The rate constant for a first order reaction is . The time required to reduce 2.0 g of the reactant to 0.2 g is [2020]

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Solution

Q.
The rate constant for a first order reaction is $4.606 \times 10^{- 3}$ $s^{- 1}$ . The time required to reduce 2.0 g of the reactant to 0.2 g is [2020]

1 100 s

2 200 s

3 500 s

4 1000 s

Ans.
(3)

For a first order reaction,

$k = \frac{2.303}{t} \log \frac{{[R]}_{0}}{[R]}$

$t = \frac{2.303}{4.606 \times 10^{- 3} s^{- 1}} \log (\frac{2}{0.2}) = \frac{2.303 \times 10^{3}}{4.606} = 500$ $s$

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