(C) For a first-order reaction,the integrated rate equation is: $\ln [A]_t = \ln [A]_0 - Kt$ This can be rearranged as: $\ln \frac{[A]_0}{[A]_t} = Kt$

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(C) For a first-order reaction,the integrated rate equation is: $\ln [A]_t = \ln [A]_0 - Kt$ This can be rearranged as: $\ln \frac{[A]_0}{[A]_t} = Kt$ Converting to base $10$: $\log_{10} \frac{[A]_0}{[A]_t} = \frac{K}{2.303} \cdot t$ Comparing this with the equation of a straight line $y = mx$,the slope $m = \frac{K}{2.303}$. Given the slope is $1 \times 10^{-3}$,we have: $\frac{K}{2.303} = 1 \times 10^{-3}$ Therefore,$K = 2.303 \times 10^{-3}$.

Class 12 Chemistry Chemical Kinetics First Order reaction

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What is the value of the rate constant of a first-order reaction if the slope of the graph between $\log_{10} \frac{[A]_0}{[A]_t}$ ($y$-axis) and time ($x$-axis) is $1 \times 10^{-3}$?

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A
$4.34 \times 10^{-3}$
B
$6.93 \times 10^{-3}$
C
$2.303 \times 10^{-3}$
D
$5.12 \times 10^{-3}$

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For the first order reaction $A \rightarrow 2B$,$1 \ mole$ of reactant $A$ gives $0.2 \ moles$ of $B$ after $100 \ minutes$. The half-life of the reaction is $..... \ min$. [Use: $\ln 2 = 0.69, \ln 10 = 2.3$]

DifficultJEE MAIN 2021

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The unit of the specific reaction rate constant for a first-order reaction (if the concentration is expressed in molarity) is:

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For the reaction $2N_2O_5 \rightarrow 4NO_2 + O_2$,the rate constant is $3.0 \times 10^{-5} \ s^{-1}$. If the rate of reaction is $2.40 \times 10^{-5} \ mol \ L^{-1} \ s^{-1}$,calculate the concentration of $N_2O_5$ in $mol \ L^{-1}$.

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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 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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What is the value of the rate constant of a first-order reaction if the slope of the graph between $\log_{10} \frac{[A]_0}{[A]_t}$ ($y$-axis) and time ($x$-axis) is $1 \times 10^{-3}$?

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For the first order reaction $A \rightarrow 2B$,$1 \ mole$ of reactant $A$ gives $0.2 \ moles$ of $B$ after $100 \ minutes$. The half-life of the reaction is $..... \ min$. [Use: $\ln 2 = 0.69, \ln 10 = 2.3$]

The unit of the specific reaction rate constant for a first-order reaction (if the concentration is expressed in molarity) is:

For the reaction $2N_2O_5 \rightarrow 4NO_2 + O_2$,the rate constant is $3.0 \times 10^{-5} \ s^{-1}$. If the rate of reaction is $2.40 \times 10^{-5} \ mol \ L^{-1} \ s^{-1}$,calculate the concentration of $N_2O_5$ in $mol \ L^{-1}$.

$A$ 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 $(t_{1/2})$.

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