The rate equation for a first-order reaction | vedclass

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Question

(A) For a first-order reaction: $[R] = [R]_0 e^{-kt}$.Taking natural logarithm on both sides: $\ln [R] = \ln [R]_0 - kt$.Rearranging the terms: $\ln [

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$\log \frac{[R]_0}{[R]}$ vs $t$

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(A) For a first-order reaction: $[R] = [R]_0 e^{-kt}$.Taking natural logarithm on both sides: $\ln [R] = \ln [R]_0 - kt$.Rearranging the terms: $\ln [R]_0 - \ln [R] = kt$,which gives $\ln \frac{[R]_0}{[R]} = kt$.Converting to base $10$ logarithm: $2.303 \log \frac{[R]_0}{[R]} = kt$.Therefore,$\log \frac{[R]_0}{[R]} = \frac{k}{2.303} t$.Comparing this with the equation of a straight line $y = mx + c$,a plot of $\log \frac{[R]_0}{[R]}$ vs $t$ gives a straight line passing through the origin with a positive slope $m = \frac{k}{2.303}$.

The rate equation for a first-order reaction is given by $[R] = [R]_0 e^{-kt}$. $A$ straight line with a positive slope is obtained by plotting: ($[R]_0 =$ initial concentration of reactant,$[R] =$ concentration of reactant at time $t$)

Similar Questions

The rate constant of a first-order reaction is $10^{-3} \ min^{-1}$ and the initial concentration of the reactant is $0.2 \ mol \ dm^{-3}$. What percentage of the reactant will be converted into product in $200 \ min$?

Which of the following is an example of a first-order reaction?

Identify $True$ $(T)$ and $False$ $(F)$ statements of the following for a first order reaction $R \rightarrow P$.
$I. \log \frac{[R]}{[R]_0} = -\frac{kt}{2.303}$
$II. \log \frac{[R]}{[R]_0} = \frac{kt}{2.303}$

If the rate constant for a first order reaction is $k$,the time $(t)$ required for the completion of $99 \%$ of the reaction is given by

$A$ flask is filled with equal moles of $A$ and $B$. The half-lives of $A$ and $B$ are $100 \, s$ and $50 \, s$ respectively and are independent of the initial concentration. The time required for the concentration of $A$ to be four times that of $B$ is $.... \, s.$
(Given : $\ln 2 = 0.693$ )

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