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: Analyze the Rate Equation

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

Step 2: Determine the Order of the Reaction

The order of reaction is determined by the sum of the exponents in the rate equation. If the rate equation is \(\text{Rate} = [\mathrm{X}]^a[\mathrm{Y}]^b\), the reaction order is \(a + b\). Here, both exponents are 1, so the order is \(1 + 1 = 2\). Thus, statement (1) is incorrect because the order is two, not one.

Step 3: Assess the Molecularity of the Reaction

Molecularity is the number of molecules involved in an elementary reaction step. Since the reaction involves the interaction of molecules \(\mathrm{X}\) and \(\mathrm{Y}\), its molecularity is two, supporting statement (2) as correct.

Step 4: Evaluate the Dependency of the Rate Constant

The rate constant in a rate equation like \(\text{Rate} = k[\mathrm{X}][\mathrm{Y}]\) is affected by external conditions such as temperature. Therefore, statement (3) is correct and the rate constant does depend on temperature.

Step 5: Synthesize Conclusions

Based on the analysis, statements (2) and (3) are correct: the molecularity of the reaction is two and the rate constant depends on temperature. Thus, choice (c) 2 and 3 are correct, is the right answer.

Key Concepts

Order of Reaction

The order of reaction is a crucial aspect when it comes to understanding chemical kinetics. It is determined by adding the powers of the concentration terms in the rate equation. Think of it as a way to sum up how each reactant concentration affects the overall rate of the reaction.

In the rate equation, \( ext{Rate} = [X][Y] \), the exponents for both \( X \) and \( Y \) are 1. Thus, the reaction order here is \( 1 + 1 = 2 \). This signifies a second-order reaction.

• A higher order implies that the reaction is more susceptible to changes in reactant concentration.
• If the order is zero, changes in concentration do not affect the rate.
• Orders can be fractional or integer values, derived from experiments.

The main takeaway is that the order of a reaction is pivotal for predicting how the rate will change if you alter concentrations.

Molecularity of Reaction

Molecularity provides insight into how many molecules come together to induce a chemical change in one step of a reaction. It differs from reaction order as it strictly applies to elementary steps, while reaction order can apply to both simple and complex reactions.

In an elementary reaction, molecularity is a simple count of the reactant molecules. For the given equation, \( [X][Y] \), there are two reactants involved. Therefore, the molecularity is two.

• Unimolecular reactions involve a single molecule decomposing or rearranging.
• Bimolecular reactions involve two molecules interacting, like in our example.
• Trimolecular reactions, which are less common, involve three molecules.

Important note: Molecularity must be a whole number, as it directly corresponds to the individual reactants in an elementary step.

Temperature Dependence of Rate Constant

Temperature can have a significant effect on the speed of a reaction. The rate constant \( k \) in the rate equation is not a fixed value; instead, it changes with temperature. This is because increasing temperature usually increases the kinetic energy of molecules, which enhances collision frequency and energy.

For most reactions, you use the Arrhenius equation to describe this dependence:\[ k = A e^{\frac{-E_a}{RT}} , \]where \( A \) is the frequency factor, \( E_a \) is the activation energy, \( R \) is the gas constant, and \( T \) is the absolute temperature.

• As temperature rises, \( k \) typically increases, making reactions faster.
• Activation energy acts as a barrier that reactants must overcome, which becomes easier at higher temperatures.
• The relation highlights why storing certain substances at cooler temperatures can slow reactions.

Understanding this helps in controlling reactions, either speeding them up or slowing down, depending on industrial or research needs.