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-order, option (b).

Step 1: Understand the relationship

The rate of a reaction is directly proportional to the concentration of the reactants raised to the power of their respective orders. Mathematically, this can be expressed as \( r = k[A]^m[B]^n \), where \( r \) is the rate of reaction, \( k \) is the rate constant, \([A]\) and \([B]\) are the concentrations of reactants, and \( m \) and \( n \) are the orders of the reaction with respect to each reactant.

Step 2: Define the condition given

According to the problem statement, the rate of reaction is equal to the rate constant, i.e., \( r = k \). This implies that changes in the concentration of the reactants do not affect the rate of the reaction.

Step 3: Determine reaction order associated with given condition

For the rate of reaction to be independent of the concentration of reactants, the sum of the orders \( m + n = 0 \). This is because any reactant concentration raised to the power of zero is equal to 1, meaning it doesn't affect the rate. Therefore, the reaction is of zero order.

Step 4: Choose the correct option

Given that the conditions match a zero-order reaction, we identify the correct answer from the options provided. The answer corresponding to a zero-order reaction is (b) 0.

Key Concepts

Understanding the Rate Constant

In the realm of chemical kinetics, the **rate constant** is a crucial aspect that links the rate of a reaction to the concentration of the reactants. It is represented by the symbol \( k \) and is specific to a given reaction under particular conditions, such as temperature. The rate equation, which is formulated as \( r = k[A]^m[B]^n \), helps in demonstrating how the concentrations of reactants \([A]\) and \([B]\) influence the reaction rate.
The rate constant itself is independent of the concentrations of the reactants. Instead, it is influenced by environmental factors such as temperature and presence of a catalyst. The units of the rate constant vary depending on the order of the reaction:

• For a zero-order reaction, the units are typically mol/L·s.
• For a first-order reaction, the units are s^-1.
• For a second-order reaction, the units are L/mol·s.

This specificity in units helps to distinguish the reaction order and understand the dynamics of the reaction.

Exploring Zero-Order Reactions

A **zero-order reaction** is characterized by a constant reaction rate that is independent of the concentration of reactants. This means that the rate remains the same regardless of changes in how much reactant is present, as long as there is some reactant to consume. Such reactions can be represented by the simple equation \( r = k \), where \( r \) stands for the rate of reaction and \( k \) is the rate constant.
In real-world scenarios, zero-order kinetics may occur in heterogeneous reactions where the surface of a catalyst is saturated by the reactant. Some enzyme-catalyzed reactions may also exhibit zero-order kinetics at high substrate concentrations where the enzyme is saturated.

• Because the rate is constant, the reaction rate graph versus time is a straight line.
• The half-life of zero-order reactions, which is the time required for half of the reactant to be consumed, is dependent on the initial concentration.
• In zero-order reactions, the concentration of the reactant decreases linearly over time.

This behavior is quite different from first or second-order reactions, where the rate is dependent on the concentrations of the reactants.

Delving into Rate of Reaction

The **rate of reaction** refers to how quickly a chemical reaction proceeds. It quantifies the change in concentration of a reactant or product over time. This can be expressed through the equation \( r = \frac{\Delta [Reactant]}{\Delta t} \) or \( r = \frac{\Delta [Product]}{\Delta t} \), where \( \Delta \) signifies the change over time \( t \).
For many reactions, the rate of reaction is directly influenced by factors such as:

• Concentration of reactants: Generally, a greater concentration can lead to a higher rate of reaction.
• Temperature: Increasing temperature usually increases reaction rates, as it raises the energy of the molecules, leading to more frequent and effective collisions.
• Catalysts: These substances increase reaction rates without being consumed in the process, by providing an alternative pathway with a lower activation energy.
• Surface area: For reactions involving solids, a larger surface area typically means a faster reaction as there are more sites available for collisions.

In the case of a zero-order reaction, where rate does not depend on concentration, these other factors like temperature and catalysts play a more significant role in determining the rate.