Problem 122 - A Complete Resource Book in Chemistry for JEE Main

Question

At the equilibrium position in the process of adsorption (a) \(\Delta \mathrm{H}>0\) (b) \(\Delta \mathrm{H}<\mathrm{T} \Delta \mathrm{S}\) (c) \(\Delta \mathrm{H}>\mathrm{T} \Delta \mathrm{S}\) (d) \(\Delta \mathrm{H}=\mathrm{T} \Delta \mathrm{S}\)

Step-by-Step Solution

Answer

At equilibrium, \( \Delta H = T \Delta S \), so the correct answer is (d).

Step 1: Understanding Adsorption Equilibrium

In the context of adsorption processes, equilibrium is when the rate of adsorption equals the rate of desorption. At this point, the system reaches a state where the Gibbs free energy change (\( \Delta G \)) is zero.

Step 2: Gibbs Free Energy Equation

The Gibbs free energy change is given by the equation: \( \Delta G = \Delta H - T \Delta S \), where \( \Delta H \) is the enthalpy change, \( T \) is the temperature, and \( \Delta S \) is the entropy change.

Step 3: Condition for Equilibrium

At equilibrium, \( \Delta G = 0 \). Therefore, substituting into the Gibbs free energy equation gives \( 0 = \Delta H - T \Delta S \). Rearranging this equation, we find that \( \Delta H = T \Delta S \).

Step 4: Choose the Correct Option

Based on the rearranged equation \( \Delta H = T \Delta S \), at equilibrium, the relationship between the enthalpy change and the product of temperature and entropy change is defined. Thus, the correct answer is option (d) \( \Delta H = T \Delta S \).

Key Concepts

Gibbs Free Energy

Gibbs free energy, represented by the symbol \(\Delta G\), is a central concept in understanding chemical reactions and processes, especially in thermodynamics. It determines the spontaneity of a reaction or process. A negative \(\Delta G\) indicates that a process is spontaneous, meaning it can occur without any external input of energy. On the other hand, a positive \(\Delta G\) means the process is non-spontaneous and requires added energy to proceed.
At equilibrium, a fascinating thing happens: \(\Delta G = 0\). This means there is no net change occurring in the system. It's like a perfectly balanced scale where no side tips over, depicting the balance between forward and reverse processes. In adsorption equilibrium, where materials adhere to surfaces, the rate of sticking to a surface equals the rate of leaving it. Hence, energy is perfectly balanced, leading to no overall change in the system's energy level.

Enthalpy Change

Enthalpy change, denoted as \(\Delta H\), is a measure of the heat absorbed or released during a process at constant pressure. It tells us about the energy changes associated with making or breaking chemical bonds.
There are two types of processes based on enthalpy:

• Exothermic processes, where \(\Delta H < 0\), indicating energy is released as heat into the surroundings.
• Endothermic processes, where \(\Delta H > 0\), showing the system absorbs heat from the surroundings.

At equilibrium, especially in the context of adsorption, the enthalpy change balances with the entropy change and temperature such that \(\Delta H = T \Delta S\). This equality points to an energy equilibrium, important for adsorption processes in fields like catalysis and environmental science.

Entropy Change

Entropy change, symbolized by \(\Delta S\), is a quantitative expression of the disorder or randomness in a system. In thermodynamics, it signifies the degree of spread of energy and matter.
Processes can affect entropy in two primary ways:

• When \(\Delta S > 0\), the system's disorder increases, leading to a more spontaneous process.
• When \(\Delta S < 0\), the system's disorder decreases, often resulting from energy being concentrated in fewer places.

At equilibrium, particularly in adsorption, the entropy change relates intricately with the enthalpy change and temperature via the equation \(\Delta H = T \Delta S\). This relation underscores how the natural tendency towards disorder is balanced by the energy in the system, maintaining equilibrium. Understanding this balance helps in designing processes where adsorption is used to remove impurities or separate mixtures.