# What does a positive or negative liquid-solid slope indicate in a phase diagram?

Aug 27, 2017

When you already know the $\Delta \overline{H}$ for the phase transition, you will know whether the solid is more dense or less dense than the liquid.

Consider the phase diagram of water.

The liquid-solid coexistence curve is $\overline{A D}$, and the slope of a any two-phase equilibrium curve is given by the Clapeyron equation:

$\frac{\mathrm{dP}}{\mathrm{dT}} = \frac{\Delta \overline{H}}{T \Delta \overline{V}}$

Consider $\overline{A D}$.

• We know that the enthalpy of fusion for melting water is $\Delta {\overline{H}}_{\text{fus" = "6.02 kJ/mol}}$, or $\text{60.20 L"cdot"bar/mol}$, a positive quantity.
• We also know that the temperature $T$ in $\text{K}$ must be positive.

Since the slope of $\overline{A D}$ is negative, i.e. $\frac{\mathrm{dP}}{\mathrm{dT}} < 0$, we can say that:

(-) = ((+))/((+)(?))

Thus, the change in molar volume $\Delta \overline{V}$ for melting ice is negative.

In other words, ice contracts when it melts and water expands when it freezes.