91Ó°ÊÓ

In thermodynamics, Gibbs Free Energy, denoted as \( \Delta G^{\circ} \), is a measure that determines the spontaneity of a reaction. It connects the enthalpy change \( \Delta H^{\circ} \), the entropy change \( \Delta S^{\circ} \), and the temperature \( T \) in Kelvin. The formula representing this relationship is given by:

• \( \Delta G^{\circ} = \Delta H^{\circ} - T \Delta S^{\circ} \)

This equation helps in predicting whether a process will occur spontaneously:

• If \( \Delta G^{\circ} < 0 \), the reaction is spontaneous.
• If \( \Delta G^{\circ} > 0 \), the reaction is non-spontaneous.

In simpler terms, a negative \( \Delta G^{\circ} \) indicates a reaction that can proceed without needing an external energy input. In our example of calculating \( \Delta G^{\circ} \) at different temperatures, we saw an increase in \( \Delta G^{\circ} \) as temperature rose to 10 K, 100 K, and 1000 K, indicating a decrease in the spontaneity of the endothermic process with increasing temperature.

Endothermic reactions are those that absorb heat from their surroundings, resulting in a positive change in enthalpy, \( \Delta H^{\circ} > 0 \). This increase in enthalpy means the system gains energy from external sources to transform reactants into products.
In the context of the exercise, with \( \Delta H^{\circ} = +15 \) kJ, the reaction absorbs 15,000 J of energy. Additionally, the entropy change \( \Delta S^{\circ} \) is negative \((-150 \, \text{J/K})\), signifying a decrease in disorder or randomness in the system during the reaction.

Endothermic reactions can often be observed in everyday processes such as:

• Melting of ice into water
• Evaporation of water
• Photosynthesis in plants

These processes are crucial for various natural and industrial activities. The combination of a positive \( \Delta H^{\circ} \) and negative \( \Delta S^{\circ} \) typically means that the Gibbs Free Energy \( \Delta G^{\circ} \) is positive at a given temperature, pointing to a decrease in spontaneity at constant temperature and pressure.

The equilibrium constant, denoted as \( K_{\text{eq}} \), is a dimensionless number that expresses the ratio of the concentrations of products to reactants at equilibrium. It provides valuable information about the position of a chemical equilibrium.

• A high \( K_{\text{eq}} \) indicates the equilibrium position lies towards the products, meaning the reaction proceeds almost to completion.
• A low \( K_{\text{eq}} \) suggests the equilibrium position favors the reactants.

Using Gibbs Free Energy, \( K_{\text{eq}} \) is calculated through the relationship:

• \( \Delta G^{\circ} = -RT \ln K_{\text{eq}} \)

Solving for \( K_{\text{eq}} \), we have:

• \( K_{\text{eq}} = e^{-\frac{\Delta G^{\circ}}{RT}} \)

Where:

• \( R = 8.314 \, \text{J/mol K} \) is the universal gas constant


• \( T \) is the temperature in Kelvin

In the provided exercise, due to the large positive \( \Delta G^{\circ} \), \( K_{\text{eq}} \) was very small across all temperatures. Consequently, the equilibrium lies significantly on the side of the reactants, showing the observable effect of the negative entropy and endothermic nature of the reaction on \( K_{\text{eq}} \).