The rate constant for a first order reaction is 4.606 × 1 0 − 3 s − 1 . Calculate the time required to reduce 2.0 g of the reactant to 0.2 g .

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For a first order reaction, the time required is given by

$t = \frac{2.303}{k} lo g \frac{[ A ] _{0}}{[ A ]}$

Given:
$k = 4.606 \times 1 0^{- 3} s^{- 1}$
$[A]_{0} = 2.0 g$
$[A] = 0.2 g$

Substituting the values:

$t = \frac{2.303}{4.606 \times 1 0 ^{- 3}} lo g \frac{2.0}{0.2}$

$t = \frac{1}{2 \times 1 0 ^{- 3}} lo g 10$

$t = \frac{1000}{2} \times 1 = 500 s$

Answer: $500$ s

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