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

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Answer 1 · 2017-08-27T19:51:06

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.

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.