MHT CET · Chemistry · Chemical Kinetics

What is rate constant of a first order reaction if \(60 \%\) reactant decompose in 45 minute?

A 0.010 minute \(^{-1}\)
B 0.015 minute \(^{-1}\)
C 0.020 minute \(^{-1}\)
D 0.025 minute \(^{-1}\)

Verified Solution

Answer & Solution

Correct Answer

(C) 0.020 minute \(^{-1}\)

Step-by-step Solution

Detailed explanation

If \([\mathrm{A}]_0=100\), then \([A]_t=100-60=40\)
For a first order reaction,
\(\begin{aligned}
\mathrm{k} & =\frac{2.303}{\mathrm{t}} \log _{10} \frac{[\mathrm{~A}]_0}{[\mathrm{~A}]_{\mathrm{t}}} \\
& =\frac{2.303}{45 \mathrm{~min}} \log _{10} \frac{100}{40} \\
\therefore \quad & =\frac{2.303 \times 0.397}{45 \mathrm{~min}} \\
& =0.020 \text { minute }^{-1}
\end{aligned}\)

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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