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 depends on (c) temperature.

Step 1: Understand the Concept of Rate Constant

The rate constant (k) is a proportionality constant in the rate equation of a chemical reaction. It is specific to each reaction and depends on various factors.

Step 2: Identify Factors Affecting Rate Constant

The rate constant is influenced by temperature based on the Arrhenius equation. It does not depend on the extent of the reaction, time of reaction, or initial concentration of reactants.

Step 3: Match Options with Rate Constant Dependence

Review each option: - (a) Extent of reaction: The rate constant does not change with how far the reaction has progressed. - (b) Time of reaction: The rate constant is independent of the time taken for the reaction. - (c) Temperature: The rate constant varies with temperature. - (d) Initial concentration of reactants: The rate constant is independent of initial concentrations.

Step 4: Conclusion

From the analysis, the only factor affecting the rate constant is temperature. Therefore, the correct answer is option (c).

Key Concepts

Arrhenius Equation

The Arrhenius Equation is a fundamental formula used in chemistry to understand how the rate constant ( k ) changes with temperature. This equation is expressed as:\[k = A \cdot e^{-\frac{E_a}{RT}}\]Here’s what each symbol represents:

• \( k \) – the rate constant of the reaction.
• \( A \) – the frequency factor, also known as the pre-exponential factor, which indicates how many collisions have the correct orientation to lead to a reaction.
• \( e \) – the base of the natural logarithm (approximately equal to 2.718).
• \( E_a \) – the activation energy, which is the minimum energy required for the reaction to occur.
• \( R \) – the universal gas constant (8.314 J/mol·K).
• \( T \) – the absolute temperature in Kelvin.

The Arrhenius Equation shows that the rate constant increases exponentially with an increase in temperature and a decrease in activation energy. This means that higher temperatures or lower activation energies will result in a faster reaction rate. Understanding this relationship is crucial for predicting how chemical reactions will behave under different conditions.

Temperature Dependence

Temperature has a profound effect on chemical reaction rates, primarily because it influences the kinetic energy of the participating molecules. An increase in temperature causes molecules to move more rapidly. As a result, they collide more frequently and with greater energy.
This escalation in collision frequency and energy directly impacts the rate constant. Specifically, as per the Arrhenius equation, higher temperatures lead to a larger rate constant. This is because more molecules have the required activation energy to undergo the transformation needed for the reaction.
The temperature dependence of reactions can be observed practically. For instance, food spoilage happens faster in warm conditions and more slowly in cooler environments, demonstrating the influence of temperature on biochemical reaction rates. Thus, controlling temperature can be a vital factor in industrial chemical processes and food preservation.

Chemical Reaction Rates

Chemical reaction rates indicate how quickly reactants convert to products over time. They are crucial in understanding and controlling how reactions proceed in both laboratory settings and industrial applications.
The rate of a chemical reaction is influenced by several factors, such as:

• The concentration of reactants, as more molecules present lead to a higher probability of collision.
• The temperature, since higher temperatures increase molecular motion, leading to more collisions.
• The presence of a catalyst that can lower the activation energy without being consumed in the reaction.
• The physical state of the reactants, where fluids might react faster than solids due to easier movement and mixing.

The rate can be expressed through a rate law, which correlates the concentration of reactants and the rate constant to the speed of the reaction. Understanding these factors allows chemists to design reactions that are faster and more efficient, saving time and resources in various chemical and biological processes.