(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

For a first order reaction,the intercept of the graph between $\log \left(\frac{[A]_0}{[A]_t}\right)$ ($Y$-axis) and time ($X$-axis) is equal to

EasyMHT CET 2021

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The half-life of a first order reaction is $30 \, min$. The time required for $75 \, \%$ completion of the same reaction will be $..... \, min$

MediumKVPY 2009

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Ethylene is produced by $C_4H_8 (\text{Cyclobutane}) \xrightarrow{\text{Heat}} 2C_2H_4$. The rate constant is $2.3 \times 10^{-4} \text{ s}^{-1}$. In what time will the molar ratio of ethylene to cyclobutane in the reaction mixture attain the value $1$? ...... $\text{min}$

Medium

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For a first order reaction,the rate constant is given as $\log_{10} K = 12 - \frac{6 \times 10^3}{T}$. What will be the value of temperature if its half-life period is $6.93 \times 10^{-3} \, \text{min}$ (in $, K$)?

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Following data was obtained for the first order decomposition of $SO_2Cl_{2(g)}$ at constant volume:
$SO_2Cl_{2(g)} \to SO_{2(g)} + Cl_{2(g)}$
$S. No.$ $Time$ $(s)$ $Total$ $pressure$ $(atm)$
$1$ $0$ $0.5$
$2$ $100$ $0.6$

Calculate the rate constant.

Medium

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$S. No.$	$Time$ $(s)$	$Total$ $pressure$ $(atm)$
$1$	$0$	$0.5$
$2$	$100$	$0.6$

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For a first order reaction,the intercept of the graph between $\log \left(\frac{[A]_0}{[A]_t}\right)$ ($Y$-axis) and time ($X$-axis) is equal to

The half-life of a first order reaction is $30 \, min$. The time required for $75 \, \%$ completion of the same reaction will be $..... \, min$

Ethylene is produced by $C_4H_8 (\text{Cyclobutane}) \xrightarrow{\text{Heat}} 2C_2H_4$. The rate constant is $2.3 \times 10^{-4} \text{ s}^{-1}$. In what time will the molar ratio of ethylene to cyclobutane in the reaction mixture attain the value $1$? ...... $\text{min}$

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Following data was obtained for the first order decomposition of $SO_2Cl_{2(g)}$ at constant volume:$SO_2Cl_{2(g)} \to SO_{2(g)} + Cl_{2(g)}$$S. No.$$Time$ $(s)$$Total$ $pressure$ $(atm)$$1$$0$$0.5$$2$$100$$0.6$Calculate the rate constant.

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Following data was obtained for the first order decomposition of $SO_2Cl_{2(g)}$ at constant volume:
$SO_2Cl_{2(g)} \to SO_{2(g)} + Cl_{2(g)}$
$S. No.$ $Time$ $(s)$ $Total$ $pressure$ $(atm)$
$1$ $0$ $0.5$
$2$ $100$ $0.6$

Calculate the rate constant.