The rate constant for a first order reaction is $4.606 imes 10^{-3} s^{-1}$. The time required to reduce 2.0

Question

The rate constant for a first order reaction is $4.606 	imes 10^{-3} s^{-1}$. The time required to reduce 2.0 g of the reactant to 0.2 g is :

Accepted Answer

For a first order reaction, $t = \frac{2.303}{k} \log \frac{[A]_0}{[A]_t}$. Given $k = 4.606 	imes 10^{-3} s^{-1}$, $[A]_0 = 2.0 g$, $[A]_t = 0.2 g$. $t = \frac{2.303}{4.606 	imes 10^{-3}} \log \frac{2.0}{0.2} = \frac{2.303}{4.606 	imes 10^{-3}} \log 10 = \frac{2.303}{4.606 	imes 10^{-3}} 	imes 1 = \frac{1000}{2} = 500 s$.

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