Sublimation and the Vapor Pressure of Solids

Some solids, such as iodine and carbon dioxide, vaporize at atmospheric pressure without passing through the liquid state. This process is known as sublimation. Solids exhibit vapor pressures just as liquids do, but they generally have much lower vapor pressures. Solids with high vapor pressures subhme easily. The characteristic odor of a common household solid, tw-dichlorobenzene (moth repellent), is due to sublimation. The reverse process, hy which a vapor solidifies without passing through the liquid phase, is called deposition. 

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O Diagram for water. For water and a tew other substances tor which the soiid is iess dense than the iiquid, the soiid-iiquid equiiibrium iine (AB) has negative slope, that is, up and to the lett. 

0 Diagram for carbon dioxide, a substance for which the solid Is denser than the liquid. Note that the solid-liquid equilibrium line has positive slope, that Is, up and to the right. This is true for most substances. 

0 Phase changes for CO2 below and above the critical point 

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Melting Point 13-11 Heat Transfer Involving Solids 13-12 Sublimation and the Vapor Pressure of Solids... 

The Liquid State 13-3 Viscosity 13-4 Surface Tension 13-5 Capillary Action 13-6 Evaporation 13-7 Vapor Pressure 13-8 Boiling Points and Distillation 13-9 HeatTransfer Involving Liquids The Solid State 13-10 Melting Point 13-11 HeatTransfer Involving Solids 13-12 Sublimation and the Vapor Pressure of Solids... 

Liquids with high vapor pressures at ordinary temperatures are said to be volatile. Diethyl ether is highly volatile mercury is not. Solids also exert a vapor pressure, but the vapor pressures of solids are usually much lower than those of liquids because the molecules in a solid are gripped more tightly than they are in a liquid. Nevertheless, solids vaporize in the process called sublimation, which we can observe in the presence of some pungent solids—such as menthol and mothballs. 

At the triple point p, and pi, the vapor pressures of solid and liquid, respectively, are equal, and so also are the temperatures T the relative values of the slopes dp,/dT and dpi/dT are thus determined by the heats of sublimation (AH,) and of vaporization (AH,), respectively. By the first law of thermodynamics, the change of heat content in the transition solid — vapor, at a given temperature, must be the same whether it is carried out directly or through the intermediate form of liquid. Hence, AH, must be equal to AH, -b AH/, at the same temperature, so that AH, is greater than AH, the slope dp,/dT of the curve AO is thus greater than dpi/dT of the curve OB, in the vicinity of the triple point. 

Selenium(IV) chloride is a bright yellow, crystalline solid which sublimes at 196°. The solid contains [SeCl3]+ and Cl- groups.3 In the vapor state, it is completely dissociated into selenium(II) chloride and chlorine, the vapor density being half that for selenium(IV) chloride, and the vapor pressure of the solid being depressed in the presence of excess chlorine.2 The heat of formation of the solid is 46.12 kcal./mol at 18°. Selenium(IV) chloride hydrolyzes readily in moist air but is stable indefinitely in an atmosphere of dry chlorine. With anhydrous aluminum chloride it forms an addition compound which has the structure [SeCUJ+lAlCU]-.4... 

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. 

At —78.5°C, the vapor pressure of solid carbon dioxide is equal to 760 torr. The triple point is at 216.55 K and 5.112 atm. Find the average enthalpy change of sublimation. 

The equilibrium pressure when (solid + vapor) equilibrium occurs is known as the sublimation pressure, (The sublimation temperature is the temperature at which the vapor pressure of the solid equals the pressure of the atmosphere.) A norma) sublimation temperature is the temperature at which the sublimation pressure equals one atmosphere (0.101325 MPa). Two solid phases can be in equilibrium at a transition temperature (solid + solid) equilibrium, and (liquid + liquid) equilibrium occurs when two liquids are mixed that are not miscible and separate into two phases. Again, "normal" refers to the condition of one atmosphere (0.101325 MPa) pressure. Thus, the normal transition temperature is the transition temperature when the pressure is one atmosphere (0.101325 MPa) and at the normal (liquid + liquid) solubility condition, the composition of the liquid phases are those that are in equilibrium at an external pressure of one atmosphere (0.101325 MPa). 

Any one of Equations (8.14), (8.15), or (8.16) is known as the Clausius-Clapeyron equation and can be used either to obtain AH from known values of the vapor pressure as a function of temperature or to predict vapor pressures of a hquid (or a solid) when the heat of vaporization (or sublimation) and one vapor pressure are known. The same equations also represent the variation in the boiling point of a liquid with changing pressure. 

Bluish-black orthorhombic crystals refractive index 3.34 density of solid 4.933 g/cm3 at 20°C density of the element in liquid form at 120°C 3.96 g/cm melts at 113.6°C to a black mobile liquid the solid can be sublimed to vapor below its melting point vapor pressure of solid at 25°C 0.3075 torr vapor pressure at 113.6°C 90.5 torr the liquid boils at 184.3°C giving violet vapors vapor density 6.75 g/L critical temperature 545.8°C critical pressure 48.9 atm critical volume 155 cm /mol dielectric constant of solid 10.3 at 23°C and... 

