For the melting of aluminum, Al(s) ⟶Al(l), ΔH^∘= 10.0 kJ mol^-1 and ΔS^∘=9.50 J / mol K. Calc

step 1 Okay, so this question is exactly similar to the previous one. We have the change in enthalpy an

For the melting of aluminum, Al(s) ⟶Al(l), ΔH^∘= 10.0 kJ...

For the melting of aluminum, $\mathrm{Al}(s) \longrightarrow \mathrm{Al}(l), \Delta H^{\circ}=$ $10.0 \mathrm{~kJ} \mathrm{~mol}^{-1}$ and $\Delta S^{\circ}=9.50 \mathrm{~J} / \mathrm{mol} \mathrm{K}$. Calculate the melting point of Al. (The actual melting point is $660^{\circ} \mathrm{C}$.)

For the melting of aluminum, $\mathrm{Al}(s) \longrightarrow \mathrm{Al}(l), \Delta H^{\circ}=$
$10.0 \mathrm{~kJ} \mathrm{~mol}^{-1}$ and $\Delta S^{\circ}=9.50 \mathrm{~J} / \mathrm{mol} \mathrm{K}$. Calculate the
melting point of Al. (The actual melting point is $660^{\circ} \mathrm{C}$.)

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Key Concepts

Enthalpy Change (?H)

Enthalpy change represents the heat absorbed or released during a process at constant pressure. In the context of phase transitions like melting, ?H quantifies the energy required to overcome intermolecular forces during the change from a solid to a liquid state.

Entropy Change (?S)

Entropy change measures the increase in disorder or the number of accessible microstates during a process. During melting, the system gains disorder as it transitions from a structured solid to a less structured liquid, and ?S quantifies this change.

Gibbs Free Energy and Equilibrium

The concept of Gibbs free energy (?G) is vital in determining the spontaneity of a process and its equilibrium state. At equilibrium, for a phase change such as melting, ?G equals zero, which leads to the relation ?H = T?S. This equilibrium condition is foundational in thermodynamics for calculating transition temperatures.

Temperature Determination from Thermodynamic Data

Using the relation from the Gibbs free energy equation at equilibrium (?H = T?S), one can calculate the melting temperature by dividing the enthalpy change by the entropy change. This method is a fundamental application of thermodynamic principles to predict phase transition temperatures.

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