(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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Chemical Kinetics

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First Order reaction

The time required for $60 \%$ completion of a first order reaction is $50 \ min$. The time required for $93.6 \%$ completion of the same reaction will be (in $min$)

MediumKCET 2020

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Calculate the rate constant of a first-order reaction if the concentration of the reactant decreases by $90 \%$ in $30 \ minutes$.

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Which of the following is a first order reaction?

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For the gaseous reaction $A(g) \longrightarrow B(g) + C(g) + D(g)$,starting with an initial pressure of $400 \ atm$. If the total pressure after $2 \ hr$ is $800 \ atm$,the value of the rate constant is: (consider the reaction to be $1^{st}$ order): (in $hr^{-1}$)

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$N_2O_5$ decomposes to $NO_2$ and $O_2$ and follows first order kinetics. After $50 \, min$,the pressure inside the vessel increases from $50 \, mm \, Hg$ to $87.5 \, mm \, Hg$. The pressure of the gaseous mixture after $100 \, min$ at constant temperature will be ........... $mm \, Hg$

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The time required for $60 \%$ completion of a first order reaction is $50 \ min$. The time required for $93.6 \%$ completion of the same reaction will be (in $min$)

Calculate the rate constant of a first-order reaction if the concentration of the reactant decreases by $90 \%$ in $30 \ minutes$.

Which of the following is a first order reaction?

For the gaseous reaction $A(g) \longrightarrow B(g) + C(g) + D(g)$,starting with an initial pressure of $400 \ atm$. If the total pressure after $2 \ hr$ is $800 \ atm$,the value of the rate constant is: (consider the reaction to be $1^{st}$ order): (in $hr^{-1}$)

$N_2O_5$ decomposes to $NO_2$ and $O_2$ and follows first order kinetics. After $50 \, min$,the pressure inside the vessel increases from $50 \, mm \, Hg$ to $87.5 \, mm \, Hg$. The pressure of the gaseous mixture after $100 \, min$ at constant temperature will be ........... $mm \, Hg$

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