MHT CET · Chemistry · Chemical Kinetics

The reaction \(2 \mathrm{~A}+\mathrm{B}+\mathrm{C} \longrightarrow \mathrm{D}+\mathrm{E}\) is found to. be first order in A , second order in B and zero order in C . What is the effect of increasing concentration of all reactants twice?

A Rate of reaction increases 8 times.
B Rate of reaction increases 24 times.
C Rate of reaction increases 36 times.
D Rate of reaction remains unaffected.

Verified Solution

Answer & Solution

Correct Answer

(A) Rate of reaction increases 8 times.

Step-by-step Solution

Detailed explanation

\(\begin{aligned}
& \text { Rate }=\mathrm{k}[\mathrm{~A}][\mathrm{B}]^2[\mathrm{C}]^0 \\
& (\text { Rate })_1=\mathrm{k} \times[2 \mathrm{~A}] \times[2 \mathrm{~B}]^2 \times[2 \mathrm{C}]^0 \\
& =8 \mathrm{k}[\mathrm{~A}][\mathrm{B}]^2[\mathrm{C}]^0 \\
& \therefore \quad \frac{(\text { Rate })_1}{\text { Rate }}=\frac{8 \mathrm{k}[\mathrm{~A}][\mathrm{B}]^2[\mathrm{C}]^0}{\mathrm{k}[\mathrm{~A}][\mathrm{B}]^2[\mathrm{C}]^0}=8 \\
& \therefore \quad(\text { Rate })_1=8 \times \text { Rate }
\end{aligned}\)
i.e., rate of reaction increases 8 times.

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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