Arrhenius equation

For reaction $\ce{A -> P}$, rate constant $k=1.5\times10^3$ s$^{-1}$ at 27 °C.
If activation energy for the above reaction is 60 kJ mol$^{-1}$, then the temperature (in °C) at which rate constant, $k=4.5\times10^3$ s$^{-1}$ is ________. (Nearest integer)
Given : $\log2=0.30$, $\log3=0.48$, $R=8.3$ J K$^{-1}$ mol$^{-1}$, $\ln10=2.3$

Decomposition of a hydrocarbon follows the equation $k=\left(5.5\times10^{11}\text{ s}^{-1}\right)e^{-28000\,\mathrm K/T}$. The activation energy of reaction is ________ kJ mol$^{-1}$. (Nearest Integer)

Given : R = 8.3 J K$^{-1}$ mol$^{-1}$

Given below are two statements :

R = 8.314 J K$^{-1}$ mol$^{-1}$ and 1 cal = 4.2 J

Statement I : When Ea = 12.6 kcal/mol, the room temperature rate constant is doubled by a 10 °C increase in temperature (298 K to 308 K)

Statement II : For a first order reactions A → B, the plot of $t_{1/2}$ against $[\mathrm A]_o$ is as shown. Here $[\mathrm A]_o$ is the initial concentration of A and $t_{1/2}$ is half life of reaction.

In the light of the above statements, choose the correct answer from the options given below :

The plot of $\log k_f$ versus $1/T$ for a reversible reaction $\ce{A(g) <=> P(g)}$ is shown.

Pre-exponential factors for the forward and backward reactions are $10^{15}\,\mathrm{s^{-1}}$ and $10^{11}\,\mathrm{s^{-1}}$, respectively. If the value of $\log K$ for the reaction at 500 K is 6, the value of $|\log k_b|$ at 250 K is _____.

[$K$ = equilibrium constant of the reaction; $k_f$ = rate constant of forward reaction; $k_b$ = rate constant of backward reaction]

The rate constants for decomposition of acetaldehyde have been measured over the temperature range 700 - 1000 K. The data has been analysed by plotting $\ln k$ vs $\dfrac{10^3}T$ graph. The value of activation energy for the reaction is ______ $\mathrm{kJ\,mol^{-1}}$. (Nearest integer)

(Given : $R=8.31\ \mathrm{J\,K^{-1}mol^{-1}}$)

Catalyst A reduces the activation energy for a reaction by 10 kJ mol$^{-1}$ at 300 K. The ratio of rate constants, $\dfrac{k_{T,\text{Catalysed}}}{k_{T,\text{Uncatalysed}}}$ is $e^x$. The value of $x$ is ______. [nearest integer]

[Assume that the pre-exponential factor is same in both the cases. Given $R=8.31$ J K$^{-1}$mol$^{-1}$]

The rate constant for a first order reaction is given by the following equation :
$$\ln k=33.24-\frac{2.0\times10^4\ \mathrm K}T$$
The Activation energy for the reaction is given by ______ kJ mol$^{-1}$. (In Nearest integer)

(Given : $R=8.3$ J K$^{-1}$ mol$^{-1}$)

It has been found that for a chemical reaction with rise in temperature by 9 K the rate constant gets doubled. Assuming a reaction to be occurring at 300 K, the value of activation energy is found to be ______ kJ mol$^{-1}$. [nearest integer]

(Given $\ln10=2.3$, $R=8.3$ J K$^{-1}$ mol$^{-1}$, $\log2=0.30$)

The activation energy of one of the reactions in a biochemical process is 532611 J mol$^{-1}$. When the temperature falls from 310 K to 300 K, the change in rate constant observed is $k_{300}=x\times10^{-3}k_{310}$. The value of $x$ is ______.

[Given : ln10 = 2.3; R = 8.3 J K$^{-1}$ mol$^{-1}$]

The equation $k=\left(6.5\times10^{12}\text{s}^{-1}\right)e^{-26000\text{K}/T}$ is followed for the decomposition of compound A. The activation energy for the reaction is ______ kJ mol$^{-1}$. [nearest integer]

(Given: R = 8.314 J K$^{-1}$mol$^{-1}$)

For the reaction P → B, the values of frequency factor A and activation energy $E_A$ are $4\times10^{13}$ s$^{-1}$ and 8.3 kJ mol$^{-1}$ respectively. If the reaction is of first order, the temperature at which the rate constant is $2\times10^{-6}$ s$^{-1}$ is ______ $\times10^{-1}$ K

(Given : ln 10 = 2.3, R = 8.3 J K$^{-1}$ mol$^{-1}$, log2 = 0.30)

For a reaction, given below is the graph of ln k vs $\dfrac1T$. The activation energy for the reaction is equal to ______ cal mol$^{-1}$. (nearest integer)

(Given : R = 2 cal K$^{-1}$ mol$^{-1}$)

Consider the following reversible reaction,

$$\mathrm{A(g) + B(g) \rightleftharpoons AB(g)}.$$

The activation energy of the backward reaction exceeds that of the forward reaction by $2RT$ (in J mol$^{-1}$). If the pre-exponential factor of the forward reaction is 4 times that of the reverse reaction, the absolute value of $\Delta G^\ominus$ (in J mol$^{-1}$) for the reaction at 300 K is ____.

(Given; ln(2) = 0.7, $RT$ = 2500 J mol$^{-1}$ at 300 K and $G$ is the Gibbs energy)

In a bimolecular reaction, the steric factor P was experimentally determined to be 4.5. The correct option(s) among the following is(are)

Two reactions $R_1$ and $R_2$ have identical pre-exponential factors. Activation energy of $R_1$ exceeds that of $R_2$ by 10 kJ mol$^{-1}$. If $k_1$ and $k_2$ are rate constants for reactions $R_1$ and $R_2$ respectively at 300 K, then $\ln(k_2/k_1)$ is equal to :

(R = 8.314 J mol$^{-1}$K$^{-1}$)

The rate of a reaction A doubles on increasing the temperature from 300 to 310 K. By how much, the temperature of reaction B should be increased from 300 K so that rate doubles if activation energy of the reaction B is twice to that of reaction A.

The rate of a reaction quadruples when the temperature changes from 300 to 310 K. The activation energy of this reaction is :

(Assume activation energy and pre-exponential factor are independent of temperature; ln 2 = 0.693; R = 8.314 J mol$^{-1}$ K$^{-1}$)

According to the Arrhenius equation,

The %yield of ammonia as a function of time in the reaction
$$\ce{N2(g) + 3H2(g) <=> 2NH3(g)},\quad\Delta H<0$$
at $(P,T_1)$ is given below.

If this reaction is conducted at $(P,T_2)$, with $T_2>T_1$, the %yield of ammonia as a function of time is represented by

For the equilibrium, $\ce{A(g) <=> B(g)}$, ΔH is −40 kJ/mol. If the ratio of the activation energies of the forward ($E_f$) and reverse ($E_b$) reactions is $\dfrac23$ then :