Question

A catalyst increases the rate of a reaction by: (a) increasing the activation energy of the reaction (b) increasing the value of rate constants \(\left(k_{f}\right.\) and \(k_{b}\) ) (c) increasing the enthalpy change of the reaction (d) decreasing the enthalpy change of the reaction

Short answer

A catalyst increases the rate of a chemical reaction by increasing the rate constants (\( k_f \) and \( k_b \) ), not by changing activation or enthalpy changes.

Step-by-step solution

Identify the Function of a Catalyst

A catalyst is a substance that increases the rate of a chemical reaction without being consumed or altered significantly during the reaction. It does so by providing an alternative reaction pathway with a lower activation energy.

Understand the Effect of Activation Energy on Reaction Rate

The activation energy is the minimum amount of energy needed for the reactants to undergo a successful chemical reaction. By lowering the activation energy, a catalyst makes it easier for the reactants to reach the transition state, leading to more frequent successful collisions and thus a faster reaction rate.

Examine the Role of Rate Constants in Reaction Rates

Rate constants (\( k_f \) for the forward reaction and \( k_b \) for the reverse reaction) are directly proportional to the reaction rate. A catalyzed reaction will have higher values of these rate constants without the need for increased temperature.

Assess the Impact of Enthalpy Changes on Reaction Rate

Enthalpy change (\( \triangle H \)) of a reaction is the overall heat content change. While changes in enthalpy can affect the position of equilibrium, they do not directly determine the reaction rate and hence are not typically affected by the addition of a catalyst.

Identify the Correct Answer

Since a catalyst provides a pathway with lower activation energy and increases the rate constants of the reaction, the correct option is (b) increasing the value of rate constants (\( k_f \) and \( k_b \) ).

Key concepts

Activation Energy

Imagine trying to push a ball over a hill. If the hill is high, it's much harder to do so. In chemistry, activation energy is like that hill for chemical reactions. It's the energy barrier that must be overcome for a reaction to occur. When a catalyst enters the scene, it's like cutting a tunnel through the hill, greatly reducing the effort needed to push the ball through. Consequently, with a lower activation energy, more reactant molecules can collide with enough energy to react, jump-starting the reaction and increasing its pace. This is how a catalyst enables reactants to reach the transition state more frequently and react more readily, quickening the reaction without being consumed in the process.

By understanding activation energy, students can grasp why certain reactions occur spontaneously while others need a bit of help, such as the presence of a catalyst, to proceed.

Reaction Rate

The reaction rate is a measure of how fast a chemical reaction occurs. It is determined by factors such as the concentration of reactants, temperature, and the presence of a catalyst. A higher reaction rate means that the reactive substances transform into products more quickly. You can think of it as a race: the faster the runners (reactants) reach the finish line (products), the higher the reaction rate. A catalyst acts like a performance-enhancing substance that lets the runners reach their full potential faster, without changing the finish line itself. It's critical to realize that while a catalyst can boost reaction rates, it doesn't alter the final amount of product formed; it simply gets there more swiftly.

In managing reaction rates, students can learn to control and optimize reactions, which is essential in various fields, from pharmaceutical development to manufacturing.

Rate Constants

Rate constants are the numbers that characterize the speed of a reaction; they are the 'speedometer' readings of a chemical process. In reactions, we often see them denoted as \( k_f \) for the forward reaction - the path that takes us to the products, and \( k_b \) for the backward reaction - the path that reverts products back to reactants. These constants are influenced by various factors, but especially by the activation energy: lower activation energy, courtesy of a catalyst, means higher rate constants. This change in the rate constant as a result of a catalyst is key because it signifies that the reaction can proceed at a faster clip without altering the temperature or concentration of reactants. This concept is pivotal in industries where controlling reaction speeds is essential without overspending on energy costs or materials.

By comprehending rate constants, students can predict how quickly a reaction will reach completion, which is incredibly valuable for practical applications like chemical engineering or environmental science.

Enthalpy Change

Enthalpy change, often represented as \( \triangle H \) in equations, is a measure of the total energy change in a system during a reaction. It tells us whether a reaction is exothermic (releases heat) or endothermic (absorbs heat). If you bake cookies, the enthalpy change is the difference in energy between the raw dough and the delicious final product. In the realm of catalysts, these clever substances do not make the reaction release more or less heat; they just make the energy hill easier to climb, so the cookies 'bake' faster, metaphorically speaking. Students should note that while enthalpy change gives clues about energy flow and can shift equilibrium positions, it is not a direct factor in accelerating reaction rates as a catalyst would.

Grasping the concept of enthalpy change allows students to predict the energy requirements of reactions and design processes with optimal energy usage, which is of high importance in tasks like material synthesis and energy production.