Question

1) In class we considered the temperature dependence of chemical potential. Roughly sketch the chemical potential vs. pressure (y vs. x) for water at 100°C from about 1 Pa to 1 MPa. Label the appropriate regions with what phase they contain. What does the slope of these curves correspond to? Hint: It will be useful to look up the appropriate phase diagram for water over this pressure range.

Answer 1

Ans: From the theory of thermodynamics, we can write chemical potential as (2) = 0 --13 (34). - - 5 -23 where, ue chemical potential ū= molar volume Ś Molar Entropy T = Temperature P = Pressure. Now, coming to our question, chemical potential dependance on pressione, the equation (y directly telling us that, at constant vet molar volume, the chemical potential is linearly related to pressure with slope of molar volume. Phase diagram of water at 100c. Liquid Chemical potential Gas stable Liquid stable 91 1 10 100 1000 10000 0000* 106 107 Pressure (pa) P8 Here, PB = Boiling pressure of water = 100 kPa Below Pe water will be in Gas phase Above Pe= . water will be in Liquid phase

Here, the slope of dependance of chemical poteritial i molar volume. [volume occupied by one mole of a substance at given temperature and pressure). . The molar volume of solide is low and for gases it is high. So the slope is greatest for gas and least for solid and moderate for liquide. where the lines cross, phase changes. At low pressures, gases are favoured and at high pressures, solids are favoured.