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NEET CHEMISTRYChemical KineticsMedium

Question

What is the rate constant for a reaction if the time taken by the first-order decomposition of SO2Cl2\text{SO}_2\text{Cl}_2 to decompose to 40%40\% is 560 seconds560 \text{ seconds}? [Given: log2.5=0.3979\log 2.5 = 0.3979]

A

2.726×105 min12.726 \times 10^{-5} \text{ min}^{-1}

B

2.276×105 min12.276 \times 10^{-5} \text{ min}^{-1}

C

2.216×105 min12.216 \times 10^{-5} \text{ min}^{-1}

D

None of the above

Step-by-Step Solution

For a first-order reaction, the integrated rate equation is given by: k=2.303tlog[R]0[R]k = \frac{2.303}{t} \log \frac{[R]_0}{[R]} Given: The substance decomposes to 40%40\%, meaning the remaining concentration is [R]=40%[R] = 40\% of the initial concentration [R]0[R]_0. So, [R]0[R]=10040=2.5\frac{[R]_0}{[R]} = \frac{100}{40} = 2.5 Time, t=560 st = 560 \text{ s} Substituting the values into the rate equation: k=2.303560log(2.5)k = \frac{2.303}{560} \log(2.5) Given log2.5=0.3979\log 2.5 = 0.3979, k=2.303×0.3979560 s1=0.91636560 s1=1.636×103 s1k = \frac{2.303 \times 0.3979}{560} \text{ s}^{-1} = \frac{0.91636}{560} \text{ s}^{-1} = 1.636 \times 10^{-3} \text{ s}^{-1} To find the rate constant in min1\text{min}^{-1}, we multiply by 60 s/min60 \text{ s/min}: k=1.636×103 s1×60 s/min=0.09816 min1=9.816×102 min1k = 1.636 \times 10^{-3} \text{ s}^{-1} \times 60 \text{ s/min} = 0.09816 \text{ min}^{-1} = 9.816 \times 10^{-2} \text{ min}^{-1} Since none of the options match the correct calculated value, 'None of the above' is the correct choice.

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 Kineticsconstantreactionfirstorderdecompositiontextsotextcl

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