Problem 11 - A Complete Resource Book in Chemistry for JEE Main

Question

If the rate of the reaction is equal to the rate constant, the order of the reaction is (a) 3 (b) 0 (c) 1 (d) 2

Step-by-Step Solution

Answer

The order of the reaction is zero (b).

Step 1: Understanding the Problem

We need to determine the order of a chemical reaction such that the rate of reaction equals the rate constant.

Step 2: Recalling Reaction Kinetics

For a reaction of order 'n', the rate of the reaction can be expressed as: \( R = k [A]^n \), where \( R \) is the rate, \( k \) is the rate constant, and \( [A] \) is the concentration of reactant.

Step 3: Setting up the Equation

In this particular case, we are given that the rate of the reaction equals the rate constant, \( R = k \). This implies \( k [A]^n = k \).

Step 4: Solving for the Order of Reaction

From the equation \( k [A]^n = k \), we can divide both sides by \( k \), assuming \( k eq 0 \): \( [A]^n = 1 \).

Step 5: Analyzing the Result

Since \( [A]^n = 1 \), this implies \( [A]^0 = 1 \) for any non-zero concentration \([A]\). Therefore, \( n = 0 \).

Step 6: Conclusion

The order of the reaction that results in the rate of reaction equaling the rate constant is zero-order.

Key Concepts

Reaction Kinetics

When studying chemical reactions, understanding the concept of reaction kinetics is crucial. Reaction kinetics is the branch of chemistry that deals with the speed (or rate) of chemical reactions and the factors that affect them. The rate of a reaction can be influenced by various factors, including temperature, pressure, concentration of reactants, and the presence of catalysts. In a typical reaction, the rate can be expressed as a change in concentration of reactants or products over time. This leads to the rate expression, which is a mathematical equation that describes the relationship between the reaction rate and the concentration of reactants. The general form of this expression is:

• \( R = k [A]^n \)

where \( R \) is the rate of reaction, \( k \) is the rate constant, \( [A] \) is the concentration of a reactant, and \( n \) is the order of the reaction with respect to that reactant. Reaction kinetics is an essential tool for predicting how changes in conditions can affect the speed of chemical processes.

Rate Constant

The rate constant, often denoted as \( k \), is a key factor in reaction kinetics. It is specific to a particular reaction at a given temperature and is a measure of the speed at which a reaction occurs. The value of the rate constant provides insight into the reaction mechanism and the energetic requirements of the reaction.Unlike the rate of the reaction, which can vary depending on the concentration of reactants, the rate constant is independent of these concentrations. This makes it a vital parameter for comparing different reactions under the same conditions. The units of the rate constant vary based on the order of the reaction, adjusting to ensure that the overall rate has units of concentration per unit time.For zero-order reactions, where the reaction rate is constant and does not depend on the concentration of reactants, the rate constant directly equals the reaction rate under these conditions. This highlights the importance of the rate constant in defining how particular reactions proceed.

Zero-Order Reaction

In a zero-order reaction, the rate of the reaction is constant and does not depend on the concentration of reactants. This means that, as the reaction proceeds, the reactants are consumed at a steady rate. The reaction rate is given by the simplified expression:

• \( R = k \)

where \( R \) represents the reaction rate, and \( k \) is the rate constant. This implies that the entire reaction rate is determined by the constant \( k \), and is independent of how much of the reactant is present. Zero-order reactions are relatively rare and often occur under conditions where the reactant concentration far exceeds the concentration of the enzyme or catalyst, saturating it. Because of this saturation, adding more reactant does not increase the reaction rate. Understanding zero-order reactions is important, especially in scenarios such as industrial processes or enzyme kinetics, where certain conditions can lead to this type of rate behavior.