The time required for 90% completion of a certain first order reaction is 1 hour. Calculate the time required for 99.9% completion of the same reaction.

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TestHub · Accepted Answer

For a first order reaction, the rate constant $k$ is given by $k = \frac{2.303}{t} lo g (\frac{a}{a - x})$

For $90%$ completion, $t_{90%} = 1$ hour.

$k = \frac{2.303}{1} lo g (\frac{100}{100 - 90}) = 2.303 lo g 10 = 2.303 hour^{- 1}$

For $99.9%$ completion, the time required is:

$t_{99.9%} = \frac{2.303}{k} lo g (\frac{100}{100 - 99.9})$

$t_{99.9%} = \frac{2.303}{2.303} lo g (\frac{100}{0.1})$

$t_{99.9%} = lo g 1000 = 3$ hours.

Answer: $3$ hours.

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