Calculate the entropy of fusion of a compound at 25^∘ C given that its enthalpy of fusion is 36

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Calculate the entropy of fusion of a compound at 25^∘ C...

Calculate the entropy of fusion of a compound at $25^{\circ} \mathrm{C}$ given that its enthalpy of fusion is $36 \mathrm{kJ} \mathrm{mol}^{-1}$ at its melting point of $151^{\circ} \mathrm{C}$ and the molar heat capacities (at constant pressure) of the liquid and solid forms are $33 \mathrm{J} \mathrm{K}^{-1} \mathrm{mol}^{-1}$ and $17 \mathrm{JK}^{-1} \mathrm{mol}^{-1},$ respectively.

Key Concepts

Enthalpy of Fusion

The enthalpy of fusion represents the amount of energy absorbed when a substance transitions from the solid phase to the liquid phase at its melting point. It is an intrinsic thermodynamic property that quantifies the energy barrier to melting and is typically provided at the substance's melting temperature.

Entropy of Fusion

The entropy of fusion is the change in entropy associated with the melting process of a substance. It is calculated by dividing the enthalpy of fusion by the temperature at which melting occurs, representing the increase in disorder as a substance changes from a structured solid to a more disordered liquid.

Heat Capacity Difference

The difference in heat capacities between the liquid and solid forms of a substance is crucial for adjusting thermodynamic quantities when transitioning the calculation from one temperature to another. This difference allows one to account for additional energy changes (or corrections) that occur when the substance is not at the melting temperature, enabling accurate evaluation of entropy and enthalpy at conditions away from the equilibrium phase transition point.

Temperature Correction via Integration

Temperature correction involves using the heat capacity difference to integrate and adjust thermodynamic quantities, such as entropy and enthalpy, from the melting point to another temperature. By integrating the difference in molar heat capacities over the temperature range of interest, one can accurately account for the variations in energy requirements and disorder that occur as the system moves away from the melting point.

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