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 (a) zero-order.

Step 1: Understanding the Given Information

We are informed that the rate of reaction is equal to its rate constant for any concentration of the reactant. Mathematically, this can be expressed as \( r = k \), where \( r \) is the reaction rate and \( k \) is the rate constant. This implies that the reaction rate does not change with changes in the concentration of the reactant.

Step 2: Understanding Reaction Order

The order of a reaction with respect to a reactant is the exponent of its concentration in the rate law expression. Generally, the rate law is written as \( r = k[A]^n \), where \([A]\) is the concentration of the reactant and \(n\) is the order. If \( r = k \), it implies that the concentration term \([A]^n = 1\).

Step 3: Deducing the Order

Given \( [A]^n = 1 \) for any concentration \([A]\), this requires that \( n = 0 \). Because only when the exponent of the concentration is zero, is \([A]^n = 1\) for any concentration \([A]\), the expression becomes \( r = k[1] = k \). Therefore, the order \( n \) is zero.

Step 4: Conclusion

Through the analysis, the definition matched that of a zero-order reaction, where the rate of reaction is constant and does not depend on the concentration of the reactant. Review the given options; the correct answer is (a) zero-order.

Key Concepts

Rate Constant

The rate constant is a crucial component in understanding reaction rates. In any reaction, the rate constant, symbolized by \( k \), is a specific value which indicates the speed or intensity of that reaction. It is important to note that the rate constant is independent of the concentrations of the reactants or products. However, it can depend on other factors such as temperature and the presence of a catalyst.
In mathematical terms, the rate of a reaction can often be expressed using a rate law, where the rate \( r \) is equal to the product of the rate constant \( k \) and the concentrations of the reactants raised to their respective powers. This is often expressed as:
\[ r = k[A]^n[B]^m \]
where \([A]\) and \([B]\) are the concentrations of two different reactants and \( n \) and \( m \) represent their respective reaction orders.
In zero-order reactions, the rate constant is especially significant because the rate of reaction is entirely equal to \( k \), meaning that regardless of how the concentration changes, the rate remains consistent as long as the temperature and other conditions remain constant. This constant behavior can provide insights into how a reaction operates at various conditions.

Zero-Order Reactions

In chemistry, a zero-order reaction is one where the rate of reaction is constant and does not depend on the concentration of the reactant. This occurs when the reactant is in excess or when it's catalyzed by a surface active site.
For zero-order reactions, the rate can be expressed simply as:
\[ r = k \]
which illustrates how the reaction rate \( r \) is equal to the rate constant \( k \).
There are key characteristics of zero-order reactions:

• The rate is constant and equal to the rate constant, meaning any change in concentration won't affect the rate.
• The reaction depletes the reactant at a constant rate over time.
• Examples include certain enzyme-catalyzed reactions and reactions occurring on solid metal surfaces where the surface is saturated.

In practical terms, such reactions maintain a consistent speed regardless of concentration changes, which can be beneficial in processes where a steady output is required, such as in industrial syntheses.

Rate Law Expression

The rate law expression is a formula that represents the relationship between the rate of a chemical reaction and the concentrations of its reactants. It provides crucial insight into how different factors influence the reaction pace.
The general form is:
\[ r = k[A]^n \]
where \( r \) is the rate of reaction, \( k \) is the rate constant, \([A]\) is the concentration of reactant \( A \), and \( n \) is the order of reaction with respect to \( A \).
Here are the steps to understand a rate law expression:

• Identify the rate constant \( k \), which governs how fast or slow the reaction occurs.
• Determine the concentration dependencies, which involve the concentration terms \([A]\), \([B]\), etc.
• Define the reaction order which dictates how changes in concentration will affect the rate.

For a zero-order reaction, the rate law simplifies to:
\[ r = k \]
This infers that the rate is entirely independent of the concentration levels, characterizing a unique aspect of zero-order reactions compared to other reaction orders. Understanding rate law expressions allows chemists to predict how changes in conditions impact the rate and design experiments and industrial processes accordingly.