Calculate the enthalpy of fusion of naphthalene (C10 H8) given that its melting point is 128^∘ C

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Calculate the enthalpy of fusion of naphthalene (C10 H8)...

Calculate the enthalpy of fusion of naphthalene $\left(\mathrm{C}_{10} \mathrm{H}_{8}\right)$ given that its melting point is $128^{\circ} \mathrm{C}$ and its entropy of fusion is 47.7 $\mathrm{J} /(\mathrm{K} \cdot \mathrm{mol})$ .

Key Concepts

Enthalpy of Fusion

Enthalpy of fusion is the amount of energy required to convert a substance from its solid phase to its liquid phase at its melting point. It is typically expressed in units of J/mol or kJ/mol and represents the latent heat absorbed during the phase change without a change in temperature.

Entropy of Fusion

Entropy of fusion quantifies the change in disorder or randomness of a substance as it melts. It is defined as the entropy change per mole during the melting process and is expressed in units of J/(K·mol). A higher entropy of fusion indicates a greater increase in disorder from the solid to the liquid phase.

Melting Temperature and Unit Conversion

The melting temperature is the specific temperature at which a substance changes from solid to liquid under standard pressure. Since thermodynamic calculations require absolute temperatures, the melting point given in degrees Celsius must be converted to Kelvin, which is done by adding 273.15 to the Celsius value.

Thermodynamic Relationship at the Melting Point

At the melting point, a substance is in equilibrium between its solid and liquid phases. This equilibrium condition leads to the thermodynamic relation ?H = T?S, where ?H is the enthalpy of fusion, T is the melting temperature in Kelvin, and ?S is the entropy of fusion. This relation allows for the calculation of one quantity if the other two are known.

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