What is value of rate constant of a first order reaction if slope of graph between $\log _{10}…
What is value of rate constant of a first order reaction if slope of graph between $\log _{10} \frac{[\mathrm{A}]_0}{[\mathrm{~A}]_{\mathrm{t}}}$ (y axis) and time (x axis) is $1 \times 10^{-3}$ ?
$4.34 \times 10^{-3}$
$6.93 \times 10^{-3}$
$2.303 \times 10^{-3}$
$5.12 \times 10^{-3}$
Solution
$\begin{aligned} & \operatorname{In}\left[A_t\right]=\operatorname{In}\left[A_O\right]-K t \\ & \operatorname{In} \frac{\left[A_0\right]}{\left[A_t\right]}=K t \\ & \log _{10} \frac{\left[A_1\right]}{\left[A_t\right]}=\frac{K}{2.303} . t \\ & =\frac{K}{2.303}=1 \times 10^{-3} \\ & K=2.303 \times 10^{-3}\end{aligned}$