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ChemistryNEET 2025Integrated rate equations and half-life

Chemical Kinetics

If the rate constant of a reaction is 0.03 s−10.03\ \mathrm{s^{-1}}, how much time does it take for a 7.2 mol L−17.2\ \mathrm{mol\,L^{-1}} concentration of the reactant to get reduced to 0.9 mol L−10.9\ \mathrm{mol\,L^{-1}}? (Given log⁡2=0.301\log 2 = 0.301)

  1. A.69.3 s✓
  2. B.23.1 s
  3. C.210 s
  4. D.21.0 s

Solution

A rate constant in s−1\mathrm{s^{-1}} means first order. t=2.303klog⁡[A]0[A]=2.3030.03log⁡8=2.303×3×0.3010.03≈69.3t = \frac{2.303}{k}\log\frac{[A]_0}{[A]} = \frac{2.303}{0.03}\log 8 = \frac{2.303 \times 3 \times 0.301}{0.03} \approx 69.3 s.

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