Problem 72 - 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) \(\Delta H^{\circ}\) (b) \(\Delta S^{\circ}\) (c) \(\Delta G^{\circ}\) at \(5.5^{\circ} \mathrm{C}\) (d) \(\Delta G^{\circ}\) at \(0.0^{\circ} \mathrm{C}\) (e) \(\Delta G^{\circ}\) at \(25.0^{\circ} \mathrm{C}\)

Step-by-Step Solution

Answer

(a) Positive, (b) Positive, (c) Zero, (d) Positive, (e) Negative.

Step 1: Understanding the Concepts

Before solving the exercise, it's important to understand that the process of melting (fusion) is endothermic, which means heat is absorbed. This implies that \(\Delta H^{\circ}\) is positive. Melting also increases the randomness of the system, which means \(\Delta S^{\circ}\) is positive. \(\Delta G^{\circ}\) at the melting point is zero.

Step 2: Evaluating \(\Delta H^{\circ}\) for Melting

For the process of melting, the enthalpy change, \(\Delta H^{\circ}\), represents the heat absorbed. Since melting is endothermic, \(\Delta H^{\circ}\) is positive.

Step 3: Evaluating \(\Delta S^{\circ}\) for Melting

During melting, the disorder of the system increases as solid transforms into liquid. Therefore, the entropy change, \(\Delta S^{\circ}\), is positive.

Step 4: Evaluating \(\Delta G^{\circ}\) at the Melting Point

At the melting point of a substance, the process is at equilibrium. Therefore, the Gibbs free energy change, \(\Delta G^{\circ}\), is zero at \(5.5^{\circ} \mathrm{C}\).

Step 5: Evaluating \(\Delta G^{\circ}\) Below the Melting Point (0.0°C)

Below the melting point, the solid is more stable than the liquid form, so melting is non-spontaneous. This means \(\Delta G^{\circ}\) is positive at \(0.0^{\circ} \mathrm{C}\).

Step 6: Evaluating \(\Delta G^{\circ}\) Above the Melting Point (25.0°C)

Above the melting point, the liquid is more stable than the solid, so melting is spontaneous. This means \(\Delta G^{\circ}\) is negative at \(25.0^{\circ} \mathrm{C}\).

Key Concepts

Enthalpy

Enthalpy (\(\Delta H\)) is a core concept in thermodynamics, especially when we talk about changes during a chemical reaction or physical process. It represents the total heat content of a system.

In the context of melting, like when benzene changes from solid to liquid at its melting point, enthalpy change tells us how much heat is absorbed. Melting is an endothermic process, meaning it requires heat. As a result:

• \(\Delta H^{\circ}\) for melting is positive because heat is gained by the substance.
• This absorbed heat is necessary to overcome the forces keeping the molecules in a solid structure.

Understanding this helps in predicting whether heat will be absorbed or released during different processes, making enthalpy a crucial part of thermodynamics.

Entropy

Entropy (\(\Delta S\)) measures the degree of chaos or disorder within a system. It's a fundamental aspect of the second law of thermodynamics, which states that the entropy of an isolated system will tend to increase over time.

When a substance like benzene melts, it transitions from a structured, orderly solid to a more disordered liquid form. This change in structure naturally leads to an increase in entropy:

• \(\Delta S^{\circ}\) for melting is positive, as the disorder increases with melting.
• This increase in disorder signifies that the molecules have more freedom to move around in the liquid state.

The concept of entropy is key to understanding why certain processes occur spontaneously and how energy is distributed in physical systems.

Gibbs Free Energy

Gibbs Free Energy (\(\Delta G\)) combines enthalpy and entropy into one value, determining whether a process is spontaneous. It's calculated through the equation:\[\Delta G = \Delta H - T\Delta S\]where \(T\) is the temperature in Kelvin.

For benzene:

• At the melting point (\(5.5^{\circ}C\)), \(\Delta G^{\circ}\) is zero, indicating equilibrium between the solid and liquid phases.
• Below \(5.5^{\circ}C\), \(\Delta G^{\circ}\) is positive, meaning the liquid to solid transition is non-spontaneous.
• Above \(5.5^{\circ}C\), \(\Delta G^{\circ}\) is negative, indicating melting is spontaneous as the liquid phase becomes more favorable.

Understanding these conditions helps predict and control reactions and phase changes in various chemical processes, making Gibbs Free Energy a vital tool in chemistry and thermodynamics.