Ethyl alcohol has ΔH_fusion = 5.02 kJ/mol and melts at - 114.1 °C. What is the value of ΔS_fusion for ethyl alcohol?

Verified step by step guidance

1. Identify the formula to calculate the change in entropy (\( \Delta S \)) during the phase transition: \( \Delta S = \frac{\Delta H}{T} \).
2. Note that \( \Delta H_{\text{fusion}} \) is given as 5.02 kJ/mol.
3. Convert the melting point from Celsius to Kelvin by adding 273.15 to the Celsius temperature: \( T = -114.1 + 273.15 \).
4. Substitute the values of \( \Delta H_{\text{fusion}} \) and \( T \) (in Kelvin) into the formula: \( \Delta S = \frac{5.02 \text{ kJ/mol}}{T} \).
5. Ensure the units are consistent, typically converting \( \Delta H \) to J/mol if \( \Delta S \) is required in J/(mol·K).

Key Concepts

Enthalpy of Fusion (ΔH_fusion)

The enthalpy of fusion is the amount of energy required to change a substance from solid to liquid at its melting point. For ethyl alcohol, this value is given as 5.02 kJ/mol, indicating the energy needed to overcome intermolecular forces during the melting process.

Entropy (ΔS)

Entropy is a measure of the disorder or randomness in a system. When a solid melts into a liquid, the entropy increases because the molecules have more freedom to move. The change in entropy during fusion (ΔS_fusion) can be calculated using the relationship between enthalpy and temperature.

Gibbs Free Energy and Phase Changes

The Gibbs free energy change (ΔG) during a phase change can be expressed as ΔG = ΔH - TΔS. At equilibrium, such as at the melting point, ΔG is zero, allowing us to relate ΔH_fusion and ΔS_fusion to find the entropy change using the formula ΔS_fusion = ΔH_fusion / T, where T is the absolute temperature in Kelvin.