Question

The rate constant of a first order reaction is 6.9×10^-3 s^-1. How much time will it take to reduce the initial concentration to it 1/8 th value?

Answer 1

Answer on Question #72441 – Chemistry – Other

Task:

The rate constant of a first order reaction is $6.9 \times 10^{-3} \, \text{s}^{-1}$. How much time will it take to reduce the initial concentration to it $1/8^{\text{th}}$ value?

Solution:

Order of reaction = first

Rate constant $k = 6.9 \times 10^{-3} \, \text{s}^{-1}$

If initial concentration $[C]_0 = x$

Then final concentration $[C] = x / 8$

Use the formula of first order reaction:

$$t = \frac{2.303}{k} * \log \frac{[C]_o}{[C]};$$ $$t = \frac{2.303}{6.9 \times 10^{-3}} * \log \frac{x}{x / 8} = 333.768 * \log(8) = 301.42 \, \text{s} \approx 5 \, \text{min}$$

Answer: $301.42 \, \text{s} = 5 \, \text{min}$

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