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Chemical Kinetics question

2025 · Q94
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Chemical Kinetics question

2025 · Q94

NEETChemistryChemical KineticsMCQ+4 / −1

If the rate constant of a reaction is 0.03 s−10.03 \mathrm{~s}^{-1}0.03 s−1, how much time does it take for 7.2 mol L−17.2 \mathrm{~mol} \mathrm{~L}^{-1}7.2 mol L−1 concentration of the reactant to get reduced to 0.9 mol L−10.9 \mathrm{~mol} \mathrm{~L}^{-1}0.9 mol L−1 ? (Given: log⁡2=0.301\log 2=0.301log2=0.301 )

  1. A
    210 s
  2. B
    21.0 s
  3. C
    69.3 s
  4. D
    23.1 s
View written solutionFree

Correct answer: C

To determine how long it takes for the concentration of a reactant to decrease from 7.2 mol L$^{-1}$ to 0.9 mol L$^{-1}$, we use the formula for the first-order reaction:

$ t = \frac{2.303}{k} \log \frac{a}{a-x} $

Where:

$ k = 0.03 \, \text{s}^{-1} $ is the rate constant.

$ a = 7.2 \, \text{mol L}^{-1} $ is the initial concentration.

$ a-x = 0.9 \, \text{mol L}^{-1} $ is the final concentration.

Plug these values into the equation:

$ \begin{aligned} t & = \frac{2.303}{0.03} \log \frac{7.2}{0.9} \\ & = \frac{2.303}{0.03} \log 8 \\ & = \frac{2.303}{0.03} \times 3 \times \log 2 \\ & = \frac{2.303}{0.03} \times 3 \times 0.301 \\ & = 69.3 \, \text{s} \end{aligned} $

Therefore, it takes 69.3 seconds for the concentration to decrease from 7.2 mol L$^{-1}$ to 0.9 mol L$^{-1}$.

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