Question

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

Answer 1

When you already know the `DeltabarH` for the phase transition, you will know whether the solid is more dense or less dense than the liquid.

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Consider the phase diagram of water.

The liquid-solid coexistence curve is `bar(AD)`, and the slope of a any two-phase equilibrium curve is given by the Clapeyron equation:

`(dP)/(dT) = (DeltabarH)/(TDeltabarV)`

Consider `bar(AD)`.

• We know that the enthalpy of fusion for melting water is `DeltabarH_"fus" = "6.02 kJ/mol"`, or `"60.20 L"cdot"bar/mol"`, a positive quantity.
• We also know that the temperature `T` in `"K"` must be positive.

Since the slope of `bar(AD)` is negative, i.e. `(dP)/(dT) < 0`, we can say that:

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

Thus, the change in molar volume `DeltabarV` for melting ice is negative.

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