Sublimation, equilibrium

For a reaction with positive gas mole change, Eq. (47) indicates that Kx decreases with pressure. Because ce is a monotonically increasing function of Kx, the equilibrium extent of a reaction with positive Avgas always decreases as pressure is increased. This is an example of Le Chatelier s principle, which states that a reaction at equilibrium shifts in response to a change in external conditions in a way that moderates the change. In this case, because the reaction increases the number of moles of gas and thus the pressure, the reaction shifts back to reactants. The isothermal compressibility of a reactive system can, therefore, be much greater than that of a nonreactive system. This effect can be dramatic in systems with condensed phases. For example, in the calcium carbonate dissociation discussed in Example 12, if the external pressure is raised above the dissociation pressure of C02, the system will compress down to the volume of the solid. Of course, a similar effect is observed in simple vaporization or sublimation equilibrium. As the pressure on water at 100°C is increased above 1.0 atm, all vapor is removed from the system. 

The corresponding rule of Le Chatelier and Matignon holds for the sublimation equilibrium AS 32 cal/mole degree. 

Gas-solid equilibrium for a single-component system is commonly referred to as sublimation equilibrium. Sublimation pressure, the vapor pressure of a solid, is basic to the modeling of solid-gas equilibrium. Sublimation pressure changes with temperature by an equation similar to that of the vapor pressure of a liquid. Equation (4.453),... 

The fugacity of the solid at sublimation equilibrium is equal to the fugacity of the pure saturated vapor and is therefore also given by EquaQon (4.531),... 

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... 

Enthalpy of Vaporization (or Sublimation) When the pressure of the vapor in equilibrium with a liquid reaches 1 atm, the liquid boils and is completely converted to vapor on absorption of the enthalpy of vaporization ISHv at the normal boiling point T. A rough empirical relationship between the normal boiling point and the enthalpy of vaporization (Trouton s rule) is ... 

Vapor pressure is the most important of the basic thermodynamic properties affec ting liquids and vapors. The vapor pressure is the pressure exerted by a pure component at equilibrium at any temperature when both liquid and vapor phases exist and thus extends from a minimum at the triple point temperature to a maximum at the critical temperature, the critical pressure. This section briefly reviews methods for both correlating vapor pressure data and for predicting vapor pressure of pure compounds. Except at very high total pressures (above about 10 MPa), there is no effect of total pressure on vapor pressure. If such an effect is present, a correction, the Poynting correction, can be applied. The pressure exerted above a solid-vapor mixture may also be called vapor pressure but is normallv only available as experimental data for common compounds that sublime. 

Pteridine [91-18-9] M 132.2, m 139.5-140°, pKj 4.05 (equilibrium, hydrate), pK 11,90 (OH of hydrate). Crystd from EtOH, benzene, n-hexane, n-heptane or pet ether. It sublimes at 120-130°/20mm. Stored at 0°, in the dark turns green in the presence of light and on long standing in the dark. 

Quinazoline [253-82-7] M 130.2, m 48.0-48.5 , b 120-121 /17-18mm, pK, -4.51 (aq H2SO4, anhydrous dication), pK 2.01 (anhydrous monocation), pK3 4.3 (equilibrium with 3,4-hydrated species), PK4 12.1 (hydrated anion). Purified by passage through an activated alumina column in benzene or pet ether (b 40-60°). Distd under reduced pressure, sublimed under vacuum and crystd from pet ether. [Armarego 7 Chem 1170 1961.]... 

The lower halides of Bi are rather different. The diatomic species BiX (X = Cl, Br, I) occur in the equilibrium vapour above heated Bi-BiX3 mixtures. A black crystalline lower chloride of composition BiCli.iev is obtained by heating Bi-BiCls mixtures to 325° and cooling them during 1-2 weeks to 270° before removing excess BiC by sublimation or extraction into... 

A similar argument can be applied to the equilibrium involved in the sublimation of iodine ... 

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. 

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). 

Equivalent expressions can be obtained for the (solid + vapor) equilibrium to give the vapor pressure of a solid, by substituting the sublimation enthalpy, AjubT/m, for Avap//m ... 

Actually, the temperature does not change as heat is added to change the solid to gas at the equilibrium sublimation temperature. Hence, the heat capacity becomes infinite at this temperature, and the dotted line shown in Figure 8.12 should extend vertically to infinity. The compressibility and coefficient of expansion would show a similar behavior. 

Example 9.1 Calculate the equilibrium sublimation pressure above diamond at 298.15 K. 

Benzotriazole can exist in two tautomeric forms, l-//-benzotriazole (6.46, R = H) and 2-/f-benzotriazole. If the aromatic ring contains a substituent, the 1- and 3-nitrogen atoms of the triazole are not equivalent, and therefore a 3-//-benzotri-azole derivative can also exist. The equilibrium between the 1 -H and 2-H tautomers of benzotriazoles is strongly on the side of the 1 -H tautomer, in contrast to triazole where the 2-H tautomer is dominant. Tomas et al. (1989) compared experimental data (enthalpies of solution, vaporization, sublimation, and solvation in water, methanol, and dimethylsulfoxide) with the results of ab initio theoretical calculations at the 6-31G level. 

Equilibrium vapor pressures were measured in this study by means of a mass spectrometer/target collection apparatus. Analysis of the temperature dependence of the pressure of each intermetallic yielded heats and entropies of sublimation. Combination of these measured values with corresponding parameters for sublimation of elemental Pu enabled calculation of thermodynamic properties of formation of each condensed phase. Previ ly reported results on the subornation of the PuRu phase and the Pu-Pt and Pu-Ru systems are correlated with current research on the PuOs and Pulr compounds. Thermodynamic properties determined for these Pu-intermetallics are compared to analogous parameters of other actinide compounds in order to establish bonding trends and to test theoretical predictions. 

The predominant reaction associated with the sublimation of each intermetallic studied was assumed to involve gaseous Pu and the associated noble metal rich adjacent phase as products. The equilibrium sublimation reactions are as follows ... 

CO2), which is known as dry ice, is one common substance that sublimes. Draw a series of molecular pictures that show how a piece of dry ice in a closed container at low temperature illustrates the principle of dynamic equilibrium. 

When determining the solubility and dissolution rate of amorphous or partially crystalline solids, the metastability of these phases with respect to the highly crystalline solid must be considered. While the low diffusivity of the molecules in the solid state can kinetically stabilize these metastable forms, contact with the solution, for example during measurements of solubility and dissolution rate, or with the vapor, if the solid has an appreciable vapor pressure, may provide a mechanism for mass transfer and crystallization. Less crystalline material dissolves or sublimes whereas more crystalline material crystallizes out. The equilibrium solubility measured will therefore approach that of the highly crystalline solid. The initial dissolution rate of the metastable form tends to reflect its higher... 

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