Difficult
$A \rightarrow B$. The molecule $A$ changes into its isomeric form $B$ following first-order kinetics at a temperature of $1000 \ K$. If the energy barrier with respect to reactant energy for such isomeric transformation is $191.48 \ kJ \ mol^{-1}$ and the frequency factor is $10^{20} \ s^{-1}$,the time required for $50 \%$ of molecules of $A$ to become $B$ is $..............$ picoseconds (nearest integer). $[R = 8.314 \ J \ K^{-1} \ mol^{-1}]$
- A$23$
- B$65$
- C$70$
- D$69$
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Similar Questions
For the following two reactions,which statement is true?
Difficult
View SolutionThe decomposition of formic acid on a gold surface follows first-order kinetics. If the rate constant at $300 \ K$ is $1.0 \times 10^{-3} \ s^{-1}$ and the activation energy $E_a = 11.488 \ kJ \ mol^{-1}$,the rate constant at $200 \ K$ is ............ $\times 10^{-5} \ s^{-1}$.
(Round off to the Nearest Integer).
(Given: $R = 8.314 \ J \ mol^{-1} K^{-1}$)
(Round off to the Nearest Integer).
(Given: $R = 8.314 \ J \ mol^{-1} K^{-1}$)
DifficultJEE MAIN 2021
View SolutionIf for two reactions $E_{a_1} > E_{a_2}$ and $\mu_1$ and $\mu_2$ are their respective temperature coefficients,then which of the following is correct?
Medium
View Solution$A$ reaction takes place in three steps with individual rate constant and activation energy,
Step Rate constant and Activation energy $Step \ 1$ $k_1, E_{a_1} = 180 \ kJ \ mol^{-1}$ $Step \ 2$ $k_2, E_{a_2} = 80 \ kJ \ mol^{-1}$ $Step \ 3$ $k_3, E_{a_3} = 50 \ kJ \ mol^{-1}$
Overall rate constant,$k = (k_1 k_2 / k_3)^{2/3}$. The overall activation energy of the reaction will be ........ $kJ \ mol^{-1}$.
| Step | Rate constant and Activation energy |
| $Step \ 1$ | $k_1, E_{a_1} = 180 \ kJ \ mol^{-1}$ |
| $Step \ 2$ | $k_2, E_{a_2} = 80 \ kJ \ mol^{-1}$ |
| $Step \ 3$ | $k_3, E_{a_3} = 50 \ kJ \ mol^{-1}$ |
Overall rate constant,$k = (k_1 k_2 / k_3)^{2/3}$. The overall activation energy of the reaction will be ........ $kJ \ mol^{-1}$.
Difficult
View SolutionThe first order rate constant for the decomposition of $CaCO_3$ at $700 \ K$ is $6.36 \times 10^{-3} \ s^{-1}$ and activation energy is $209 \ kJ \ mol^{-1}$. Its rate constant (in $s^{-1}$) at $500 \ K$ is $x \times 10^{-6}$. The value of $x$ is ..... (Nearest integer)
Given $R=8.31 \ J \ K^{-1} \ mol^{-1} ; \log(6.36 \times 10^{-3})=-2.19 ; [10^{-4.79}=1.62 \times 10^{-5}]$
Given $R=8.31 \ J \ K^{-1} \ mol^{-1} ; \log(6.36 \times 10^{-3})=-2.19 ; [10^{-4.79}=1.62 \times 10^{-5}]$
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