For the melting point of sodium chloride, ΔHfusion = 28.16 kJ/mol and ΔSfusion = 26.22 J/(K·mol). Does NaCl melt at 1100 K? Calculate the melting point of NaCl.

Verified step by step guidance

1. Identify the relationship between the melting point, enthalpy change (\(\Delta H_{\text{fusion}}\)), and entropy change (\(\Delta S_{\text{fusion}}\)) using the equation for Gibbs free energy: \(\Delta G = \Delta H - T\Delta S\).
2. At the melting point, the system is at equilibrium, so \(\Delta G = 0\). Therefore, set the equation to 0: \(0 = \Delta H_{\text{fusion}} - T_{\text{melt}} \Delta S_{\text{fusion}}\).
3. Rearrange the equation to solve for the melting temperature \(T_{\text{melt}}\): \(T_{\text{melt}} = \frac{\Delta H_{\text{fusion}}}{\Delta S_{\text{fusion}}}\).
4. Convert \(\Delta S_{\text{fusion}}\) from J/(K·mol) to kJ/(K·mol) by dividing by 1000, so the units match with \(\Delta H_{\text{fusion}}\).
5. Substitute the given values \(\Delta H_{\text{fusion}} = 28.16\, \text{kJ/mol}\) and \(\Delta S_{\text{fusion}} = 0.02622\, \text{kJ/(K·mol)}\) into the equation to find \(T_{\text{melt}}\).

Key Concepts

Gibbs Free Energy

Gibbs Free Energy (G) is a thermodynamic potential that helps predict the spontaneity of a process at constant temperature and pressure. The relationship is given by the equation ΔG = ΔH - TΔS, where ΔH is the change in enthalpy, T is the temperature in Kelvin, and ΔS is the change in entropy. A process is spontaneous when ΔG is negative, indicating that the system can proceed without external energy input.

Phase Transition

A phase transition is a transformation between different states of matter, such as solid, liquid, and gas. The melting point is the specific temperature at which a solid becomes a liquid, characterized by the balance between the enthalpy change (ΔHfusion) and the entropy change (ΔSfusion). Understanding these changes is crucial for determining the conditions under which a substance will change phases.

Calculating Melting Point

To calculate the melting point of a substance, one can use the Gibbs Free Energy equation at equilibrium, where ΔG = 0. By rearranging the equation to T = ΔHfusion / ΔSfusion, we can find the temperature at which the solid and liquid phases coexist. This calculated temperature indicates the melting point, allowing us to determine if a given temperature, such as 1100 K, is above or below this threshold.