(B) For a first-order reaction,the rate constant $k$ is given by $k = \frac{0.693}{t_{1/2}}$.Given $t_{1/2} = 3 \ min$,so $k = \frac{0.693}{3} = 0.231

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(B) For a first-order reaction,the rate constant $k$ is given by $k = \frac{0.693}{t_{1/2}}$.Given $t_{1/2} = 3 \ min$,so $k = \frac{0.693}{3} = 0.231 \ min^{-1}$.Let the initial concentration $[A]_0 = 100$.Since the concentration is reduced by $90 \%$,the remaining concentration $[A]_t = 100 - 90 = 10$.Using the first-order integrated rate equation: $t = \frac{2.303}{k} \log_{10} \frac{[A]_0}{[A]_t}$.$t = \frac{2.303}{0.231} \log_{10} \frac{100}{10} = \frac{2.303}{0.231} \times 1 = 9.969 \ min$.

Class 12 Chemistry Chemical Kinetics First Order reaction

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The half-life of a first-order reaction $X \longrightarrow Y + Z$ is $3 \ minutes$. What is the time required to reduce the concentration of $X$ by $90 \%$ of its initial concentration?

MHT CET 2020 All MHT CET

A
$4.12 \ minutes$
B
$9.969 \ minutes$
C
$9.105 \ minutes$
D
$12.05 \ minutes$

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Chemical Kinetics

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First Order reaction

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$A$ reaction has a half-life of $1 \, \text{min}$. The time required for $99.9 \, \%$ completion of the reaction is ......... $\text{min}$. (Round off to the nearest integer)
[Use: $\ln 2 = 0.69, \ln 10 = 2.3$]

DifficultJEE MAIN 2021

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The half-life of a first-order reaction is $6.0 \ h$. How long will it take for the concentration of the reactant to decrease from $0.4 \ M$ to $0.12 \ M$ (in $h$)?

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Calculate the half-life of the first-order reaction $C_2H_4O_{(g)} \to CH_{4(g)} + CO_{(g)}$. If the initial pressure of $C_2H_4O_{(g)}$ is $80 \ mm$ and the total pressure at the end of $20 \ minutes$ is $120 \ mm$,find the half-life in $\text{min}$.

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The ratio of the time taken to complete $60\%$ and $20\%$ of a first-order reaction $[A \rightarrow \text{product}]$ is : $(\log 2 = 0.3)$

Medium

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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:

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The half-life of a first-order reaction $X \longrightarrow Y + Z$ is $3 \ minutes$. What is the time required to reduce the concentration of $X$ by $90 \%$ of its initial concentration?

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$A$ reaction has a half-life of $1 \, \text{min}$. The time required for $99.9 \, \%$ completion of the reaction is ......... $\text{min}$. (Round off to the nearest integer)[Use: $\ln 2 = 0.69, \ln 10 = 2.3$]

The half-life of a first-order reaction is $6.0 \ h$. How long will it take for the concentration of the reactant to decrease from $0.4 \ M$ to $0.12 \ M$ (in $h$)?

Calculate the half-life of the first-order reaction $C_2H_4O_{(g)} \to CH_{4(g)} + CO_{(g)}$. If the initial pressure of $C_2H_4O_{(g)}$ is $80 \ mm$ and the total pressure at the end of $20 \ minutes$ is $120 \ mm$,find the half-life in $\text{min}$.

The ratio of the time taken to complete $60\%$ and $20\%$ of a first-order reaction $[A \rightarrow \text{product}]$ is : $(\log 2 = 0.3)$

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:

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$A$ reaction has a half-life of $1 \, \text{min}$. The time required for $99.9 \, \%$ completion of the reaction is ......... $\text{min}$. (Round off to the nearest integer)
[Use: $\ln 2 = 0.69, \ln 10 = 2.3$]