At what temperature does the substance melt?
The melting point is the temperature at which the solid and liquid phases of a pure substance coexist in equilibrium at a specified pressure (often \(1~\text{atm}\)), so the substance melts at that equilibrium temperature.
Melting point as a phase-equilibrium temperature
Melting is a phase transition between an ordered solid and a less ordered liquid. At the melting point, both phases are stable at the same temperature and pressure, so the chemical potentials of the substance in the two phases are equal. The thermodynamic signature of this equilibrium can be stated using Gibbs free energy for fusion:
\[ \Delta G_{\text{fus}} = \Delta H_{\text{fus}} - T\,\Delta S_{\text{fus}}. \]
At the melting point \(T=T_m\), the phase boundary condition is \(\Delta G_{\text{fus}}=0\), giving:
\[ T_m=\frac{\Delta H_{\text{fus}}}{\Delta S_{\text{fus}}}. \]
A pure substance typically shows a sharp melting point, while mixtures and impure samples often show a melting range because composition varies between solid and liquid during the transition.
Thermodynamic calculation example
Consider a substance with \(\Delta H_{\text{fus}}=18.0~\text{kJ mol}^{-1}\) and \(\Delta S_{\text{fus}}=52.9~\text{J mol}^{-1}\text{K}^{-1}\) at \(1~\text{atm}\). Unit consistency requires joules:
\[ \Delta H_{\text{fus}} = 18.0~\text{kJ mol}^{-1} = 18.0 \times 10^{3}~\text{J mol}^{-1}. \]
\[ T_m=\frac{18.0 \times 10^{3}}{52.9}~\text{K} \approx 340~\text{K}. \]
In Celsius, \[ T_m(^{\circ}\text{C}) = 340 - 273.15 \approx 66.9~^{\circ}\text{C}. \]
Experimental determination from a heating curve
A heating curve records temperature while heat is added at a steady rate. During melting, added energy largely goes into breaking the solid structure (latent heat of fusion) rather than raising temperature, so a plateau appears. The plateau temperature corresponds to the melting point at the experimental pressure.
| Time (min) | Temperature (°C) | Phase behavior |
|---|---|---|
| 0 | 25 | Solid warming |
| 2 | 45 | Solid warming |
| 4 | 65 | Solid warming |
| 6 | 80 | Onset of melting |
| 8 | 80 | Solid + liquid present (plateau) |
| 10 | 80 | Solid + liquid present (plateau) |
| 12 | 92 | Liquid warming |
| 14 | 105 | Liquid warming |
Pressure and purity considerations
The melting point depends on pressure. The solid–liquid equilibrium slope is described by the Clapeyron relation:
\[ \frac{dT}{dP}=\frac{T\,\Delta V}{\Delta H_{\text{fus}}}. \]
Most substances show a modest pressure dependence because \(\Delta V\) for melting is usually small; water is a notable exception because ice is less dense than liquid water, giving a negative slope near \(0~^{\circ}\text{C}\).
Impurities and mixtures commonly lower the observed freezing/melting temperature and broaden the transition into a range. Colligative effects for solutions connect the freezing-point change to solute amount via \[ \Delta T_f = i\,K_f\,m, \] where \(i\) is the van ’t Hoff factor, \(K_f\) is the cryoscopic constant of the solvent, and \(m\) is molality.
Common interpretation errors
- Pressure mismatch: melting points tabulated at \(1~\text{atm}\) differ from values measured under reduced or elevated pressure.
- Sample purity effects: broadened melting ranges can mask the true equilibrium melting point of the pure substance.
- Superheating and thermal lag: rapid heating can shift the apparent plateau if temperature sensors do not track the sample temperature closely.