(A) For a first-order reaction,the rate constant is given by $k_1 = \frac{0.693}{t_{1/2}}$. Given $t_{1/2} = 40 \ s$,so $k_1 = \frac{0.693}{40} \ s^{-

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(A) For a first-order reaction,the rate constant is given by $k_1 = \frac{0.693}{t_{1/2}}$. Given $t_{1/2} = 40 \ s$,so $k_1 = \frac{0.693}{40} \ s^{-1}$.For a zero-order reaction,the rate constant is given by $k_0 = \frac{[A]_0}{2t_{1/2}}$. Given $[A]_0 = 1.386 \ mol \ m^{-3}$ and $t_{1/2} = 20 \ s$,so $k_0 = \frac{1.386}{2 \times 20} = \frac{1.386}{40} \ mol \ m^{-3} \ s^{-1}$.The ratio $\frac{k_1}{k_0} = \frac{0.693 / 40}{1.386 / 40} = \frac{0.693}{1.386} = 0.5 \ m^3 \ mol^{-1}$.

Class 12 Chemistry Chemical Kinetics Mix Examples-Chemical Kinetics

Medium

Under identical reaction conditions,the concentration of a substance is $1.386 \ mol \ m^{-3}$. It is halved in $40 \ s$ and $20 \ s$ by first-order and zero-order kinetics,respectively. The ratio of the rate constants for the first-order $(k_1)$ and zero-order $(k_0)$ reactions,$\left( \frac{k_1}{k_0} \right)$,is ............ $m^3 \ mol^{-1}$.

A
$0.5$
B
$1.0$
C
$1.5$
D
$2.0$

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Chemical Kinetics

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Mix Examples-Chemical Kinetics

The given graph is a representation of kinetics of a reaction. The $y$ and $x$ axes for zero and first order reactions,respectively are

MediumNEET 2022

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$t_{100\%}$ is the time required for the $100\%$ completion of the reaction, while $t_{1/2}$ is the time required for $50\%$ of the reaction to be completed. Which of the following options correctly represents the relation between $t_{100\%}$ and $t_{1/2}$ for zero and first-order reactions, respectively?

MediumJEE MAIN 2026

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Fill in the blanks:
$(1)$ The time required to complete $99.9\%$ of a first-order reaction is ............ times the ${t_{1/2}}$.
$(2)$ The reaction in which the rate is given by $-\frac{d[R]}{dt} = k$ has an order of reaction equal to ........
$(3)$ For the reaction $[R] = [R]_0 e^{-kt}$,the order is .......

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The consecutive reaction $X$ $\longrightarrow Y$ $\longrightarrow Z$ takes place in a closed container. Initially,the container has $A_{0}$ moles of $X$ (and no $Y$ and $Z$). The plot of total moles of the constituents in the container as a function of time will be:

DifficultKVPY 2017

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Half-lives of a first order and a zero order reaction are same. Then the ratio of the initial rates of first order reaction to that of the zero order reaction is

MediumAIIMS 2014

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The given graph is a representation of kinetics of a reaction. The $y$ and $x$ axes for zero and first order reactions,respectively are

The consecutive reaction $X$ $\longrightarrow Y$ $\longrightarrow Z$ takes place in a closed container. Initially,the container has $A_{0}$ moles of $X$ (and no $Y$ and $Z$). The plot of total moles of the constituents in the container as a function of time will be:

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