The rate constant for a first order reaction | vedclass

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Question

(C) For a first order reaction, the integrated rate equation is given by:$k = \frac{2.303}{t} \log \frac{[R]_0}{[R]}$Given: $k = 60 	ext{ s}^{-1}$ an

Vedclass · Accepted Answer

$0.0499$

Vedclass · Answer

(C) For a first order reaction, the integrated rate equation is given by:$k = \frac{2.303}{t} \log \frac{[R]_0}{[R]}$Given: $k = 60 	ext{ s}^{-1}$ and $[R] = \frac{[R]_0}{20}$, so $\frac{[R]_0}{[R]} = 20$.Substituting the values:$60 = \frac{2.303}{t} \log(20)$$t = \frac{2.303}{60} 	imes \log(20)$Since $\log(20) = \log(2 	imes 10) = \log(2) + \log(10) = 0.3010 + 1 = 1.3010$.$t = \frac{2.303 	imes 1.3010}{60}$$t = \frac{2.9962}{60} \approx 0.0499 	ext{ s}$.

The rate constant for a first order reaction is $60 \text{ s}^{-1}$. How much time will it take to reduce the concentration of the reactant to $1/20^{th}$ of its initial value (in $\text{ s}$)?

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