1}\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(\mathrm{s}^{-1}\)

Step-by-step Solution

Detailed explanation

For the reaction,
\(A+2 B \longrightarrow \text { Products }\)
Half-life \(\left(t_{1 / 2}\right)\) remains same as \([B]\) increases for lst order, \(t_{1 / 2} \propto \frac{l}{[B]}\)
\(\therefore\) w.r.t. \(B\), reaction is of first order.
Also, as \([A]\) is doubled, rate remains constant.
\(\therefore\) It is zero order w.r.t. \(A\).
\(\therefore\) Rate law expression is \(k[A]^{0}[B]^{1}\)
\(\therefore\) Overall order \(=0+1=1\)
\(\therefore\) Unit of \(k=\mathrm{s}^{-1}\)

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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