Problem 89 - A Complete Resource Book in Chemistry for JEE Main

Question

The rate equation for a chemical reaction is Rate of reaction \(=[\mathrm{X}][\mathrm{Y}]\) Consider the following statements in this regard (1) The order of reaction is one (2) The molecularity of reaction is two (3) The rate constant depends upon temperature Of these statements (a) 1 and 3 are correct (b) 1 and 2 are correct (c) 2 and 3 are correct (d) 1,2 and 3 are correct

Step-by-Step Solution

Answer

Option (c) 2 and 3 are correct.

Step 1: Understanding the Rate Equation

The given rate equation for the reaction is \( \text{Rate} = [\mathrm{X}][\mathrm{Y}] \). This means the rate of reaction depends on the concentration of X and Y.

Step 2: Analyzing the Order of Reaction

The order of the reaction is the sum of the powers of concentration terms in the rate equation. Here, the order is \(1 (X) + 1 (Y) = 2\).

Step 3: Examining the Molecularity of Reaction

Molecularity refers to the number of molecules participating in an elementary reaction. In this case, two molecules (X and Y) participate, which makes the molecularity of the reaction two.

Step 4: Understanding the Rate Constant Dependency

The rate constant \(k\) is a parameter independent of concentrations but dependent on temperature according to the Arrhenius equation. Hence, the rate constant depends upon temperature.

Step 5: Evaluating the Statements

Evaluate the given statements: 1) is incorrect as the order of reaction is 2, not 1. 2) is correct as the molecularity is two. 3) is correct because the rate constant depends on temperature.

Key Concepts

Rate Equation

In chemical kinetics, the rate equation is a fundamental concept that describes how the rate of a chemical reaction is related to the concentration of the reactants. For a reaction where the rate equation is given by \[ \text{Rate} = [\mathrm{X}][\mathrm{Y}] \]This expression indicates that the rate of the reaction is directly proportional to the concentration of reactant X and reactant Y. Each concentration term is raised to the power of one, meaning the effect on the rate is linear for each reactant.
It's crucial to understand that the rate equation is empirical, derived from experimental data, and not necessarily related to the stoichiometric equation of the reaction. The rate equation provides invaluable insights into the kinetics of the reaction and helps in determining the reaction conditions for desired results.

Order of Reaction

The order of reaction is a key concept that tells us how the concentration of reactants affects the rate of the reaction. It's calculated by summing the exponents of the concentration terms in the rate equation. For our given equation, \[ \text{Rate} = [\mathrm{X}][\mathrm{Y}] \]We find that the order of the reaction is \[ 1 (\text{for } [\mathrm{X}]) + 1 (\text{for } [\mathrm{Y}]) = 2 \]Thus, the reaction is second-order.
An important thing to remember about the order of reaction is that it may or may not coincide with the molecularity, and it provides information about the overall number of species affecting the rate in the rate-determining step of a reaction. Understanding the order is essential for calculating the rate constant and predicting how changes in concentration will affect reaction speed.

Molecularity

Molecularity refers to the number of reacting species (molecules, atoms, or ions) that participate in a single elementary step of a reaction. For the reaction described by\[ \text{Rate} = [\mathrm{X}][\mathrm{Y}] \],Two molecules are involved: X and Y. This implies that the molecularity of this elementary reaction is two, or it is a bimolecular reaction. Remember:

• Molecularity is applicable only to elementary reactions, which are steps within a complex reaction.
• It's always a whole number and cannot be zero, a fraction, or a negative number.

Molecularity provides insight into the reaction mechanism at a microscopic level and is crucial in understanding the dynamics of reactions.

Rate Constant Dependency

The rate constant, often denoted by \( k \), plays a critical role in defining the speed of a reaction. Importantly, \( k \) is not influenced by the concentrations of reactants; instead, it is dependent on temperature. According to the Arrhenius equation:\[ k = A e^{-\frac{E_a}{RT}} \]where \( A \) is the frequency factor, \( E_a \) is the activation energy, \( R \) is the gas constant, and \( T \) is the temperature in Kelvin. This equation shows that as the temperature increases, the rate constant typically increases, speeding up the reaction.
Understanding how the rate constant changes with temperature is vital for controlling reaction kinetics in industrial processes and laboratory settings. This dependency allows chemists to optimize conditions to achieve more efficient and faster reactions.