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For the thermal decomposition of \( \mathrm{N_2O_5} \, (g) \) at constant volume, the following table can be formed, for the reaction mentioned below.
\( 2\mathrm{N_2O_5}(g) \rightarrow 2\mathrm{N_2O_4}(g) + \mathrm{O_2}(g) \)

\( x = \) ________ \( \times 10^{-3} \) atm [nearest integer]
Given: Rate constant for the reaction is \( 4.606 \times 10^{-2} \, \text{s}^{-1} \).

Which of the following statement is not true for radioactive decay?

In a reaction \( \mathrm{A} + \mathrm{B} \rightarrow \mathrm{C} \), initial concentrations of \( \mathrm{A} \) and \( \mathrm{B} \) are related as \( [\mathrm{A}]_{0} = 8[\mathrm{B}]_{0} \). The half lives of \( \mathrm{A} \) and \( \mathrm{B} \) are \( 10 \, \text{min} \) and \( 40 \, \text{min} \), respectively. If they start to disappear at the same time, both following first order kinetics, after how much time will the concentration of both the reactants be same?

\( \mathrm{A \rightarrow B} \)
The molecule A changes into its isomeric form B by following a first order kinetics at a temperature of \( 1000 \,\text{K} \). If the energy barrier with respect to reactant energy for such isomeric transformation is \( 191.48 \,\text{kJ mol}^{-1} \) and the frequency factor is \( 10^{20} \), the time required for \( 50\% \) molecules of A to become B is __________ picoseconds (nearest integer). \([R = 8.314 \,\text{J K}^{-1} \text{ mol}^{-1}]\)

Consider the following statements related to temperature dependence of rate constants. Identify the correct statements.
(A) The Arrhenius equation holds true only for an elementary homogenous reaction.
(B) The unit of \( A \) is same as that of \( k \) in Arrhenius equation.
(C) At a given temperature, a low activation energy means a fast reaction.
(D) \( A \) and \( E_a \) as used in Arrhenius equation depend on temperature.
(E) When \( E_a \>>> RT \), \( A \) and \( E_a \) become interdependent.
Choose the correct answer from the options given below:

Consider a complex reaction taking place in three steps with rate constants \( k_1 \), \( k_2 \) and \( k_3 \) respectively. The overall rate constant \( k \) is given by the expression \(\displaystyle k = \sqrt{\frac{k_1 k_3}{k_2}} \). If the activation energies of the three steps are \( 60 \), \( 30 \) and \( 10 \) \( \text{kJ mol}^{-1} \) respectively, then the overall energy of activation in \( \text{kJ mol}^{-1} \) is ________. (Nearest integer)

For a given reaction \( R \rightarrow P \), \( t_{1/2} \) is related to \( [A]_{0} \) as given in table. [Given : \( \log 2 = 0.30 \)]
Which of the following is true?

For the reaction \( \text{A} \rightarrow \text{B} \) the following graph was obtained. The time required (in seconds) for the concentration of \( \text{A} \) to reduce to \( 2.5 \, \text{g L}^{-1} \) (if the initial concentration of \( \text{A} \) was \( 50 \, \text{g L}^{-1} \)) is ________. (Nearest integer)
Given: \( \log 2 = 0.3010 \).

A person’s wound was exposed to some bacteria and then bacterial growth started to happen at the same place. The wound was later treated with some antibacterial medicine and the rate of bacterial decay(\( r \)) was found to be proportional with the square of the existing number of bacteria at any instance. Which of the following set of graphs correctly represents the ‘before’ and ‘after’ situation of the application of the medicine?
[Given: \( N = \) No. of bacteria, \( t = \) time, bacterial growth follows \( 1^{\text{st}} \) order kinetics.]

Consider the given figure and choose the correct option:

Reactant \( A \) converts to product \( D \) through the given mechanism (with the net evolution of heat):
\( A \rightarrow B \) slow; \( \Delta H = +\text{ve} \)
\( B \rightarrow C \) fast; \( \Delta H = -\text{ve} \)
\( C \rightarrow D \) fast; \( \Delta H = -\text{ve} \)
Which of the following represents the above reaction mechanism?

The reaction $\text{A}_2 + \text{B}_2 \rightarrow 2\text{AB}$ follows the mechanism

$\text{A}_2 \overset{k_1}{\underset{k_{-1}}{\rightleftharpoons}} \text{A} + \text{A} \quad \text{(fast)}$

$\text{A} + \text{B}_2 \overset{k_2}{\longrightarrow} \text{AB} + \text{B} \quad \text{(slow)}$

$\text{A} + \text{B} \rightarrow \text{AB} \quad \text{(fast)}$

The overall order of the reaction is :

Consider the following plots of log of rate constant \( k \) \( (\log k) \) vs \( \frac{1}{T} \) for three different reactions.
The correct order of activation energies of these reactions is:

Rate law for a reaction between A and B is given by \( r = k[A]^n[B]^m \) If concentration of A is doubled and concentration of B is halved from their initial value, the ratio of new rate of reaction to the initial rate of reaction \( \left( \frac{r_2}{r_1} \right) \) is:

Drug \( X \) becomes ineffective after \( 50\% \) decomposition. The original concentration of drug in a bottle was \( 16 \, \text{mg/mL} \) which becomes \( 4 \, \text{mg/mL} \) in \( 12 \) months. The expiry time of the drug in months is ________.
Assume that the decomposition of the drug follows first order kinetics.

Reaction \( \mathrm{A(g) \rightarrow 2B(g) + C(g)} \) is a first order reaction. It was started with pure A

Which of the following option is incorrect?

Half life of zero order reaction \( A \rightarrow \) product is \( 1 \) hour, when initial concentration of reactant is \( 2.0 \, mol \, L^{-1} \). The time required to decrease concentration of \( A \) from \( 0.50 \) to \( 0.25 \, mol \, L^{-1} \) is:

In a first order decomposition reaction, the time taken for the decomposition of reactant to one fourth and one eighth of its initial concentration are \( t_1 \) and \( t_2 \) (\( \text{s} \)), respectively. The ratio \( \frac{t_1}{t_2} \) will be:

Which of the following graphs most appropriately represents a zero order reaction?

For \( \mathrm{A_2 + B_2 \rightleftharpoons
2AB} \)
\( E_a \) for forward and backward reaction are \( 180 \) and \( 200 \ \mathrm{kJ\,mol^{-1}} \) respectively
If catalyst lowers \( E_a \) for both reaction by \( 100 \ \mathrm{kJ\,mol^{-1}} \). Which of the following statement is correct?

For the reaction \( A \rightarrow \) products.

The concentration of \( A \) at \( 10 \) minutes is ________ \( \times 10^{-3} \, \text{mol L}^{-1} \) (nearest integer)

For bacterial growth in a cell culture, growth law is very similar to the law of radioactive decay. Which of the following graphs is most suitable to represent bacterial colony growth?
Where \( N \) - Number of bacteria at any time, \( N_{0} \) – Initial number of Bacteria.

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JEE Main 2025 22nd Jan Evening Shift

Consider the given figure and choose the correct option: