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 0.

Step 1: Understand the rate law equation

If the rate of the reaction is equal to the rate constant, this implies a specific scenario. The rate law equation is given by: \[\text{rate} = k [A]^n \]where \(k\) is the rate constant, \( [A] \) is the concentration of reactant \(A\), and \( n \) is the order of the reaction.

Step 2: Set up the equation based on given condition

According to the problem, the rate of the reaction is equal to the rate constant, so: \[\text{rate} = k \] Now plug this into the rate law equation: \[k = k [A]^n \]

Step 3: Analyze the equation

To find when the rate is equal to the rate constant: \[k = k [A]^n \]Divide both sides by \(k\) (assuming \(k\) is not zero): \[1 = [A]^n \]This implies \([A]^n = 1\), which holds true when \([A] = 1\) or when \(n = 0\). In a general case, \( [A] = 1 \) for non-zero concentration, accommodating any order \( n \), but specific to this condition, it means \( n = 0 \).

Step 4: Conclusion

The equation \([A]^n = 1\) indicates that \(n = 0\), identifying it as a zero-order reaction since the rate is constant and does not depend on the concentration of the reactants.

Key Concepts

Rate Law

When we discuss chemical reactions, the rate law is fundamental. It describes how the concentration of reactants affects the rate at which a reaction occurs. The general form of the rate law is expressed as \(\text{rate} = k [A]^n [B]^m\). Here, \([A]\) and \([B]\) are the concentrations, and \(n\) and \(m\) are their respective orders in the reaction. The rate constant, \(k\), is a unique value for a given reaction at a specific temperature.
The rate law provides essential insights:

• It allows chemists to understand how changing reactant concentrations impacts the reaction rate.
• It helps in determining the mechanism of the reaction, offering clues on the steps the reaction takes at a molecular level.

In this exercise, the special scenario where the rate equals the rate constant suggests interesting insights about the reaction order.

Reaction Order

Reaction order is a critical concept in determining how reactant concentrations affect reaction rates. The order is determined by the exponents in the rate law equation. For example, in \(\text{rate} = k [A]^n\), the reaction order with respect to \(A\) is \(n\).

Orders can be:

• Zero-order: The rate is constant and independent of reactant concentration. Here, the rate = \(k\), and changes in \([A]\) do not affect the rate.
• First-order: The rate changes linearly with a change in \([A]\). Doubling \([A]\) doubles the rate.
• Second-order: The rate depends on the square of \([A]\). Doubling \([A]\) quadruples the rate.

In our problem, we discovered that when the rate of the reaction equals \(k\), the reaction is zero-order. This means the reaction rate does not change with changes in reactant concentration.

Rate Constant

The rate constant, often represented by \(k\), is a crucial component of the rate law. It quantifies the rate of a reaction for a given set of conditions, without the influence of concentrations. Despite being called a constant, the rate constant can vary with temperature.

• Each reaction has a specific rate constant, expressed in units that depend on the overall reaction order.
• For a zero-order reaction \((\text{rate} = k)\), \(k\) has units of concentration/time, such as mol/L·s.
• In first-order reactions, \(k\) has units of 1/time, such as s⁻¹.

The rate constant provides insight into the speed of the reaction. A larger \(k\) indicates a faster reaction. In our specific case, assuming the rate equals \(k\) shows the significance of \(k\) as an intrinsic measure of reaction speed, independent of reactant concentration changes.