For a first order reaction ${A(g) \to 2B(g) + C(g)}$ at constant volume and $300\, K$, the total pressure at the beginning $(t = 0)$ and at time $t$ are $P_0$ and $P_t$, respectively. Initially, only $A$ is present with concentration $[A]0$, and $t_{1/3}$ is the time required for the partial pressure of $A$ to reach $1/3^{rd}$ of its initial value. The correct option(s) is (are)
(Assume that all these gases behave as ideal gases)
The Correct Option is D
Solution and Explanation
$P_0 + 2P = P_t$
$K = \frac{1}{t} In \frac{P_{0}}{P_{0} - P} = \frac{1}{t} In \frac{P_{0}}{P_{0} - P} = \frac{1}{t} In \frac{P_{0}}{P_{0} - \frac{\left(P_{t} - P_{0}\right)}{2}}$
$ K = \frac{1}{t} In \frac{2P_{0}}{3P_{0} - P_{t}} \Rightarrow -Kt + In 2P_{0} = In \left(3P_{0} - P_{t}\right) $ and $t_{1/3} = \frac{1}{K} In \frac{P_{0}}{P_{0}/3}= \frac{1}{K} In 3 $ = constant
Rate constant does not depends on concentration
Top Questions on Chemical Kinetics
- If the rate constant of a reaction is 0.03 s$^{-1}$, how much time does it take for a 7.2 mol L$^{-1}$ concentration of the reactant to get reduced to 0.9 mol L$^{-1}$?
(Given: log 2 = 0.301)- NEET (UG) - 2025
- Chemistry
- Chemical Kinetics
- State a condition under which a bimolecular reaction is kinetically first-order reaction. Give an example. For which type of reactions, do order and molecularity have the same value?
- CBSE CLASS XII - 2025
- Chemistry
- Chemical Kinetics
- A certain reaction is 50 complete in 20 minutes at 300 K and the same reaction is 50 complete in 5 minutes at 350 K. Calculate the activation energy if it is a first order reaction.
Given: \[ R = 8.314 \, \text{J K}^{-1} \, \text{mol}^{-1}, \quad \log 4 = 0.602 \]- CBSE CLASS XII - 2025
- Chemistry
- Chemical Kinetics
- The reaction between H$_2$ (g) and I$_2$ (g) was carried out in a sealed isothermal chamber. The rate law for the reaction was found to be: \[ \text{Rate} = k[\text{H}_2][\text{I}_2] \] If 1 mole of H$_2$ (g) was added to the reaction chamber and the temperature was kept constant, then predict the change in rate of the reaction and the rate constant.
- CBSE CLASS XII - 2025
- Chemistry
- Chemical Kinetics
In the given graph, \( E_a \) for the reverse reaction will be
- KCET - 2025
- Chemistry
- Chemical Kinetics
Questions Asked in JEE Advanced exam
Let $ y(x) $ be the solution of the differential equation $$ x^2 \frac{dy}{dx} + xy = x^2 + y^2, \quad x > \frac{1}{e}, $$ satisfying $ y(1) = 0 $. Then the value of $ 2 \cdot \frac{(y(e))^2}{y(e^2)} $ is ________.
- JEE Advanced - 2025
- Differential equations
- Let $ a_0, a_1, ..., a_{23} $ be real numbers such that $$ \left(1 + \frac{2}{5}x \right)^{23} = \sum_{i=0}^{23} a_i x^i $$ for every real number $ x $. Let $ a_r $ be the largest among the numbers $ a_j $ for $ 0 \leq j \leq 23 $. Then the value of $ r $ is ________.
- JEE Advanced - 2025
- binomial expansion formula
The left and right compartments of a thermally isolated container of length $L$ are separated by a thermally conducting, movable piston of area $A$. The left and right compartments are filled with $\frac{3}{2}$ and 1 moles of an ideal gas, respectively. In the left compartment the piston is attached by a spring with spring constant $k$ and natural length $\frac{2L}{5}$. In thermodynamic equilibrium, the piston is at a distance $\frac{L}{2}$ from the left and right edges of the container as shown in the figure. Under the above conditions, if the pressure in the right compartment is $P = \frac{kL}{A} \alpha$, then the value of $\alpha$ is ____
- JEE Advanced - 2025
- Thermodynamics
- The total number of real solutions of the equation $$ \theta = \tan^{-1}(2 \tan \theta) - \frac{1}{2} \sin^{-1} \left( \frac{6 \tan \theta}{9 + \tan^2 \theta} \right) $$ is
(Here, the inverse trigonometric functions $ \sin^{-1} x $ and $ \tan^{-1} x $ assume values in $[-\frac{\pi}{2}, \frac{\pi}{2}]$ and $(-\frac{\pi}{2}, \frac{\pi}{2})$, respectively.)- JEE Advanced - 2025
- Inverse Trigonometric Functions
- Let $$ \alpha = \frac{1}{\sin 60^\circ \sin 61^\circ} + \frac{1}{\sin 62^\circ \sin 63^\circ} + \cdots + \frac{1}{\sin 118^\circ \sin 119^\circ}. $$ Then the value of $$ \left( \frac{\csc 1^\circ}{\alpha} \right)^2 $$ is \rule{1cm}{0.15mm}.
- JEE Advanced - 2025
- Some Applications of Trigonometry
Concepts Used:
Chemical Kinetics
Chemical kinetics is the description of the rate of a chemical reaction. This is the rate at which the reactants are transformed into products. This may take place by abiotic or by biological systems, such as microbial metabolism.
Rate of a Chemical Reaction:
The speed of a reaction or the rate of a reaction can be defined as the change in concentration of a reactant or product in unit time. To be more specific, it can be expressed in terms of: (i) the rate of decrease in the concentration of any one of the reactants, or (ii) the rate of increase in concentration of any one of the products. Consider a hypothetical reaction, assuming that the volume of the system remains constant. R → P
Read More: Chemical Kinetics MCQ
Factors Affecting The Reaction Rate:
- The concentration of Reactants - According to collision theory, which is discussed later, reactant molecules collide with each other to form products.
- Nature of the Reactants - The reaction rate also depends on the types of substances that are reacting.
- Physical State of Reactants - The physical state of a reactant whether it is solid, liquid, or gas can greatly affect the rate of change.
- Surface Area of Reactants - When two or more reactants are in the same phase of fluid, their particles collide more often than when either or both are in the solid phase or when they are in a heterogeneous mixture. In a heterogeneous medium, the collision between the particles occurs at an interface between phases. Compared to the homogeneous case, the number of collisions between reactants per unit time is significantly reduced, and so is the reaction rate.
- Temperature - If the temperature is increased, the number of collisions between reactant molecules per second. Increases, thereby increasing the rate of the reaction.
- Effect Of Solvent - The nature of the solvent also depends on the reaction rate of the solute particles.
- Catalyst - Catalysts alter the rate of the reaction by changing the reaction mechanism.