The Vapor Pressure of a substance is the the pressure of its gaseous phase in equilibrium with its condensed phase. Vapor Pressure is strongly dependent on ambient temp. Thus, the boiling point of a substance is the temp at which its vapor pressure equals that of the ambient atm. The heat required to change a unit weight of solid substance to vapor is known as the heat of sublimation, and that of a unit weight of liquid is known as the heat of vaporization... 

So far we have considered only liquids. If the temperature for which the vapor pressure is to be estimated is below the melting point Tm, the liquid phase is not stable at that temperature. To find the vapor pressure of the equilibrium solid phase, we consequently must correct for the heat of melting. Sublimation is equivalent to melting of the supercooled liquid followed by vaporization, and therefore... 

Gallium(III) bromide is a hygroscopic, white solid which sublimes readily and melts at 122.5° to a covalent, dimeric liquid. The solid is ionic and its electrical conductivity at the melting point is twenty-three times that of the liquid.5 The vapor pressure of the liquid at T°K is given by the equation log p(mm.) = 8.554 — 3129/T and the heat of dissociation of the dimer in the gas phase is 18.5 kcal./mol.3 At 125° the liquid has the following properties 5,6 density, 3.1076 dynamic viscosity, 2.780 c.p. surface tension, 34.8 dynes/cm. and specific conductivity, 7.2 X 10-7 ohm-1 cm.-1 Gallium(III) bromide readily hydrolyzes in water and forms addition compounds with ligands such as ammonia, pyridine, and phosphorus oxychloride. 

Below 500 K heating of the solid salt results primarily in the vaporization of the covalent molecule as a monomer. In this temperature range the only thermal decomposition, into NOz and 02, is exhibited by the solid. The vapor is more stable. The vapor pressure of Cu(N03)2 was determined by Addison and Hathaway48 by extrapolating pressure-time curves to zero time in order to subtract the pressures of N02 and 02. These vapor pressures increased from 0.32 torr at 430 K to 3.59 torr at 405 K. A plot of log P vs. 1/T is linear and yields a sublimation enthalpy of 67.0 kJ. Above 500 K both the solid and the vapor phase decompose to N02 + 02. 

Aihara70 has measured the vapor pressure of pure solid NMA over the temperature range of 15 to 30 °C. From these data he has calculated values (298.1 K) of the free energy (20.6 kJ mol-1), enthalpy (54.1 kJ mol-1) and entropy (112 J mol-1 K-1) of sublimation for NMA. It should, however, be noted that the value determined for the enthalpy of sublimation at 298.1 K is slightly smaller than the calculated value of the enthalpy of vaporization of liquid NMA at 100 °C (cf. Section IV-b). 

The enthalpy of formation of YF3 was determined by Rudzitis, Feder, and Hubbard 164) using fluorine bomb calorimetry. NdCla was done by solution methods (179), and the enthalpies of formation of LaFs and PrFa were determined by Polyachenok 161) who employed an indirect equilibration technique. A recent torsion-effusion study of the vapor pressure of CeFs 115) yields second and third law values for the enthalpy of sublimation. The thermodynamics of the chlorination of rare earths with gaseous chlorine have also been investigated 144). Gibbs energies of formation were determined for CeClg by solid-state electromotive force techniques 41). 

If (T, P) falls on the soUd-vapor equilibrium curve, then P is the vapor pressure of the solid at temperature T, and T is the sublimation point at pressure P. 

FIGURE 10.17 The vapor pressure of a solid or liquid depends strongly on temperature. The temperature at which the vapor pressure becomes 1 atm defines the normal boiling point of a liquid and the normal sublimation point of a solid. 

Because molecules are more tightly held in a sohd, the vapor pressure of a solid is generally much less than that of the corresponding liquid. Molar heat of sublimation (AHsub) of a substance is the energy (usually in kilojoules) required to sublime one mole of a solid. It is equal to the sum of the molar heats of fusion and vaporization ... 

The vapor pressures above solid a- (201) and /S-zirconium tetra-fluoride (16) are described by the equations in Table XXIII over the temperature ranges specified. The calculated heat of sublimation for the tetrafluoride of zirconium is some 20 kcal/mole greater than the heats of sublimation of the other tetrahalides of zirconium (Table XXIII), which is consistent with the greater complexity of the fluoride solid state compared to the probable structures of the other halides in the solid state. Zirconium tetrafluoride in the gaseous state is known to be monomeric by mass spectroscopy (96). Fluorine bomb calorimetry (223, 224) has been used to determine the standard heats of formation of the tetra-fluorides ZrF4, —456.80 0.25 kcal and HfF4, —461.40 0.85 kcal. 

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