There is a report of a compound with an interesting melting behavior, but you’re

Question

There is a report of a compound with an interesting melting behavior, but you’re not quite sure if you should believe it. The melting point increases from 789.2 K at 700 MPa to 805 K at 1000 MPa, and has a maximum of 815 K at 1500 MPa. As the pressure is increased further, the melting point is reduced to 797.3 K at 2200 MPa. The enthalpy of fusion was measured to be 10,000 J/mol and independent of temperature (and pressure). (a) Assuming the data is correct, sketch what the melting curve (solid/liquid equilibrium line in a P-T phase diagram would look like. (3 of 25 points) (b) Assuming the data is correct, sketch what the solid and liquid G-P curves of one mole of this material would have to look like at 800 K (5 of 25 points). (c) Plausible G-P curves in (b) will show that the melting point variation is possible if the liquid phase has sufficiently greater compressibility than the solid phase. You then measure the isothermal compressibility, , which is defined as: = ! ! !" !" ! You make measurements over a large pressure range (500 – 2500 MPa). You measure 1.0 × 10-11 m2 /N for the solid and 20.0 × 10-11 m2 /N for the liquid. At 1000 MPa, you measure the molar volumes of the solid and liquid to be 5.0 × 10-6 m3 /mol and 5.5 × 10-6 m3 /mol, respectively. Is your data consistent with the melting point data? You may assume the compressibility values are independent of pressure and temperature and thermal expansion may be neglected for this small temperature range.

Explanation / Answer

Phase diagrams illustrate the variations between the states of matter of elements or compounds as they relate to pressure and temperatures.

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