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Phases Diagrams

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Phase Diagrams

A diagram showing the various phases of a system is called a phase diagram. Phase diagrams for a pure compound such as phase diagrams for water and carbon dioxide are phase diagrams for a single component system. In these diagrams, pressure (P) and temperature (T) are usually the coordinates. The phase diagrams usually show the (P, T) conditions for stable phases.

Phase diagrams are useful for material engineering and material applications. With their aid, scientists and engineers understand the behavior of a system which may contain more than one component (compounds). Multicomponent phases diagrams show the conditions for the formation of solutions and new compounds. Thus, phase equilibria is still a field of research, and there is a Journal of Phase Equilibria for the publication of these research results.

At this introduction point, we take a look of the behavior of water and carbon dioxide when the temperature and pressure are changing.

Phase Diagram of Water

The phase diagram of water is shown here. It shows that at low temperature, (solid) ice is the stable phase. At moderate temperatures and high pressure, (liquid) water is the stable phase, and at high temperature and low pressure, (gas) vapor is the stable phase. Lines separate these phases. We discuss these items separately below.

The sublimation curve separate the solid from the gas. This line indicates the vapor pressure of ice as a function of temperature. The relationship can be shown in table or graph form. The diagram is a sketch, and the following table gives more accurate numbers.

Vapor Pressure P in mm Hg of Ice at Temperature T in K
T KP in mm HgT KP in mm HgT KP in mm Hg
1900.000252611.6322713.880
2000.00122621.785 2724.217
2100.00532631.950 272.54.40
2200.026 2642.131 2734.579
2300.074 2652.326
2400.25 2662.537
2450.351 2672.765
2500.58 2683.103
2550.939 2693.280
2601.49 2703.568

The vaporization curve is a plot of (equilibrium) vapor pressure P as a function of temperature T. The equilibrium vapor pressure at various temperature has been carefully measured, and a detail table can be found in the CRC Hand Book of Chemistrty and Physics. A simplified table is given here.

Vapor Pressure P in mm Hg of Water at Temperature T in K
T KP in mm HgT KP in mm HgT KP in mm HgT KP in mm Hg
2734.579* 31047.067370682.07400682.07
2744.926 32079.60 371707.2750019848.92
2755.294 330129.82372733.2460092826.40
2807.513 340204.96373760.00*
29014.53 350314.1 374787.57647165467.20*
30026.74 360468.77375815.86
---
*Tripple point 273 K, Normal boiling point 373 K, Critical point 674 K.

Note that the vapor pressures for ice and water at 273 K (0oC) are the same 4.579 mm Hg (torr). At this temperature, all three phases (ice, water, and vapor coexist. The teperature and pressure (4.579 torr) are fixed.

At temperature greater than 647 K, water cannot be liquified. The fluid shares the properties of gas. Thus, no vapor pressure beyond this temperature is measured. The temperature of 647 K is called the critical temperature, and the vapor pressure at this temperature is called the critical pressure.

The melting curve or fusion curve of ice/water is very special. It has a negative slope due to the fact that when ice melt, the molar volume decreases. Ice actually melt at lower temperature at higher pressure. Most Canadians skate, and the liquid formed between the skate and ice act as a lubricate so that the skater moves gracefully accross the ice. The skate apply a very high pressure on to the ice.

Phase Diagram of Carbon Dioxide

The phase diagram of CO2 has some common features with that of water: sublimation curve, vaporization curve, triple point, critical temperature and pressure. Of course, the P and T values of are unique to carbon dioxide. The phase diagrams of water and carbon dioxide are compared here.

The triple point of carbon dioxide occure at a pressure of 5.2 atm (3952 torr) and 216.6 K (-56.4oC). At temperature of 197.5 K (-78.5oC), the vapor pressure of solid carbon dioxide is 1 atm (760 torr). At this pressure, the liquid phase is not stable, the solid simply sublimates. Thus solid carbon dioxide is called dry ice, because it does not go through a liquid state in its phase transition at room pressure.

The critical temperature for carbon dioxide is 31.1°C, and the critical pressure is 73 atm. Above the critical temeprature, the fluid is called super-critical fluid.

To be more precise, the various point of the phase diagram are further descibed below. In the phase diagram of (a) H2O and (b) CO2, the axes are not drawn to scale. In (a), for water, note the triple point A (0.0098°C, 4.58 torr), the normal melting (or freezing) point B (0°C, 1 atm), the normal boiling point C (100°C, 1 atm), and the critical point D (374.4°C, 217.7 atm). In (b), for carbon dioxide, note the triple point X(-56.4°C, 5.11 atm), the normal sublimation point Y(-78.5°C, 1 atm), and the critical point Z (31.1°C, 73.0 atm).

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