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(D) The given rate constant $k = 2 	imes 10^{-2} \ s^{-1}$ indicates a first-order reaction. The integrated rate equation for a first-order reaction

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$0.868$

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(D) The given rate constant $k = 2 	imes 10^{-2} \ s^{-1}$ indicates a first-order reaction. The integrated rate equation for a first-order reaction is $\ln \frac{[A]_0}{[A]_t} = kt$,which can be written as $2.303 \log \frac{[A]_0}{[A]_t} = kt$. Given $[A]_0 = 1.0 \ mol \ dm^{-3}$,$t = 100 \ s$,and $k = 2 	imes 10^{-2} \ s^{-1}$. Substituting the values: $\log \frac{1}{[A]_t} = \frac{kt}{2.303} = \frac{2 	imes 10^{-2} 	imes 100}{2.303} = \frac{2}{2.303} \approx 0.868$.

For a reaction $A \rightarrow$ product,the rate constant is $2 \times 10^{-2} \ s^{-1}$. The initial concentration of $A$ is $1.0 \ mol \ dm^{-3}$. What is the value of $\log \frac{1}{[A]_{t}}$ after $100 \ s$?

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