Problem 40 - A Complete Resource Book in Chemistry for JEE Main

Question

Rate constant of a reaction \((k)\) is \(175 \mathrm{~L}^{2} \mathrm{~mol}^{-2} \mathrm{sec}^{-1}\). What is the order of reaction? (a) first (b) second (c) third (d) zero

Step-by-Step Solution

Answer

The reaction is third order.

Step 1: Understand the Relationship Between Rate Constant and Order of Reaction

The unit of the rate constant can help determine the order of a reaction. For a reaction of the form \( n \) order, the general unit for the rate constant \( k \) is \( \mathrm{L}^{n-1} \mathrm{~mol}^{-(n-1)} \mathrm{~s}^{-1} \).

Step 2: Analyze the Given Unit of Rate Constant

The rate constant given is \( 175 \mathrm{~L}^{2} \mathrm{~mol}^{-2} \mathrm{~s}^{-1} \). By comparing the unit \( \mathrm{L}^{2} \mathrm{~mol}^{-2} \mathrm{~s}^{-1} \) with the general form \( \mathrm{L}^{n-1} \mathrm{~mol}^{-(n-1)} \mathrm{~s}^{-1} \), we can observe that \( n-1 = 2 \) and \( -(n-1) = -2 \).

Step 3: Solve for the Reaction Order

We have \( n-1 = 2 \). Therefore, solving for \( n \), we get \( n = 2 + 1 = 3 \). This indicates that the reaction is third order.

Key Concepts

Rate constant units

The rate constant The rate constant, often symbolized as \( k \), plays a crucial role in understanding reaction kinetics. It is a numerical value that reflects the speed at which a reaction reaches completion. Importantly, the unit of this rate constant is not only key for calculations but also for determining the order of the reaction.

Every reaction order, whether zero, first, second, or third, has a characteristic unit for its rate constant:

• Zero Order: The unit is \( ext{s}^{-1} \).
• First Order: The unit is \( ext{s}^{-1} \).
• Second Order: The unit is \( ext{L mol}^{-1} ext{s}^{-1} \).
• Third Order: The unit is \( ext{L}^{2} ext{mol}^{-2} ext{s}^{-1} \).

Recognizing these units quickly becomes a powerful tool in identifying the kind of reaction you are dealing with.

Thus, when given a rate constant like \( 175 \text{ L}^{2} \text{~mol}^{-2} \text{~s}^{-1} \), one can immediately deduce that the reaction is third order by matching this unit against the standard units for different order reactions.

Reaction kinetics

Understanding how reactions proceedReaction kinetics delves into the study of reaction rates and the steps through which they occur. It seeks to explain how different factors such as temperature, concentration, and presence of catalysts impact the speed of chemical reactions.

Within the realm of reaction kinetics, several terms are often encountered:

• Rate of Reaction: The speed at which reactants turn into products. It can be expressed in terms of concentration change over time.
• Activation Energy: This is the minimum energy required to initiate a reaction. Lowering this energy through catalysts facilitates faster reactions.
• Mechanism: The series of steps through which reactants transform into products. Understanding the mechanism offers insights into the reaction pathway.

The rate law, a fundamental concept in reaction kinetics, mathematically expresses the relationship between the concentrations of reactants and the rate of reaction. It is expressed as \( ext{Rate} = k[ ext{A}]^m[ ext{B}]^n \), where each exponent represents the reaction order with respect to that reactant.

Overall, reaction kinetics provides a comprehensive framework for understanding the dynamic process of chemical reactions, allowing scientists and students alike to predict and explain how reactions will behave under various conditions.

Determining reaction order

Finding the order of a reaction involves understanding how the concentration of reactants affects the rate of the reaction. This process is essential for predicting how changes in conditions will alter the speed of a chemical reaction.

Two primary methods are used:

• Method of Initial Rates: By measuring the initial rate of reaction with varying concentrations, one can deduce the order by observing how changes in concentration affect the rate. If doubling a reactant's concentration doubles the rate, it is first order. If it quadruples the rate, it's second order, and so on.
• Integrated Rate Laws: These mathematical expressions relate the concentration of reactants to time. By fitting data to these equations, the reaction order can be obtained. This method can provide more precise insights, especially for complex reactions.

Identifying the reaction order is significant because it dictates the kinetics of the reaction. Knowing whether a reaction is zero, first, or second order illuminates its dependence on reactant concentrations and helps in crafting strategies to control the reaction rate.

For instance, in our exercise, given the unit \( \text{L}^{2} \text{~mol}^{-2} \text{~s}^{-1} \) for the rate constant, we determined the reaction to be third order. This has meaningful implications for how the reaction behaves and allows us to predict its behavior under different scenarios.