(C) For a first-order reaction,the rate constant $k$ is given by $k = \frac{2.303}{t} \log(\frac{[A]_0}{[A]_t})$.For flask $I$: $[A]_0 = 1 \ M$,$[A]_t

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(C) For a first-order reaction,the rate constant $k$ is given by $k = \frac{2.303}{t} \log(\frac{[A]_0}{[A]_t})$.For flask $I$: $[A]_0 = 1 \ M$,$[A]_t = 0.25 \ M$,$t = 8 \ hours$.$k = \frac{2.303}{8} \log(\frac{1}{0.25}) = \frac{2.303}{8} \log(4) = \frac{2.303 \times 0.602}{8} \approx 0.1733 \ h^{-1}$.For flask $II$: $[A]_0 = 0.6 \ M$,$[A]_t = 0.3 \ M$.Since $[A]_t = \frac{[A]_0}{2}$,the time taken is the half-life $t_{1/2}$.$t_{1/2} = \frac{0.693}{k} = \frac{0.693}{0.1733} \approx 4.0 \ hours$.

Class 12 Chemistry Chemical Kinetics First Order reaction

Easy

The decomposition of substance $A$ follows first-order kinetics. Flask $I$ contains $1 \ L$ of $1 \ M$ solution of $A$,and flask $II$ contains $100 \ mL$ of $0.6 \ M$ solution of $A$. After $8 \ hours$,the concentration of $A$ in flask $I$ becomes $0.25 \ M$. How many hours will it take for the concentration of $A$ in flask $II$ to become $0.3 \ M$?

A
$0.4$
B
$2.4$
C
$4.0$
D
Cannot be determined as the rate constant is not given.

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Class 12

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Chemical Kinetics

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First Order reaction

Calculate the time required for a reactant to decrease in concentration from $100 \%$ to $20 \%$,if the rate constant of the first-order reaction is $0.02303 \ hour^{-1}$. (in $hour$)

MediumMHT CET 2024

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The half-life of a first order reaction $X \to Y$ is $100 \ min$. The concentration of $X$ would be reduced to $10 \%$ of the initial concentration in .......... $min$.

Medium

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$10 \ g$ mixture of two gases $A_2$ (mol. wt. $= 20$) and $B_2$ (mol. wt. $= 30$),which decompose by first order kinetics,was taken in a vessel. The half-life of decomposition of $A_2$ and $B_2$ are $2 \ hours$ and $3 \ hours$ respectively. After $6 \ hours$,the weight of the mixture of $A_2$ and $B_2$ is found to be $2 \ g$. Find the weight of $A_2$ in the initial mixture in $g$.

Medium

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The rate constant for a first order reaction is $60 \text{ s}^{-1}$. How much time (in seconds) will it take to reduce the initial concentration of the reactant to its $1/16^{th}$ value?

EasyGUJCET 2021

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In a first-order reaction,the concentration of reactant $X$ decreases from $0.1 \, M$ to $0.005 \, M$ in $40 \, min$. What will be the rate of reaction when the concentration of $X$ is $0.01 \, M$?

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Calculate the time required for a reactant to decrease in concentration from $100 \%$ to $20 \%$,if the rate constant of the first-order reaction is $0.02303 \ hour^{-1}$. (in $hour$)

The half-life of a first order reaction $X \to Y$ is $100 \ min$. The concentration of $X$ would be reduced to $10 \%$ of the initial concentration in .......... $min$.

The rate constant for a first order reaction is $60 \text{ s}^{-1}$. How much time (in seconds) will it take to reduce the initial concentration of the reactant to its $1/16^{th}$ value?

In a first-order reaction,the concentration of reactant $X$ decreases from $0.1 \, M$ to $0.005 \, M$ in $40 \, min$. What will be the rate of reaction when the concentration of $X$ is $0.01 \, M$?

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