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NEET CHEMISTRYChemical KineticsMedium

Question

A first order reaction has a specific reaction rate of 102 s110^{-2} \text{ s}^{-1}. How much time will it take for 20 g20 \text{ g} of the reactant to reduce to 5 g5 \text{ g}?

A

238.6 s

B

138.6 s

C

346.5 s

D

693.0 s

Step-by-Step Solution

For a first-order reaction, the time required is given by the integrated rate equation:

t=2.303klog[R]0[R]t = \frac{2.303}{k} \log \frac{[R]_0}{[R]}

Given data: Rate constant, k=102 s1k = 10^{-2} \text{ s}^{-1} Initial amount, [R]0=20 g[R]_0 = 20 \text{ g} Final amount, [R]=5 g[R] = 5 \text{ g}

Substituting the values into the equation: t=2.303102log(205)t = \frac{2.303}{10^{-2}} \log \left( \frac{20}{5} \right) t=2.303×102×log(4)t = 2.303 \times 10^2 \times \log(4) t=230.3×2log(2)t = 230.3 \times 2 \log(2) t=230.3×2×0.3010t = 230.3 \times 2 \times 0.3010 t=230.3×0.6020138.64 st = 230.3 \times 0.6020 \approx 138.64 \text{ s}

Therefore, the time required is approximately 138.6 s138.6 \text{ s}.

Exam Context & Concepts Covered

This question aligns with the NEET CHEMISTRY syllabus, specifically targeting concepts from Chemical Kinetics. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

CHEMISTRYChemical Kineticsreactionspecificreactionreactantreduce

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