Problem 80 - Chemistry and Chemical Reactivity

Question

The normal melting point of benzene, \(\mathrm{C}_{6} \mathrm{H}_{6}\), is \(5.5^{\circ} \mathrm{C}\). For the process of melting, what is the sign of each of the following? (a) \(\Delta H^{\circ}\) (c) \(\Delta G^{\circ}\) at \(5.5^{\circ} \mathrm{C}\) (c) \(\Delta G^{\circ}\) at \(25.0^{\circ} \mathrm{C}\) (b) \(\Delta S^{\circ}\) (d) \(\Delta G^{\circ}\) at \(0.0^{\circ} \mathrm{C}\)

Step-by-Step Solution

Answer

(a) ΔH° = positive, (b) ΔS° = positive, (c) ΔG° at 5.5°C = zero, (c) ΔG° at 25.0°C = negative, (d) ΔG° at 0.0°C = positive.

Step 1: Understanding Enthalpy Change (ΔH°) for Melting

Melting is an endothermic process because it requires energy to change the state from solid to liquid. Therefore, the enthalpy change \( \Delta H^\circ \) for the melting of benzene is positive. It indicates that heat is absorbed by the system.

Step 2: Evaluating Entropy Change (ΔS°) for Melting

When benzene melts, the molecules move from a more ordered (solid) state to a less ordered (liquid) state, increasing the disorder or randomness. Thus, the entropy change \( \Delta S^\circ \) is positive at the normal melting point.

Step 3: Assessing Gibbs Free Energy Change (ΔG°) at Melting Point (5.5 °C)

At the melting point of benzene, the system is in equilibrium between the solid and liquid phases. This means that the Gibbs free energy change \( \Delta G^\circ \) is zero (\( \Delta G^\circ = 0 \)) at the normal melting point, as no net change (transition) occurs.

Step 4: Determining Gibbs Free Energy Change (ΔG°) above Melting Point (25.0 °C)

Above the melting point, benzene is already melted, and the forward phase transition has occurred. The Gibbs free energy change \( \Delta G^\circ \) becomes negative, indicating that the process is spontaneous in the direction of liquid formation.

Step 5: Determining Gibbs Free Energy Change (ΔG°) below Melting Point (0.0 °C)

Below the melting point, the transformation from solid to liquid is non-spontaneous because energy needs to be supplied. Therefore, \( \Delta G^\circ \) is positive, as the process is not favored without external energy.

Key Concepts

Enthalpy Change (ΔH°)

Enthalpy Change, represented as \( \Delta H^{\circ} \), is a concept in thermodynamics that describes the heat absorbed or released during a chemical process at constant pressure. When it comes to phase changes, like melting, knowing the sign of \( \Delta H^{\circ} \) helps us understand whether energy is required or released.
When benzene, a common organic compound, melts from solid to liquid, it needs to absorb heat energy. This is because melting is an endothermic process. In simple terms, an endothermic process is one where the system absorbs energy from its surroundings. Consequently, for the melting of benzene, \( \Delta H^{\circ} \) is positive.

• Positive \( \Delta H^{\circ} \): Indicates heat is absorbed, characteristic of endothermic processes.

This absorbed energy breaks the intermolecular forces holding the solid structure together, allowing the molecules to move more freely as a liquid. Understanding the positive sign of \( \Delta H^{\circ} \) in phase transitions helps clarify why input of heat causes substances like benzene to change state.

Entropy Change (ΔS°)

Entropy Change, symbolized as \( \Delta S^{\circ} \), reflects the change in disorder or randomness of a system. As substances transition between phases, their degree of order changes, impacting entropy.
During the melting of benzene, the molecules shift from a highly ordered solid phase to a more disordered liquid phase. This increase in disorder corresponds to an increase in entropy, meaning that \( \Delta S^{\circ} \) is positive.

• Positive \( \Delta S^{\circ} \): Implies increased randomness, typical of transitions from solid to liquid.

Greater entropy indicates greater randomness and dispersion of energy within the molecules during the liquid phase. For students, acknowledging that \( \Delta S^{\circ} \) is positive during melting helps solidify the understanding of how energy dynamics and disorder interact within physical transitions.

Gibbs Free Energy Change (ΔG°)

Gibbs Free Energy Change is denoted as \( \Delta G^{\circ} \) and dictates whether a process will occur spontaneously. It's the balance of enthalpy, entropy, and temperature in determining the favorability of a chemical reaction or phase transition.
For benzene at its melting point of \( 5.5^{\circ} \mathrm{C} \), the system is in equilibrium, meaning \( \Delta G^{\circ} = 0 \). Here, the energy requirements for the forward and reverse transitions are equal – neither progressing more than the other.

• At melting point: \( \Delta G^{\circ} = 0 \) for equilibrium.

Above the melting point, \( 25.0^{\circ} \mathrm{C} \), the process becomes spontaneous towards melting, as indicated by a negative \( \Delta G^{\circ} \). In this condition, liquification is favored, and benzene tends to remain in the liquid state.

• Above melting point: \( \Delta G^{\circ} < 0 \) for spontaneous liquid formation.

Below the melting point, such as at \( 0.0^{\circ} \mathrm{C} \), the transformation is non-spontaneous with \( \Delta G^{\circ} > 0 \), signifying that without added heat, benzene will not melt.

• Below melting point: \( \Delta G^{\circ} > 0 \) for non-spontaneous melting.

Gibbs Free Energy Change is crucial for understanding the directionality and spontaneity of phase changes under varying temperatures.