Sublimation pressure curve

The molar enthalpy of sublimation A// is rigorously related to the slope dpIdTof the sublimation pressure curve by the Clapeyron equation, which has been discussed in Exp. 13. The exact expression is... 

The Sh-G two-phase coexistence line, or the sublimation pressure curve, f-t, starts from the triple-point t to proceed downward toward the left. The Sh-L two-phase coexistence line, t-h, is the melting point curve. Typically the melting temperature is higher at elevated pressure, as shown in... 

Below a certain temperature, a condensate forms as a solid and not a liquid. The direct transition from a gaseous to a solid state, or vice versa, is called sublimation and the vapor pressure curve of a solid substance, the sublimation (pressure) curve (Fig. 11.9). Gas and solid are in equilibrium with each other along this phase boundary. As long as pressure remains below this curve at constant temperature during the compression of the gas, only gas will be present in the cylinder. However, if the pressure lies above this, only a solid condensate will appear. 

The other phase boundaries can also be calculated using the chemical potential. For example, the sublimation pressure curve can be described analogously to the boiling pressure curve. We only need the drive Ag,o = /sublimation entropy A gSo (both at temperature To and pressure po)-... 

Vacuum sublimation 3 2 s, g 2 Components without mixed crystals load 1 Temperature Temperature determines the vapor-pressure of the sublimable components, corresponding to the sublimation pressure curve (k)... 

An increase in the boiling point or a decrease in the freezing point of a solution containing a nonvolatile component is compared to pure solvent caused by a reduction in the vapor pressure. The reduction of the freezing point AT of a solution is T — T, as shown in Fig. 1-42 where T is the freezing point (or melting point) of the pure solvent. At Tg the vapor pressure is the same for the liquid and solid phases of the solvent. Tg is defined by the intersection A of the vapor pressure curve VC and the sublimation pressure curve SC of the solvent. If only pure solvent freezes, the freezing point T of the solution occurs at the intersection B of the vapor pressure curve of the solution VCS and the sublimation pressure curve of the solvent SC. 

VCS Solution vapor pressure curve SC Solvent sublimation pressure curve... 

The frozen product is usually granulated, sieved and then charged to the dryer. Under vacuum it is then dried either discon-tinuously on heated plates or continuously while mixed and moved over a heated surface. The pressure for moisture sublimation is about 0.1-1 mbar and essentially depends on the moisture sublimation pressure curve the partial pressure of inerts should not exceed 0.01 mbar. 

Desublimation is a pure molding process if the vapor phase contains only one component. The operating pressure and temperature of the desublimation unit are fixed by the sublimation pressure curve of the component to be treated (see Chapter 1.4.4.1). At least the heat of sublimation has to be removed during sublimation. If the vapor contains several eomponents, a partial desublimation leads after separation of the solid phase from the vapor phase to a partial separation of the original vapor mixture. 

FIGURE 4 Schematic phase diagram of a pure compound. The diagram exhibits a section around a triple point T where solid (s), liquid (I), and gaseous phases (g) are in equilibrium C is the critical point 1. g is the vapor pressure curve, s. g is the sublimation pressure curve, and s. 1 is the fusion pressure curve. 

The p T) phase diagram of carbon dioxide is presented in Fig. la [21]. On the vapor pressure curve (Ig) a liquid (1) and a gaseous (g) phase coexist. With increasing pressure the vapor pressure curve rises and ends at the critical point CP ((304.1282 0.015) K, (7.3773 0.0030) MPa, (0.4676 0.0006) g cm [22]), where the two coexisting phases (1 and g) become identical. With decreasing pressures it ends at the triple point Tr (216.58 K, 0.5185 MPa [22]), where solid, liquid, and gaseous carbon dioxide are in equilibrium. The sublimation pressure curve (gs) and the melting pressure curve (Is) are not important within the scope of the present chapter. 

