Phase change solid-liquid equilibria

Vapor pressure Partitioning between phases solubility of a gas in a liquid sorption of a solute in a fluid onto a sorbent Chemical reaction equilibrium Electric charge Phase change solid/liquid liquid/gas Diffusivity Ionic mobility Molecular size and shape... 

Experience indicates that the Third Law of Thermodynamics not only predicts that So — 0, but produces a potential to drive a substance to zero entropy at 0 Kelvin. Cooling a gas causes it to successively become more ordered. Phase changes to liquid and solid increase the order. Cooling through equilibrium solid phase transitions invariably results in evolution of heat and a decrease in entropy. A number of solids are disordered at higher temperatures, but the disorder decreases with cooling until perfect order is obtained. Exceptions are... 

Under certain pressure and temperature conditions, a system can contain two or more phases in equilibrium. An example is the temperature and pressure where solid and liquid are in equilibrium. We refer to this condition as (solid + liquid) equilibrium, and the temperature as the melting temperature. This temperature changes with pressure and with composition. The melting temperature when the... 

For the solid-liquid system changes of the state of interface on formation of surfactant adsorption layers are of special importance with respect to application aspects. When a liquid is in contact with a solid and surfactant is added, the solid-liquid interface tension will be reduced by the formation of a new solid-liquid interface created by adsorption of surfactant. This influences the wetting as demonstrated by the change of the contact angle between the liquid and the solid surface. The equilibrium at the three-phase contact solid-liquid-air or oil is described by the Young equation ... 

An exceptional case of a very different type is provided by helium [15], for which the third law is valid despite the fact that He remains a liquid at 0 K. A phase diagram for helium is shown in Figure 11.5. In this case, in contrast to other substances, the solid-liquid equilibrium line at high pressures does not continue downward at low pressures until it meets the hquid-vapor pressure curve to intersect at a triple point. Rather, the sohd-hquid equilibrium line takes an unusual turn toward the horizontal as the temperature drops to near 2 K. This change is caused by a surprising... 

PI4.2 Given the following (solid + liquid) equilibrium temperatures for phase changes in the JC1CFCI3 + X2HCON(CH3)2 system 7... 

Equation (25.7) now gives an expression for the rate of change of pressure with temperature (= dP/dT ) which corresponds to the gradient of the line representing the solid-liquid equilibrium in the phase diagram (gradient of AD Figure 25.1). This quantitative equation (25.7) now enables us to rationalise that since ... 

The most common example of a solid-liquid equilibrium is ice and water. In a well-stirred system of ice and water, the temperature remains at 0°C as long as both phases are present. The melting point changes only slightly with pressure unless the pressure change is very large. 

The more important calorimeters used for measuring heats of adsorption are phase-change calorimeters, such as the Bunsen-type ice calorimeter. More recently, phase-change calorimeters using diphenyl ether as the calorimetric fluid are commonly used. In these calorimeters, the calorimetric fluid exists in a solid-liquid equilibrium state so that the heat evolved as a result of adsorption melts a corresponding amount of the solid fluid and causes a movement of mercury in the capillary tube connected to the calorimeter. This mercury movement in the capillary is first calibrated by standard reactions so that the movement of the thread of mercury in the capillary directly gives the amount of heat evolved. 

The principal business of this chapter is to establish the thermodynamic relations obeyed by two or more phases that are at equilibrium with each other. A phase is a portion of a system (or an entire system) inside which intensive properties do not change abruptly as a function of position. The principal kinds of phases are solids, liquids, and gases, although plasmas (ionized gases), liquid crystals, and glasses are sometimes considered to be separate types of phases. Solid and liquid phases are called condensed phases and a gas phase is often called a vapor phase. Several elements such as carbon exhibit solid-phase allotropy. That is, there is more than one kind of solid phase of the element. For example, diamond and graphite are both solid carbon, but have different crystal structures and different physical properties. With compounds, this phenomenon is called polymorphism instead of allotropy. Most pure substances have only one liquid phase, but helium exhibits allotropy in the liquid phase. 

In the three areas of the phase diagram labeled solid, liquid, and vapor, only one phase is present. To understand this, consider what happens to an equilibrium mixture of two phases when the pressure or temperature is changed. Suppose we start at the point on AB... 

Changing the pressure will have a similar effect. If we increase p by dp, the solid melts. This process can be reversed at any time by decreasing the pressure by dp. Note that at p = 1 atm (101.325 kPa), only at T = 273.15 K can the phase change be made to occur reversibly because this is the temperature where solid and liquid are in equilibrium at this pressure. If we tried to freeze liquid water aip— atm and a lower temperature such as 263.15 K, the process, once started, would proceed spontaneously and could not be reversed by an infinitesimal change in p or T. 

Solution (a) At 7 — 600 K, liquid Sn freezes at 3 GPa to form solid III. Apparently, no other phase changes occur with increasing pressure, (b) At 550 K, liquid Sn freezes to form solid II at 1.5 GPa, then changes to solid III at 3.5 MPa. (c) At 250 K, solid I converts to solid II at 0.3 GPa, which presumably would convert to solid III at approximately 11 MPa. (The equilibrium line stops at 10 GPa.)... 

A triple point is a point where three phase boundaries meet on a phase diagram. For water, the triple point for the solid, liquid, and vapor phases lies at 4.6 Torr and 0.01°C (see Fig. 8.6). At this triple point, all three phases (ice, liquid, and vapor) coexist in mutual dynamic equilibrium solid is in equilibrium with liquid, liquid with vapor, and vapor with solid. The location of a triple point of a substance is a fixed property of that substance and cannot be changed by changing the conditions. The triple point of water is used to define the size of the kelvin by definition, there are exactly 273.16 kelvins between absolute zero and the triple point of water. Because the normal freezing point of water is found to lie 0.01 K below the triple point, 0°C corresponds to 273.15 K. 

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