Problem 31 - A Complete Resource Book in Chemistry for JEE Main

Question

The rate constant of a reaction depends on (a) extent of reaction (b) time of reaction (c) temperature (d) initial concentration of the reactants

Step-by-Step Solution

Answer

The rate constant of a reaction depends on temperature (option c).

Step 1: Understanding the Concept of Rate Constants

The rate constant, often denoted as k, is a fundamental aspect of chemical kinetics. It is a proportionality constant in the rate equation that correlates the reaction rate with the concentration of the reactants. Importantly, the rate constant is distinct from the rate of reaction, which depends on the concentrations of reactants.

Step 2: Exploring the Temperature Factor

The Arrhenius equation describes how the rate constant changes with temperature: \( k = A e^{-E_a/(RT)} \), where \( A \) is the pre-exponential factor, \( E_a \) is the activation energy, \( R \) is the gas constant, and \( T \) is the temperature in Kelvin. This indicates that the rate constant is dependent on temperature, as changes in \( T \) will influence the rate constant's value.

Step 3: Analyzing Other Factors

While the temperature affects the rate constant, the extent of reaction (a), time of reaction (b), and initial concentration of the reactants (d) do not directly influence the rate constant. The extent of reaction refers to the progress of the reaction, and time refers to how long the reaction has been occurring. Both of these relate to the reaction's progress rather than affecting the intrinsic properties like the rate constant. Similarly, initial concentration of reactants influences reaction rate itself but not the rate constant, which is characteristic of a particular reaction at a given temperature.

Step 4: Conclusion and Correct Option

Considering the analysis, the only factor that influences the rate constant directly is temperature. Thus, among the given options, the correct choice is (c) temperature.

Key Concepts

Chemical Kinetics

Chemical kinetics is the branch of chemistry that explores the rates of chemical reactions. It provides insight into the speed or pace at which reactants convert into products. This field examines how different conditions, such as concentration and temperature, affect the reaction rate.

The core aspects of chemical kinetics include:

• Understanding the rate of reaction and its dependence on the concentration of reactants.
• Exploring the role of catalysts, which can speed up reactions without being consumed.
• Investigating the mechanisms or step-by-step sequences through which reactions occur.

Chemical kinetics is essential because it helps chemists determine optimal conditions for reactions, crucial in industrial and laboratory processes. It also aids in understanding the dynamics of processes, whether in nature or controlled environments.

Arrhenius Equation

The Arrhenius equation is a fundamental formula in chemical kinetics that relates the rate constant of a reaction to temperature. It is expressed as \[ k = A \cdot e^{-E_a/(RT)} \].

In this equation:

• The variable \( k \) represents the rate constant, a measure of the rate at which a reaction proceeds.
• \( A \) is the pre-exponential factor, a constant representing the frequency of collisions with correct orientation between reactant molecules.
• \( E_a \) stands for activation energy, the minimum energy that reactant molecules need to undertake a transformation into products.
• \( R \) is the gas constant with a value of 8.314 J/(mol K), important for calculations involving energy and temperature.
• \( T \) represents the temperature in Kelvin, highlighting the sensitivity of the rate constant to temperature changes.

The equation showcases how an increase in temperature typically results in an increase in the rate constant, thereby speeding up the reaction. This mathematical representation is crucial for predicting how reactions will behave under varying temperature conditions.

Temperature Dependence of Reactions

Temperature plays a pivotal role in the rate at which chemical reactions occur. According to the Arrhenius equation, as the temperature increases, the rate constant \( k \) also increases, which in turn speeds up the reaction.

This temperature dependence occurs because:

• Higher temperatures provide more thermal energy, which translates to more kinetic energy among molecules.
• Increased kinetic energy means more frequent and more forceful collisions between reacting molecules.
• These energetic collisions overcome the activation energy \( E_a \), increasing the likelihood of transforming reactants into products.

Understanding the temperature's influence helps chemists and engineers control and optimize reaction speeds. It is especially important in industrial processes where maintaining a specific reaction rate is critical for efficiency and safety.