Question

The melting point of benzene is \(5.5^{\circ} \mathrm{C}\). Predict the signs of \(\Delta H, \Delta S\), and \(\Delta G\) for melting of benzene at: (a) \(0{ }^{\circ} \mathrm{C}\) (b) \(15^{\circ} \mathrm{C}\)

Short answer

At \\( 0^{\circ} \\\mathrm{C} \\), \\( \\Delta G > 0 \\); At \\( 15^{\circ} \\mathrm{C} \\), \\( \\Delta G < 0 \\).

Step-by-step solution

Understanding Melting Parameters

Melting is an endothermic process because energy is absorbed to break the solid structure. Therefore, the change in enthalpy \( \Delta H \) is positive. Also, since the solid phase becomes more disordered as it turns into a liquid, the change in entropy \( \Delta S \) is also positive.

Determine \\( \\Delta G \\) at lower temperatures

At temperatures below the melting point, \( \Delta G = \Delta H - T \Delta S \) is positive because the process is not spontaneous. Therefore, at \( 0^{\circ} \mathrm{C} \), since it's below benzene's melting point, \( \Delta G > 0 \).

Determine \\( \\Delta G \\) at higher temperatures

At temperatures above the melting point, \( \Delta G = \Delta H - T \Delta S \) is negative because the process becomes spontaneous. Therefore, at \( 15^{\circ} \mathrm{C} \), which is above benzene's melting point, \( \Delta G < 0 \).

Conclusion for \\( 0{ }^{\\circ} \mathrm{C} \\)

For \( 0^{\circ} \mathrm{C} \, \Delta H > 0 \), \( \Delta S > 0 \), and \( \Delta G > 0 \). The melting is non-spontaneous as \( 0^{\circ} \mathrm{C} \) is below the melting point.

Conclusion for \\( 15{ }^{\\circ} \mathrm{C} \\)

For \( 15^{\circ} \mathrm{C} \, \Delta H > 0 \), \( \Delta S > 0 \), and \( \Delta G < 0 \). The melting is spontaneous since \( 15^{\circ} \mathrm{C} \) is above the melting point.

Key concepts

Enthalpy Change

In thermodynamics, enthalpy change \( \Delta H \) refers to the heat absorbed or released in a process at constant pressure. For processes like melting, where a substance transitions from solid to liquid, the process is endothermic. This means it absorbs energy to overcome the structured bonds in the solid phase. As a result, the enthalpy change for melting is always positive.

• Think of \( \Delta H \) as capturing the energy cost needed to break bonds or change states.
• For benzene melting, since energy is absorbed to transition from solid to liquid, \( \Delta H \) is positive.

This absorption is necessary because the particles in a liquid are more dispersed and move more freely compared to in a solid. Understanding \( \Delta H \) as a measure of the energy involved in these transitions helps predict how a process behaves under different conditions.

Entropy Change

Entropy change \( \Delta S \) details how much disorder or randomness increases in a system. When a substance melts, like benzene, it goes from a tightly bound solid to a more loosely arranged liquid. This increase in disorder results in a positive change in entropy.

• Entropy is often seen as a measure of randomness or disorder within a system.
• A solid has a structured, ordered arrangement; in contrast, a liquid is more fluid and unstructured.

Thus, when benzene melts, \( \Delta S \) is positive, indicating that the new liquid state is more disorganized than the solid state. Keeping this concept in mind, \( \Delta S \) signifies nature’s tendency to lean towards more randomness, especially during phase changes such as melting.

Gibbs Free Energy

Gibbs free energy \( \Delta G \) offers insight into whether a process or reaction is spontaneous. It's determined by the equation \( \Delta G = \Delta H - T \Delta S \), where \( T \) represents temperature in Kelvin.

• Spontaneity means a process can occur without needing an external influence.
• When \( \Delta G < 0 \), the process is spontaneous; \( \Delta G > 0 \) indicates a non-spontaneous process.

In the case of benzene, at temperatures below its melting point (e.g., \( 0^{\circ} \mathrm{C}\)), \( \Delta G \) is positive, reflecting that the melting isn't spontaneous. Conversely, if the temperature is above the melting point (e.g., \( 15^{\circ} \mathrm{C}\)), \( \Delta G \) becomes negative, signifying that melting can happen spontaneously. By understanding \( \Delta G \), you gain a window into the thermodynamic feasibility and behavior of phase transitions like melting under varying temperature conditions.