Problem 18 - A Complete Resource Book in Chemistry for JEE Main

Question

Among which of the following factor the specific reaction rate of a first- order reaction depends on (a) temperature (b) concentration of reactant (c) pressure (d) volume

Step-by-Step Solution

Answer

Temperature (a) primarily affects the specific reaction rate of a first-order reaction.

Step 1: Understanding First-Order Reactions

First-order reactions are characterized by their reaction rate being directly proportional to the concentration of a single reactant. The rate law for a first-order reaction can be expressed as \( r = k[A] \), where \( k \) is the rate constant and \( [A] \) is the concentration of the reactant. The unique property of first-order reactions is that they depend on a single reactant's concentration raised to the first power.

Step 2: Identifying Dependence of Reaction Rate

For a first-order reaction, the specific reaction rate is represented by the rate constant \( k \) in the rate law equation. The factors that can affect \( k \) include changes in reaction conditions, primarily temperature. According to the Arrhenius equation, \( k = Ae^{-E_a/RT} \), the rate constant \( k \) is affected by the temperature \( T \), where \( A \) is the frequency factor, and \( E_a \) is the activation energy.

Step 3: Evaluating Other Given Options

Other aspects, like concentration of the reactant, are components of the rate equation but actually do not affect the specific rate constant \( k \). The same reasoning applies to pressure and volume; they might influence the concentration aspect if gases are involved but do not directly change \( k \) for a first-order reaction. Thus, among the provided factors, temperature remains the primary condition influencing \( k \).

Step 4: Conclusion of Specific Reaction Rate Dependency

Considering all the factors provided, the specific reaction rate \( k \) for a first-order reaction is primarily dependent on temperature. Neither the concentration of reactant, pressure, nor volume directly affects \( k \).

Key Concepts

Rate Constant

The rate constant, often denoted as "\( k \)", is a crucial component in understanding chemical kinetics. It is a part of the rate law, which describes how the rate of reaction depends on the concentration of reactants. For a first-order reaction, this relationship is given by \( r = k[A] \), where \( r \) is the reaction rate and \( [A] \) is the concentration of the reactant. The rate constant \( k \) is unique in that it encapsulates all the factors affecting the speed of a reaction except for the concentration of reactants.

Unlike concentration, pressure, or volume, \( k \) itself is only influenced by temperature and catalysts, not by the amounts of substances present. In first-order reactions, changes in these conditions can impact \( k \), thus altering the rate of reaction.

• Temperature: An increase in temperature typically increases \( k \), speeding up reactions.
• Catalysts: Catalysts can lower the activation energy required for the reaction, affecting \( k \).

Arrhenius Equation

The Arrhenius equation provides a quantitative basis for understanding the impact of temperature on the rate constant. It is given by the formula \( k = Ae^{-E_a/RT} \), where:

• \( k \) is the rate constant.
• \( A \) is the pre-exponential factor, also known as the frequency factor, which indicates how often particles collide in the correct orientation.
• \( E_a \) is the activation energy, the minimum energy required for the reaction to proceed.
• \( R \) is the universal gas constant.
• \( T \) is the temperature in Kelvin.

This equation shows that the rate constant \( k \) increases with an increase in temperature, as the exponential term \( e^{-E_a/RT} \) becomes larger. A higher temperature means increased particle movement, leading to more frequent and energetic collisions, hence an increased rate of reaction. It highlights why temperature is such a critical factor in affecting reaction rates.

Temperature Dependency

Temperature plays a pivotal role in chemical reactions, especially in influencing the rate constant \( k \). For first-order reactions, any change in temperature can significantly impact how quickly a reaction proceeds. According to the Arrhenius equation, a rise in temperature results in an increase in the rate constant, hence a faster reaction. This is because higher temperatures provide reactant molecules with greater kinetic energy.

As molecules move faster:

• They collide more often, increasing the likelihood of successful collisions.
• The energy of collisions also increases, which can overcome the activation energy barrier more readily.

This temperature dependency means that even a small increase in temperature can lead to a noticeably faster reaction rate. While other factors like pressure or concentration may influence the concentration terms in the rate law, they do not affect \( k \) directly. Thus, understanding and controlling temperature is fundamental in managing and anticipating the behavior of chemical reactions.