To understand the conditions which control sublimation, it is necessary to study the solid - liquid - vapour equilibria. In Fig. 1,19, 1 (compare Fig. 1,10, 1) the curve T IF is the vapour pressure curve of the liquid (i.e., it represents the conditions of equilibrium, temperature and pressure, for a system of liquid and vapour), and TS is the vapour pressure curve of the solid (i.e., the conditions under which the vapour and solid are in equili-hrium). The two curves intersect at T at this point, known as the triple point, solid, liquid and vapour coexist. The curve TV represents the... 

Kirchhoffs investigation does not show that the sublimation and evaporation curves meet each other at the temperature at which solid and liquid are in equilibrium with vapour it proves that they are inclined at an angle, but the further fact that they intersect requires separate proof, which was inferred by James Thomson, and experimentally demonstrated by Ferche (1891) in the case of benzene the point of intersection, calculated from the vapour-pressure curves, was 5 405° C, whereas the melting-point was 5 42° C. 

Curve AB It is sublimation or vapour pressure curve of solid a. Along this curve, two phases a and vapour are in equilibrium. 

In this approach the standard state fugacity of a liquid or solid component is usually the fugacity of die pure solid or liquid component, and is closely related to the sublimation pressure P- b or vapour pressure P.at, respectively. I.e., on the sublimation curve of a pure component we have... 

The sublimation temperature has been estimated at 160° C.,1 160° to 165° C.,2 162-8° C.3 A thermometer suspended in the vapour of the compound which was subliming freely and condensing on the bulb showed 160° C.4 An extrapolation of the vapour pressure curve (see below) would give a somewhat higher temperature. 

It is possible to infer the shape of curves of the normal boiling (or sublimation) point (that is, the temperature at which p = 1 atmosphere) versus concentration from the vapor-pressure curves described above. Since vapor pressures increase as T increases [see equation (23)], a typical graph of p versus X at successively higher T values would show a series of curves with shapes similar to the p - X, curves of Figure A.l but at continually... 

The horizontal line at 101.3 kPa intersects the vapor pressure curve for the solid at -78.5°C. Therefore, solid carbon dioxide sublimes at this temperature. This sublimation point is equivalent to the normal boiling point of a liquid such as water. Because dry ice is at equilibrium with carbon dioxide gas at -78.5°C, it is frequently used to provide this low temperature in the laboratory. 

Another consequence of lowering of vapour pressure is that the freezing point of the solution is lower than that of the pure solvent. The freezing point of a solution is the temperature at which the solution exists in equilibrium with solid solvent. In such an equilibrium, the solvent must have the same vapour pressure in both solid and liquid states. Consequently, the freezing point is the temperature at which the vapour pressure curves of the solvent and solution intersect the sublimation curve of the solid solvent that is, points C and D, respectively, in Fig. 2.8. The freezing point depression is T-To = ATf. An expression for freezing... 

Draw a p-T chart for water. Label the following clearly vapor-pressure curve, dew-point curve, saturated region, superheated region, subcooled region, and triple point. Show where evaporation, condensation, and sublimation take place by arrows. 

The line separating the solid and liquid phases is known as the melting or freezing curve. The line separating the solid and vapor phases is known as the sublimation curve. The point where the vapor pressure curve, the melting curve, and the sublimation curves meet is the triple point. At these conditions, the solid, liquid, and vapor phases can simultaneously coexist. 

Figure 2.12 is the classic pressure-temperature (FT) representation of the phase changes of a pure component. There are three primary phases of pure components solid liquid, and vapor solid-solid transitions, liquid crystal phases, and so on, are also possible but will not be considered here. The solid lines represent the sublimation curve (solid —> vapor), the vapor pressure curve (liquid —> vapor) and the melting curve (solid liquid) of the pure component. The triangle represents the triple point, at which a solid, liquid and vapor coexist in equilibrium. The circle represents the pure component critical point, where the supercritical region begins. 

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