What is the value of the rate constant of a f | vedclass

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(C) For a first-order reaction,the integrated rate equation is: $\ln [A]_t = \ln [A]_0 - Kt$ This can be rearranged as: $\ln \frac{[A]_0}{[A]_t} = Kt$

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$2.303 	imes 10^{-3}$

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(C) For a first-order reaction,the integrated rate equation is: $\ln [A]_t = \ln [A]_0 - Kt$ This can be rearranged as: $\ln \frac{[A]_0}{[A]_t} = Kt$ Converting to base $10$: $\log_{10} \frac{[A]_0}{[A]_t} = \frac{K}{2.303} \cdot t$ Comparing this with the equation of a straight line $y = mx$,the slope $m = \frac{K}{2.303}$. Given the slope is $1 	imes 10^{-3}$,we have: $\frac{K}{2.303} = 1 	imes 10^{-3}$ Therefore,$K = 2.303 	imes 10^{-3}$.

What is the value of the rate constant of a first-order reaction if the slope of the graph between $\log_{10} \frac{[A]_0}{[A]_t}$ ($y$-axis) and time ($x$-axis) is $1 \times 10^{-3}$?

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