(A) The integrated rate equation for a first-order reaction is given by: $\ln \frac{[R]_0}{[R]} = Kt$. Converting to base $10$ logarithm: $\log \frac{

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$\log \frac{[R]_0}{[R]} \text{ vs } t \text{ (Time)}$

(A) The integrated rate equation for a first-order reaction is given by: $\ln \frac{[R]_0}{[R]} = Kt$. Converting to base $10$ logarithm: $\log \frac{[R]_0}{[R]} = \frac{Kt}{2.303}$. Comparing this with the equation of a straight line $y = mx + c$,where $y = \log \frac{[R]_0}{[R]}$ and $x = t$,the slope $m$ is equal to $\frac{K}{2.303}$. Therefore,the graph of $\log \frac{[R]_0}{[R]}$ versus $t$ gives a slope of $\frac{K}{2.303}$.

Class 12 Chemistry Chemical Kinetics First Order reaction

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For which of the following graphs of a first-order reaction will the value of the slope be $\frac{K}{2.303}$?

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A
$\log \frac{[R]_0}{[R]} \text{ vs } t \text{ (Time)}$
B
$\log \frac{[R]}{[R]_0} \text{ vs } t \text{ (Time)}$
C
$\ln \frac{[R]_0}{[R]} \text{ vs } t \text{ (Time)}$
D
$\ln \frac{[R]}{[R]_0} \text{ vs } t \text{ (Time)}$

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For a first order reaction $R \longrightarrow P$,the rate constant is $k$. If the initial concentration of $R$ is $[R_0]$,the concentration of $R$ at any time $t$ is given by the expression:

MediumKVPY 2010

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The units of rate constant for a first-order reaction are:

EasyMHT CET 2010

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For the reaction shown in the image,the half-life does not depend on the concentration of the reactant. After $10 \, \text{min}$,the volume of $N_2$ gas evolved is $20 \, \text{L}$ and after the completion of the reaction,it is $100 \, \text{L}$. Hence,the rate constant is:

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Identify True $(T)$ and False $(F)$ statements of the following for a first order reaction $R \rightarrow P$.
$(i) \ t_{1/2} \propto [R]_0^0$
$(ii) \ t_{1/2} = \frac{0.693}{k}$

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Which one of the following plots is correct for a first order reaction?

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For which of the following graphs of a first-order reaction will the value of the slope be $\frac{K}{2.303}$?

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For a first order reaction $R \longrightarrow P$,the rate constant is $k$. If the initial concentration of $R$ is $[R_0]$,the concentration of $R$ at any time $t$ is given by the expression:

The units of rate constant for a first-order reaction are:

For the reaction shown in the image,the half-life does not depend on the concentration of the reactant. After $10 \, \text{min}$,the volume of $N_2$ gas evolved is $20 \, \text{L}$ and after the completion of the reaction,it is $100 \, \text{L}$. Hence,the rate constant is:

Identify True $(T)$ and False $(F)$ statements of the following for a first order reaction $R \rightarrow P$.$(i) \ t_{1/2} \propto [R]_0^0$$(ii) \ t_{1/2} = \frac{0.693}{k}$

Which one of the following plots is correct for a first order reaction?

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Identify True $(T)$ and False $(F)$ statements of the following for a first order reaction $R \rightarrow P$.
$(i) \ t_{1/2} \propto [R]_0^0$
$(ii) \ t_{1/2} = \frac{0.693}{k}$