Problem 42 - A Complete Resource Book in Chemistry for JEE Main

Question

The rate of reaction was found to be equal to its rate constant at any concentration of the reactant. The order of the reaction is (a) zero-order (b) first-order (c) second-order (d) third-order

Step-by-Step Solution

Answer

The order of the reaction is zero-order (a).

Step 1: Understanding the Relationship

The problem states that the rate of reaction is equal to its rate constant at any concentration of the reactant. This implies that the reaction rate does not depend on the concentration of the reactant, as it remains constant.

Step 2: Analyzing Reaction Order

A zero-order reaction has a rate that is constant and independent of the concentration of the reactant. Mathematically, the rate can be expressed as: \[\text{Rate} = k\]where \(k\) is the rate constant. This matches the condition stated in the problem.

Step 3: Conclusion Based on Conditions

Given that the rate is constant and independent of reactant concentration, this aligns with the definition of a zero-order reaction. Hence, the order of the reaction must be zero.

Key Concepts

Zero-Order Reaction

In chemistry, when we talk about reaction orders, we're referring to the power to which the concentration of a reactant is raised in the rate law of a reaction. A zero-order reaction is unique because its rate is constant and independent of the concentration of the reactants. This means that no matter how much reactant you start with, the rate at which the reaction proceeds doesn’t change.
Instead, it's governed solely by the rate constant. Mathematically, this principle for zero-order reactions can be represented by the equation:

• \[\text{Rate} = k\]
• Here, \( k \) represents the rate constant.

This equation highlights that, in zero-order reactions, the reaction rate is entirely independent of the reactant concentration. It's a constant value throughout the reaction.
These reactions are uncommon and typically occur under conditions where a catalyst is saturated by the reactants, or when a surface reaction limits the rate.

Rate Constant

The rate constant, represented by \( k \), is a crucial parameter in the rate law of chemical reactions. It determines the speed of a reaction at a given temperature. In a zero-order reaction, the rate constant is numerically equal to the rate of the reaction itself. For this type of reaction, no matter how much or how little reactant is present, the rate remains constant because it's solely dependent on \( k \).
This might suggest that how quickly the reaction occurs is entirely governed by the constant, without interaction from reactant concentration.The rate constant varies with temperature and can be influenced by catalysts. Important things to note about the rate constant in zero-order reactions include:

• It has units of concentration/time, like mol/L·s.
• Its value provides insights into how quickly a reaction can occur under specified conditions.

Thus, knowing the rate constant gives chemists a clearer picture of a reaction's behavior at microscopic levels.

Reaction Rate Independence

In many chemical reactions, the rate at which they proceed is significantly influenced by the concentration of the reactants. However, for zero-order reactions, the rate is completely independent of the concentration of the reactant. Instead, the reaction rate remains unchanged unless external factors, such as temperature or catalysts, are altered.
This trait is particularly intriguing because it places zero-order reactions apart from most other reactions which typically display some concentration dependence. In a zero-order reaction, since the reaction rate does not depend on reactant concentration, even as reactants are consumed, the rate remains steady. Situations like this might arise when a reaction is catalyzed and reaches the maximum capacity of the catalyst, or within systems controlled by surface phenomena. Crucial points about reaction rate independence in zero-order reactions:

• It’s a rare occurrence in chemical reactions.
• The rate is affected by changes in external conditions rather than changes in reactant concentrations.

This independence from concentration changes offers an intriguing exploration into reaction mechanics and can potentially be harnessed in industrial applications where constant reaction rates are advantageous.