If the rate constant of a reaction is , how much time does it take for concentration of the reactant to get reduced to ? (Given: )
- A210 s
- B21.0 s
- C69.3 s
- D23.1 s
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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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