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NEET CHEMISTRYChemical KineticsMedium

Question

A first-order reaction has a rate constant of 2.303×103 s12.303 \times 10^{-3} \text{ s}^{-1}. The time required for 40 g40 \text{ g} of this reactant to reduce to 10 g10 \text{ g} will be [Given that log102=0.3010\log_{10} 2 = 0.3010]

A

230.3 s230.3 \text{ s}

B

301 s301 \text{ s}

C

2000 s2000 \text{ s}

D

602 s602 \text{ s}

Step-by-Step Solution

For a first-order reaction, the integrated rate equation is given by: t=2.303klog[R]0[R]t = \frac{2.303}{k} \log \frac{[R]_0}{[R]} Given: Rate constant, k=2.303×103 s1k = 2.303 \times 10^{-3} \text{ s}^{-1} Initial amount, [R]0=40 g[R]_0 = 40 \text{ g} Final amount, [R]=10 g[R] = 10 \text{ g} Substituting the values into the formula: t=2.3032.303×103log(4010)t = \frac{2.303}{2.303 \times 10^{-3}} \log \left(\frac{40}{10}\right) t=103×log4t = 10^3 \times \log 4 t=1000×2log2t = 1000 \times 2 \log 2 Given log102=0.3010\log_{10} 2 = 0.3010, t=1000×2×0.3010=1000×0.6020=602 st = 1000 \times 2 \times 0.3010 = 1000 \times 0.6020 = 602 \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 Kineticsfirstorderreactionconstantrequiredreactant

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