(C) For a first order reaction,the time $t$ is given by the formula: $t = \frac{2.303}{K} \log \frac{[A]_0}{[A]_t}$ Given: Initial concentration $[A]_

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(C) For a first order reaction,the time $t$ is given by the formula: $t = \frac{2.303}{K} \log \frac{[A]_0}{[A]_t}$ Given: Initial concentration $[A]_0 = 0.5 \; mol/L$ Final concentration $[A]_t = 0.05 \; mol/L$ Rate constant $K = 6 \; sec^{-1}$ Substituting the values: $t = \frac{2.303}{6} \log \frac{0.5}{0.05}$ $t = \frac{2.303}{6} \log 10$ Since $\log 10 = 1$,$t = \frac{2.303}{6} = 0.3838 \; sec \approx 0.384 \; sec$.

Class 12 Chemistry Chemical Kinetics First Order reaction

Medium

$A$ first order reaction with respect to the reactant $A$ has a rate constant of $6 \; sec^{-1}$. If we start with $[A] = 0.5 \; mol/L$,then in what time the concentration of $A$ becomes $0.05 \; mol/L$ ........... $sec$

A
$0.38$
B
$0.214$
C
$0.384$
D
$0.402$

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Class 12

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Chemical Kinetics

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First Order reaction

Identify True $(T)$ and False $(F)$ statements of the following for a first-order reaction $R \rightarrow P$.
Statement $I$: $k = \frac{1}{(t_1 - t_2)} \ln \frac{[R]_1}{[R]_2}$
Statement $II$: $k = -\frac{1}{(t_1 - t_2)} \ln \frac{[R]_2}{[R]_1}$

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$A$ radioactive substance decomposes such that after $100 \ min$,its concentration becomes $1/8$ of the original concentration. Calculate the rate constant $(k)$ and half-life time $(t_{1/2})$.

Difficult

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The half-life of a first-order reaction is $69.35 \, \text{sec}$. The value of the rate constant of the reaction is .......... $\sec^{-1}$.

MediumAIPMT 1990

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The rate constant of a first order reaction is $3 \times 10^{-6} \ s^{-1}$. If the initial concentration is $0.10 \ M$,the initial rate of reaction is:

MediumAIIMS 1999

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After how many seconds will the concentration of the reactant in a first order reaction be halved if the rate constant is $1.155 \times 10^{-3} \ s^{-1}$?

DifficultMHT CET 2008

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$A$ first order reaction with respect to the reactant $A$ has a rate constant of $6 \; sec^{-1}$. If we start with $[A] = 0.5 \; mol/L$,then in what time the concentration of $A$ becomes $0.05 \; mol/L$ ........... $sec$

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Identify True $(T)$ and False $(F)$ statements of the following for a first-order reaction $R \rightarrow P$.Statement $I$: $k = \frac{1}{(t_1 - t_2)} \ln \frac{[R]_1}{[R]_2}$Statement $II$: $k = -\frac{1}{(t_1 - t_2)} \ln \frac{[R]_2}{[R]_1}$

$A$ radioactive substance decomposes such that after $100 \ min$,its concentration becomes $1/8$ of the original concentration. Calculate the rate constant $(k)$ and half-life time $(t_{1/2})$.

The half-life of a first-order reaction is $69.35 \, \text{sec}$. The value of the rate constant of the reaction is .......... $\sec^{-1}$.

The rate constant of a first order reaction is $3 \times 10^{-6} \ s^{-1}$. If the initial concentration is $0.10 \ M$,the initial rate of reaction is:

After how many seconds will the concentration of the reactant in a first order reaction be halved if the rate constant is $1.155 \times 10^{-3} \ s^{-1}$?

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Identify True $(T)$ and False $(F)$ statements of the following for a first-order reaction $R \rightarrow P$.
Statement $I$: $k = \frac{1}{(t_1 - t_2)} \ln \frac{[R]_1}{[R]_2}$
Statement $II$: $k = -\frac{1}{(t_1 - t_2)} \ln \frac{[R]_2}{[R]_1}$