(A) For a first-order reaction,the integrated rate equation is $k = \frac{2.303}{t} \log \frac{[A]_0}{[A]_t}$.Given: $t = 100 \ min$,$[A]_t = \frac{1}

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$k = 2.08 \times 10^{-2} \ min^{-1}, t_{1/2} = 33.3 \ min$

(A) For a first-order reaction,the integrated rate equation is $k = \frac{2.303}{t} \log \frac{[A]_0}{[A]_t}$.Given: $t = 100 \ min$,$[A]_t = \frac{1}{8} [A]_0$,so $\frac{[A]_0}{[A]_t} = 8$.Substituting the values: $k = \frac{2.303}{100} \log(8) = \frac{2.303}{100} \times 0.903 = 2.08 \times 10^{-2} \ min^{-1}$.The half-life time is calculated as $t_{1/2} = \frac{0.693}{k} = \frac{0.693}{2.08 \times 10^{-2}} \approx 33.3 \ min$.

Class 12 Chemistry Chemical Kinetics First Order reaction

Difficult

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

A
$k = 2.08 \times 10^{-2} \ min^{-1}, t_{1/2} = 33.3 \ min$
B
$k = 1.04 \times 10^{-2} \ min^{-1}, t_{1/2} = 66.6 \ min$
C
$k = 2.08 \times 10^{-2} \ min^{-1}, t_{1/2} = 16.6 \ min$
D
$k = 4.16 \times 10^{-2} \ min^{-1}, t_{1/2} = 33.3 \ min$

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Chemical Kinetics

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First Order reaction

The plot of $\log(a - x)$ versus time $t$ is a straight line,which indicates that the reaction is of ....... order.

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For the first-order reaction $2N_2O_{5(g)} \rightarrow 4NO_{2(g)} + O_{2(g)}$,which of the following statements is incorrect?

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For the reaction ${N_2}{O_{5(g)}} \to 2N{O_{2(g)}} + \frac{1}{2}{O_{2(g)}}$,the rate constant is $2.3 \times 10^{-2} \ s^{-1}$. Which of the following equations represents the variation of $[{N_2}{O_5}]$ with time?

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The half-life of a first-order reaction is $10 \ minutes$. If the initial concentration is $0.08 \ mol/L$ and at some instant the concentration is $0.01 \ mol/L$,then the time elapsed is ...... minutes.

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

Similar Questions

The plot of $\log(a - x)$ versus time $t$ is a straight line,which indicates that the reaction is of ....... order.

For the first-order reaction $2N_2O_{5(g)} \rightarrow 4NO_{2(g)} + O_{2(g)}$,which of the following statements is incorrect?

For the reaction ${N_2}{O_{5(g)}} \to 2N{O_{2(g)}} + \frac{1}{2}{O_{2(g)}}$,the rate constant is $2.3 \times 10^{-2} \ s^{-1}$. Which of the following equations represents the variation of $[{N_2}{O_5}]$ with time?

The half-life of a first-order reaction is $10 \ minutes$. If the initial concentration is $0.08 \ mol/L$ and at some instant the concentration is $0.01 \ mol/L$,then the time elapsed is ...... minutes.

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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