Problem 15 - Advanced Problems in Physical Chemistry for Competitive Examinations

Question

Which of the following statements about a catalyst is true? (a) A catalyst accelerates reaction by bringing down the free energy of activation. (b) A catalyst does not take part in the reaction mechanism. (c) A catalyst makes the reaction more feasible by making the \(\Delta G^{\circ}\) more negative. (d) A catalyst makes the equilibrium constant of the reaction more favourable for the forward reaction.

Step-by-Step Solution

Answer

The true statement about a catalyst is (a) A catalyst accelerates reaction by bringing down the free energy of activation.

Step 1: Understanding a Catalyst

A catalyst is a substance that increases the rate of a chemical reaction without being consumed in the process. It provides an alternative pathway for the reaction with a lower activation energy.

Step 2: Analyzing Option (a)

Option (a) states that a catalyst accelerates the reaction by bringing down the free energy of activation. This statement is true as catalysts provide an alternative reaction pathway with a lower activation energy.

Step 3: Analyzing Option (b)

Option (b) asserts that a catalyst does not take part in the reaction mechanism. This is false because catalysts do participate in the mechanism of the reaction, facilitating the process and then being regenerated at the end.

Step 4: Analyzing Option (c)

Option (c) proposes that a catalyst makes the reaction more feasible by making the Gibbs free energy change (\(\text{\Delta} G^{\text{\circ}}\)) more negative. This is incorrect; a catalyst does not affect the Gibbs free energy change of a reaction.

Step 5: Analyzing Option (d)

Option (d) suggests that a catalyst makes the equilibrium constant more favorable for the forward reaction. This is incorrect; a catalyst does not alter the equilibrium constant or the position of equilibrium.

Key Concepts

Activation Energy

Understanding the concept of activation energy is crucial for students studying chemistry, as it is central to how reactions occur. Activation energy is the minimum amount of energy that reactant molecules must possess for a chemical reaction to occur. Imagine it as a barrier that reactants need to overcome to transform into products.

To help visualize this, picture activation energy as a hill. Reactants must climb this hill to reach the product side. A catalyst serves as a shortcut or a tunnel through this hill, effectively lowering the height of the hill and thus reducing the energy required by the reactants to turn into products. This is why catalysts are vital; they speed up reactions by providing a path that requires less energy, which was correctly described in option (a) of the original exercise.

Reaction Mechanism

In chemistry, the term reaction mechanism refers to the step-by-step sequence of elementary reactions by which overall chemical change occurs. A proper grasp of reaction mechanisms can be quite beneficial for students as it reveals how atoms rearrange during reactions.

A catalyst participates actively in this process. It often temporarily forms an intermediate with the reactants, altering the path the reaction takes while remaining unchanged by the reaction's conclusion. This temporary interactions help to lower the activation energy. However, as mentioned in the exercise solution, the statement in option (b) is misconceived. Since catalysts are indeed involved in the reaction mechanism, they may appear in the reaction steps but will always be regenerated by the end.

Gibbs Free Energy

Gibbs free energy (G), named after Josiah Willard Gibbs, is a thermodynamic quantity used to predict whether a process will occur spontaneously at constant pressure and temperature. The change in Gibbs free energy, denoted as \(\Delta G\), must be negative for a spontaneous reaction.

It is a common misunderstanding, perhaps reflected in option (c) of the exercise, that the catalyst affects the value of \(\Delta G\). However, the actual role of a catalyst is to speed up the reaction rate by lowering the activation energy. The \(\Delta G\) of a reaction is a measure of the overall thermodynamic driving force and is not altered by the presence of a catalyst. The catalyst helps the reaction proceed more quickly to reach the thermodynamic equilibrium, but the change in Gibbs free energy remains unchanged.

Equilibrium Constant

The equilibrium constant (\(K\)) is another fundamental concept in chemical reactions, representing the ratio of product concentrations to reactant concentrations at equilibrium, each raised to the power of their respective stoichiometric coefficients in the balanced chemical equation.

When students learn about catalysts, there might be confusion, such as that presented in option (d), regarding the effect on \(K\). The truth is, a catalyst does not alter the equilibrium constant or the position of the equilibrium; it merely allows the system to reach equilibrium faster. The position of equilibrium is solely dependent on the reaction conditions, such as temperature and pressure, not on the presence of a catalyst.