Since the molar volume of a condensed phase is frequently insensitive lo pressure. Eq. (L.2-31) cen often he approximated by [Pg.8]

If the partial molar volumes of the condensed phase are negligibly small with respect to the molar volume of the gas phase, this becomes [Pg.327]

The chemical potentials of condensed phases are relatively pressure independent, due to their small molar volumes.) Rewriting, [Pg.175]

Because, at constant temperature, dGm = Vm dP and the molar volumes of condensed phases are very small, it is usually sufficiently accurate to take their molar free energy as pressure independent and the same as that at the 1.0-bar standard state. This is equivalent to setting the activity of pure, condensed phases equal to unity. (See Problem 9.) The activity of a condensed phase is also independent of just how much of the phase is present. As a result of these considerations, no variable describing the condensed phase appears in the equilibrium constant and the equilibrium is independent of just how much condensed phase is present. [Pg.208]

Since a Maxwell relation for equation (6) shows that the partial molar volume of the condensed phase is [Pg.549]

Abstract Isotope effects on the PVT properties of non-ideal gases and isotope effects on condensed phase physical properties such as vapor pressure, molar volume, heats of vaporization or solution, solubility, etc., are treated in some thermodynamic detail. Both pure component and mixture properties are considered. Numerous examples of condensed phase isotope effects are employed to illustrate theoretical and practical points of interest. [Pg.139]

In Fig. 2, the chemical potential curves of Fig. la are shown for two different pressures. Because the molar volume of a gas is greater than that of condensed phases, the chemical potential of the gas is increased much more than those of liquid or solid by increasing pressure. The boiling point and sublimation point therefore increase with pressure. The molar volume of the liquid and solid are comparable, and either one may be larger. As a result, the melting point may either increase or decrease with pressure. [Pg.172]

Table II presents some consequences of these analogies for a vapor phase and a condensed phase together with the thermal analogs. Here rti is the concentration of the vapor in molecules per unit volume, Nt is the mole fraction in the condensed phase, Vc is the molar volume of the substrate, p< is the partial pressure, and y< is the rational activity coefficient. |

In order to see the dependence of AG on the dimensions of the condensed particle, let us substitute for n the number of moles of condensed vapor, n = 4irr /3V, where V = M/p is the molar volume of the condensed phase, M is its atomic weight, and p is the density. We have [Pg.299]

It is also useful to note that several simplifications can be made in computing the thermodynamic propenies of solids and liquids. First, because the molar volumes of condensed phases are small, the product PV can be neglected unless the pressure is high. Thus, for solids and liquids. [Pg.67]

We see that under these conditions the value of the derivative becomes zero (a maximum) when xx = 2x2. The maximum then occurs when the composition of the condensed phase is that of the species A2B. When the partial molar volumes of the condensed phase are not negligibly small and when the nonideality of the gas is included, the maximum does not occur at this exact composition, but does occur very close to it [32]. [Pg.327]

The Clapeyron equation can be simplified to some extent for the case in which a condensed phase (liquid or solid) is in equilibrium with a gas phase. At temperatures removed from the critical temperature, the molar volume of the gas phase is very much larger than the molar volume of the condensed phase. In such cases the molar volume of the condensed phase may be neglected. An equation of state is then used to express the molar volume of the gas as a function of the temperature and pressure. When the virial equation of state (accurate to the second virial coefficient) is used, [Pg.234]

The effect of curvature is much more pronounced for the thermodynamics of a gas bubble than for the liquid droplet. The curvature is a pressure effect, which is much larger for gases than for condensed phases, reflecting the much larger molar volume of the gas. [Pg.178]

Strictly speaking the partial pressures depend on the total pressure, but it is readily shown, as in 1, that the variation is negligible at ordinary pressure because of the small molar volumes of condensed phases. Equation (21.53) therefore reduces to the Duhem-Margules equation, [Pg.344]

Although Equations (8.28) and (8.32) are formally alike, they refer to different types of processes. The former is strictly true for a process that occurs at a constant pressure throughout a temperature range. Vaporization or sublimation does not fulfill this restriction, but nevertheless. Equation (8.32) is approximately correct because the molar volume of the condensed phase is small compared with that of the gas, and the vapor pressure is small enough that the vapor behaves as an ideal gas. [Pg.202]

According to quantum mechanics, isolated molecules do not have a finite boundary, but rather fade away into the regions of low electron density. It has been well established, however, from properties of condensed matter and molecular interactions, that individual molecules occupy a finite and measurable volume. This notion is at the core of the concept of molecular structure. 33 A number of physical methods yield estimations of molecular dimensions. These methods include measurements of molar volumes in condensed phases, critical parameters (lattice spacings and bond distances), and collision diameters in the gas phase. 34 From these results, one derives values of atomic radii from which a number of empirical molecular surfaces can be built. Note that the values of the atomic radii depend on the physical measurement chosen. 35-i37 [Pg.222]

© 2019 chempedia.info