What is the melting point of benzene in kelvin if ΔH_fusion = 9.95 kJ/mol and ΔS_fusion = 35.7 J/(K mol)?

Verified step by step guidance

1. Identify the relationship between the melting point, enthalpy of fusion (\( \Delta H_{\text{fusion}} \)), and entropy of fusion (\( \Delta S_{\text{fusion}} \)). The melting point is the temperature at which the solid and liquid phases are in equilibrium, meaning \( \Delta G = 0 \).
2. Use the Gibbs free energy equation at equilibrium: \( \Delta G = \Delta H - T \Delta S = 0 \).
3. Rearrange the equation to solve for the temperature (melting point, \( T \)): \( T = \frac{\Delta H}{\Delta S} \).
4. Substitute the given values into the equation: \( \Delta H_{\text{fusion}} = 9.95 \text{ kJ/mol} \) and \( \Delta S_{\text{fusion}} = 35.7 \text{ J/(K mol)} \).
5. Convert \( \Delta H_{\text{fusion}} \) from kJ/mol to J/mol by multiplying by 1000, then calculate \( T \) using the rearranged equation.

Key Concepts

Phase Change and Melting Point

The melting point is the temperature at which a solid becomes a liquid at a given pressure. For substances like benzene, this is a critical phase transition point where the solid structure breaks down into a liquid state. Understanding the melting point is essential for predicting the behavior of substances under varying temperature conditions.

Gibbs Free Energy and Phase Equilibrium

The Gibbs free energy change (ΔG) determines the spontaneity of a phase change. At equilibrium, ΔG is zero, which can be expressed using the equation ΔG = ΔH - TΔS. Here, ΔH is the enthalpy change and ΔS is the entropy change. This relationship is crucial for calculating the melting point using the provided enthalpy and entropy values.

Thermodynamic Relationships

The relationship between enthalpy (ΔH), entropy (ΔS), and temperature (T) is fundamental in thermodynamics. The melting point can be calculated using the formula T = ΔH/ΔS, where ΔH is the heat absorbed during fusion and ΔS is the change in entropy. This equation allows us to find the temperature at which the solid and liquid phases coexist in equilibrium.