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

step 1 For this question, we need to recognize that the melting point is an equilibrium point, and any

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 $\Delta S^{\circ}=9.50 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$ 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 $\Delta S^{\circ}=9.50 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$
Calculate the melting point of Al. (The actual melting point is $660^{\circ} \mathrm{C}$.)

Key Concepts

Melting Point Calculation

The melting point, or phase transition temperature, can be determined by setting the Gibbs free energy change to zero (?G = 0) during melting. This leads to the relationship T = ?H/?S, which provides a method to compute the melting point when the enthalpy and entropy changes are known, emphasizing the interplay of thermodynamic quantities in phase transitions.

Entropy Change

Entropy change, represented by ?S, measures the change in disorder or randomness in a system during a process. During melting, the increase in entropy reflects the transition from the ordered structure of a solid to the more disordered arrangement of a liquid, thereby favoring the process at higher temperatures.

Enthalpy Change

Enthalpy change, often denoted as ?H, represents the heat absorbed or released during a process at constant pressure. In the context of a phase transition like melting, ?H corresponds to the energy required to overcome intermolecular forces, enabling the substance to change from a solid to a liquid state.

Thermodynamic Equilibrium

Thermodynamic equilibrium is the state in which a system's macroscopic properties remain constant over time because the forward and reverse processes occur at the same rate. In phase transitions, equilibrium is reached when the driving forces for change, as described by Gibbs free energy, balance out, resulting in a ?G of zero.

Gibbs Free Energy

Gibbs free energy is a thermodynamic potential that predicts the spontaneity of a process. The relationship ?G = ?H - T?S encapsulates how enthalpy, entropy, and temperature interact to determine whether a process will occur spontaneously. At equilibrium, particularly during a phase transition such as melting, ?G equals zero.

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