91Ó°ÊÓ

Enthalpy, often symbolized as \( H \), is a measure of the total energy of a thermodynamic system. It includes both the internal energy and the energy required to make room for it by displacing its environment. When examining changes in a system, we often talk about the change in enthalpy, \( \Delta H \). This is calculated as the difference in enthalpy between two states: state A and state B.

• State A has an enthalpy of \(-25 \text{ kJ}\).
• State B has an enthalpy of \(-20 \text{ kJ}\).

The change in enthalpy, \( \Delta H \), from state A to state B is therefore \( -20 - (-25) \), which equals \( 5 \text{ kJ}\).

A positive \( \Delta H \) suggests that energy is absorbed from the surrounding environment by the system, indicating an endothermic process. Conversely, if \( \Delta H \) were negative, it would suggest energy is released, indicative of an exothermic process. For our system, because \( \Delta H \) is positive (\(5 \text{ kJ}\)), the transition from state A to state B absorbs energy.

Entropy, denoted as \( S \), is a measure of the disorder or randomness of a system. It helps to predict the direction of spontaneous processes and is central to the second law of thermodynamics. Entropy, in essence, defines how much energy in a system is unavailable to do work.

• State A has an entropy of \(2 \text{ J} \cdot \text{K}^{-1}\).
• State B has an entropy of \(10 \text{ J} \cdot \text{K}^{-1}\).

The change in entropy, \( \Delta S \), is calculated as \( 10 - 2 = 8 \text{ J} \cdot \text{K}^{-1}\). Converting this to the same units as enthalpy yields \( \Delta S = 0.008 \text{ kJ} \cdot \text{K}^{-1}\).

A positive \( \Delta S \) signifies an increase in disorder, which often accompanies systems moving toward equilibrium and spontaneity. Here, the increase in entropy indicates the system is becoming more disordered from state A to state B.

Spontaneity in a chemical process indicates that the process can occur without external influence. The Gibbs Free Energy Change, \( \Delta G \), is key to determining spontaneity. The formula for \( \Delta G \) combines enthalpy and entropy changes: \[ \Delta G = \Delta H - T \Delta S \]where

• \( T \) is the temperature in Kelvin (\( 275 \text{ K} \))
• \( \Delta H = 5 \text{ kJ}\)
• \( \Delta S = 0.008 \text{ kJ} \cdot \text{K}^{-1}\)

Substituting into the formula produces:
\[ \Delta G = 5 \text{ kJ} - 275 \text{ K} \times 0.008 \text{ kJ} \cdot \text{K}^{-1} \] \[ \Delta G = 5 - 2.2 = 2.8 \text{ kJ} \]

Because \( \Delta G \) is positive (\( 2.8 \text{ kJ} \)), the process from state A to state B is not spontaneous. A spontaneous process would require \( \Delta G \) to be less than zero, which indicates that the system releases free energy and moves toward a more stable state on its own.