Question:
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)
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)
Updated On: June 02, 2025
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The Correct Option is D
Solution and Explanation
$\begin{matrix}&A&\to&2B&+&C\\ t=0&P_{0}&&-&&-\\ t=t&P_{0}-P&&2P&&P\end{matrix}$
$P_0 + 2P = P_t$
$K = \frac{1}{t} In \frac{P_{0}}{P_{0} - P} = \frac{1}{t} In \frac{P_{0}}{P_{0} - P} = \frac{1}{t} In \frac{P_{0}}{P_{0} - \frac{\left(P_{t} - P_{0}\right)}{2}}$
$ 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
$P_0 + 2P = P_t$
$K = \frac{1}{t} In \frac{P_{0}}{P_{0} - P} = \frac{1}{t} In \frac{P_{0}}{P_{0} - P} = \frac{1}{t} In \frac{P_{0}}{P_{0} - \frac{\left(P_{t} - P_{0}\right)}{2}}$
$ 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
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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.