Problem 109 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following is true in respect of adsorption? (a) \(\Delta \mathrm{G}<0 ; \Delta \mathrm{S}>0 ; \Delta \mathrm{H}<0\) (b) \(\Delta \mathrm{G}<0 ; \Delta \mathrm{S}<0 ; \Delta \mathrm{H}<0\) (c) \(\Delta \mathrm{G}>0 ; \Delta \mathrm{S}>0 ; \Delta \mathrm{H}<0\) (d) \(\Delta \mathrm{G}<0 ; \Delta \mathrm{S}<0 ; \Delta \mathrm{H}>0\)

Step-by-Step Solution

Answer

Option (b) is true: \(\Delta G < 0 ; \Delta S < 0 ; \Delta H < 0\).

Step 1: Understanding Adsorption in Thermodynamics

Adsorption is the process where particles stick to the surface of a solid or liquid. In thermodynamic terms, the Gibbs free energy change (\(\Delta G\)) during adsorption must be negative for the process to be spontaneous, meaning \(\Delta G < 0\). Entropy change (\(\Delta S\)) is often negative because the adsorbed molecules become more ordered. The enthalpy change (\(\Delta H\)) is usually negative, as adsorption often releases heat.

Step 2: Analyze the Gibbs Free Energy Change

In spontaneous processes like adsorption, the change in Gibbs free energy \(\Delta G\) is negative. This factor helps rule out options where \(\Delta G > 0\), thus eliminating option c.

Step 3: Examine the Entropy Change

Adsorption typically involves a decrease in randomness as molecules are fixed to surfaces, so \(\Delta S\) is usually negative. This eliminates options like (a), where \(\Delta S > 0\).

Step 4: Consider the Enthalpy Change

Adsorption is an exothermic process (it releases heat), usually making \(\Delta H < 0\). This helps rule out option (d), where \(\Delta H > 0\).

Step 5: Final Comparison of Options

Based on the thermodynamic properties of adsorption, \(\Delta G < 0\), \(\Delta S < 0\), and \(\Delta H < 0\) are all indicative of option (b) being the correct choice.

Key Concepts

Gibbs Free Energy

Gibbs Free Energy is a key concept in understanding spontaneous processes, such as adsorption. In thermodynamics, for a process to occur spontaneously, the change in its Gibbs Free Energy, \(\Delta G\), must be negative. This means the system releases free energy, a driving force that allows the process to happen without external energy input. In the context of adsorption, this condition is met when the particles adhere to a surface, which is naturally favorable under lower energy conditions. Spontaneity in Gibbs Free Energy is like rolling a ball downhill - it occurs naturally due to gravitational pull, similar to how thermodynamic processes prefer a state with lower free energy. When examining any reaction or physical process:-

• If \(\Delta G < 0\): The process is spontaneous.
• If \(\Delta G = 0\): The system is in equilibrium.
• If \(\Delta G > 0\): The process is non-spontaneous.

In cases where adsorption is being studied, ruling out options where \(\Delta G\) is greater than zero is crucial, as those processes won't happen on their own.

Enthalpy Change

Enthalpy Change, represented by \(\Delta H\), relates to the heat absorbed or released during a process at constant pressure. For adsorption, \(\Delta H\) is usually negative, which means the process is exothermic. This indicates that heat is released when particles attach to a surface, reminiscent of how a warm hug releases comfort and warmth. Understanding whether a process is exothermic or endothermic helps in predicting the heat exchanges involved:

• If \(\Delta H < 0\): The process releases heat (exothermic).
• If \(\Delta H = 0\): No heat exchange occurs.
• If \(\Delta H > 0\): The process absorbs heat (endothermic).

In adsorption, a negative enthalpy change confirms that heat is discharged as the particles embrace the surface, aligning with lower energy flows. Hence, when solving problems concerning adsorption, looking for \(\Delta H\) less than zero is key to identifying correct scenarios.

Entropy Change

Entropy Change, denoted by \(\Delta S\), measures the change in randomness or disorder within a system caused by a reaction or process. When discussing adsorption, \(\Delta S\) is typically negative, implying a decrease in entropy. This happens because when particles become fixed on a surface, the system becomes more ordered. Imagine organizing and stacking books on a shelf - while it might appear stable and ordered, it limits the books' freedom to move around, symbolic of a decline in entropy. Entropy changes reveal the nature of molecular order during processes:

• If \(\Delta S > 0\): The process increases randomness or disorder.
• If \(\Delta S = 0\): No change in order or disorder.
• If \(\Delta S < 0\): The process leads to a more ordered system.

Given adsorption typically results in a negative entropy change, it helps in discarding any alternatives where \(\Delta S\) is positive. This understanding is critical for accurate predictions and analysis of reaction spontaneity and heat exchanges in adsorption scenarios.