MHT CET · Chemistry · Chemical Kinetics

In a first order reaction if concentartion of reactant drops from \(0.8 \mathrm{~mol} \mathrm{~L}^{-1}\) to \(0.4 \mathrm{~mol} \mathrm{~L}^{-1}\) in 15 minute. What is the time required to drop concentration from \(0.1 \mathrm{~mol} \mathrm{~L}^{-1}\) to 0.025 mol \(\mathrm{L}^{-1}\).

A 7.5 minute
B 15 minute
C 30 minute
D 60 minute

Verified Solution

Answer & Solution

Correct Answer

(C) 30 minute

Step-by-step Solution

Detailed explanation

As the concentration of reactant is reduced to half i.e., from \(0.8 \mathrm{~mol} \mathrm{~L}^{-1}\) to \(0.4 \mathrm{~mol} \mathrm{~L}^{-1}\) in 15 minutes,
\(\therefore \quad \mathrm{t}_{1 / 2}=15\) minutes
For a first order reaction,

\(\therefore \) Time required to drop the concentration from
\(\begin{aligned}
0.1 \mathrm{~mol} \mathrm{~L}^{-1} \text { to } 0.025 \mathrm{~mol} \mathrm{~L}^{-1} & =2 \times \mathrm{t}_{1 / 2} \\
& =2 \times 15 \text { minutes } \\
& =30 \text { minutes }
\end{aligned}\)

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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