Calculate the rate constant of a first-order | vedclass

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Question

(A) For a first-order reaction,the rate constant $k$ is given by the formula: $k = \frac{2.303}{t} \log_{10} \frac{[A]_0}{[A]_t}$.Given that the conce

Vedclass · Accepted Answer

$7.7 	imes 10^{-2} \ minute^{-1}$

Vedclass · Answer

(A) For a first-order reaction,the rate constant $k$ is given by the formula: $k = \frac{2.303}{t} \log_{10} \frac{[A]_0}{[A]_t}$.Given that the concentration decreases by $90 \%$,the remaining concentration $[A]_t$ is $10 \%$ of the initial concentration $[A]_0$.Therefore,$[A]_t = 0.1 [A]_0$ or $\frac{[A]_0}{[A]_t} = 10$.Substituting the values $t = 30 \ minutes$ and $\frac{[A]_0}{[A]_t} = 10$ into the formula:$k = \frac{2.303}{30} \log_{10} (10)$.Since $\log_{10} (10) = 1$,we get $k = \frac{2.303}{30} \approx 0.07676 \ minute^{-1}$.Rounding to two significant figures,$k = 7.7 	imes 10^{-2} \ minute^{-1}$.

Calculate the rate constant of a first-order reaction if the concentration of the reactant decreases by $90 \%$ in $30 \ minutes$.

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