(A) For a $1^{st}$ order reaction,the integrated rate equation is $K = \frac{2.303}{t} \log \frac{[A]_0}{[A]}$.At half-life,$t = t_{\frac{1}{2}}$ and

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$t_{\frac{1}{2}} = \frac{0.693}{K}$

(A) For a $1^{st}$ order reaction,the integrated rate equation is $K = \frac{2.303}{t} \log \frac{[A]_0}{[A]}$.At half-life,$t = t_{\frac{1}{2}}$ and $[A] = \frac{[A]_0}{2}$.Substituting these values,$K = \frac{2.303}{t_{\frac{1}{2}}} \log 2$.Since $\log 2 \approx 0.3010$,we get $K = \frac{2.303 \times 0.3010}{t_{\frac{1}{2}}} = \frac{0.693}{t_{\frac{1}{2}}}$.Therefore,the relationship is $t_{\frac{1}{2}} = \frac{0.693}{K}$.

Class 12 Chemistry Chemical Kinetics First Order reaction

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The rate constant and half-life of a first-order reaction are related to each other as -

MHT CET 2016 All MHT CET

A
$t_{\frac{1}{2}} = \frac{0.693}{K}$
B
$t_{\frac{1}{2}} = 0.693 K$
C
$K = 0.693 t_{\frac{1}{2}}$
D
$K t_{\frac{1}{2}} = \frac{1}{0.693}$

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Chemical Kinetics

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First Order reaction

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MHT CET 2016 Paper All MHT CET years →

If the decomposition reaction $A_{(g)} \longrightarrow B_{(g)}$ follows first-order kinetics,then the graph of the rate of formation of $B$,denoted by $R$,against time $t$ will be:

EasyAP EAMCET 2011

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The following results were obtained during kinetic studies of the reaction $2A + B \to$ products:

Experiment $[A]$ $(mol \ L^{-1})$ $[B]$ $(mol \ L^{-1})$ Initial rate $(mol \ L^{-1} \ min^{-1})$

$I$ $0.10$ $0.20$ $6.93 \times 10^{-3}$

$II$ $0.10$ $0.25$ $6.93 \times 10^{-3}$

$III$ $0.20$ $0.30$ $1.386 \times 10^{-2}$

The time (in minutes) required to consume half of $A$ is:

Experiment	$[A]$ $(mol \ L^{-1})$	$[B]$ $(mol \ L^{-1})$	Initial rate $(mol \ L^{-1} \ min^{-1})$
$I$	$0.10$	$0.20$	$6.93 \times 10^{-3}$
$II$	$0.10$	$0.25$	$6.93 \times 10^{-3}$
$III$	$0.20$	$0.30$	$1.386 \times 10^{-2}$

DifficultJEE MAIN 2019

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For the first order reaction $A \rightarrow 2B$,$1 \ mole$ of reactant $A$ gives $0.2 \ moles$ of $B$ after $100 \ minutes$. The half-life of the reaction is $..... \ min$. [Use: $\ln 2 = 0.69, \ln 10 = 2.3$]

DifficultJEE MAIN 2021

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Which of the following graphs represents a first-order reaction?

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Identify True $(T)$ and False $(F)$ statements for the first order reaction $R \rightarrow P$ given below:
$I. \ k = \frac{1}{t} \ln \frac{[R]_0}{[R]}$
$II. \ k = \frac{1}{t} \ln \frac{[R]}{[R]_0}$

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The rate constant and half-life of a first-order reaction are related to each other as -

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If the decomposition reaction $A_{(g)} \longrightarrow B_{(g)}$ follows first-order kinetics,then the graph of the rate of formation of $B$,denoted by $R$,against time $t$ will be:

For the first order reaction $A \rightarrow 2B$,$1 \ mole$ of reactant $A$ gives $0.2 \ moles$ of $B$ after $100 \ minutes$. The half-life of the reaction is $..... \ min$. [Use: $\ln 2 = 0.69, \ln 10 = 2.3$]

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Identify True $(T)$ and False $(F)$ statements for the first order reaction $R \rightarrow P$ given below:
$I. \ k = \frac{1}{t} \ln \frac{[R]_0}{[R]}$
$II. \ k = \frac{1}{t} \ln \frac{[R]}{[R]_0}$