Chemical potential vapor

In general, equaHty of component fugacities, ie, chemical potentials, in the vapor and Hquid phases yields the foUowing relation for vapor—Hquid equiHbrium ... 

In a state of equilibrium the chemical potentials of water and water vapor are equal ... 

For crystal growth from the vapor phase, one better chooses the transition probability appropriate to the physical situation. The adsorption occurs ballistically with its rate dependent only on the chemical potential difference Aj.1, while the desorption rate contains all the information of local conformation on the surface [35,48]. As long as the system is close to equilibrium, the specific choice of the transition probability is not of crucial importance. 

The desorption rate contains an exponential factor with a chemical potential (Iq for desorption into the vapor phase, since it is a thermally excited process. In a nonequilibrium situation, the chemical potential increases by Afi and increases the adsorption rate The rate difference is given as... 

Here rj is the viscosity of the dewetting liquid. Note that a relaxational term proportional to a has been added, with fi(j)) being the chemical potential of the vapor. This term alone guarantees that a homogeneous liquid film will relax to its equilibrium value hooip) by evaporation or condensation. For h = hooip) this term vanishes. 

The pair of Eqs. 12, 13 epitomizes the relation between the equilibrium vapor pressure, composition, and chemical potential of the solvent in a clathrate obeying the present model. These expressions were used in the calculation of the thermodynamic properties of gas hydrates30 and have also been formulated by Barrer and Stuart 4 for a clathrate with a single type of cavity and one occluded component they reduce to the equations of ref. 52. 

In connection with the thermodynamic state of water in SAH, it is appropriate to consider one more question, i.e., their ability to accumulate water vapor contained in the atmosphere and in the space of soil pores. It is clear that this possibility is determined by the chemical potential balance of water in the gel and in the gaseous phase. In particular, in the case of saturated water vapor, the equilibrium swelling degree of SAH in contact with vapor should be the same as that of the gel immersed in water. However, even at a relative humidity of 99%, which corresponds to pF 4.13, SAH practically do not swell (w 3-3.5 g g1). In any case, the absorbed water will be unavailable for plants. Therefore, the only real possibility for SAH to absorb water is its preliminary condensation which can be attained through the presence of temperature gradients. 

Substitution of vapor fugacities for chemical potentials (d/i, RT d ln /i) and dividing by RT gives... 

If we could prevent the mixture from separating into two phases at temperatures below Tc, we would expect the point of inflection to develop into curves similar to those shown in Figure 8.17 as the dotted line for /2, with a maximum and minimum in the fugacity curve. This behavior would require that the fugacity of a component decreases with increasing mole fraction. In reality, this does not happen, except for the possibility of a small amount of supersaturation that may persist briefly. Instead, the mixture separates into two phases. These phases are in equilibrium so that the chemical potential and vapor fugacity of each component is the same in both phases, That is, if we represent the phase equilibrium as... 

Another general type of behavior that occurs in polymer manufacture is shown in Figure 3. In many polymer processing operations, it is necessary to remove one or more solvents from the concentrated polymer at moderately low pressures. In such an instance, the phase equilibrium computation can be carried out if the chemical potential of the solvent in the polymer phase can be computed. Conditions of phase equilibrium require that the chemical potential of the solvent in the vapor phase be equal to that of the solvent in the liquid (polymer) phase. Note that the polymer is essentially involatile and is not present in the vapor phase. 

Using standard thermodynamics, it can be shown that, at modest pressures, the equality of solvent chemical potential in both liquid and vapor phases can be transformed to... 

If applied pressure P is increased from condition 1 to 2, then a(pyjpj) = V (Pi — PSi/RT, where molar volume is V, the gas constant is R and temperature is T. From this, e.g., for water, a 1000-fold increase in P only approximately doubles saturated vapor pressure p. For hydrocarbons, p could be doubled by a lower pressure increase, in the order of 150 times or so however for moderate pressures, a tenfold increase in P even here only increases p by some 5%. Hence, for most practical situations, vapor pressure of a liquid can be considered as independent of applied pressure. Vapor-free liquid may need chemical potential represented differently (possibly by work done). 

The NPT + test particle method [8, 9] aims to determine phase coexistence points based on calculations of the chemical potentials for a number of state points. A phase coexistence point is determined at the intersection of the vapor and liquid branches of the chemical potential versus pressure diagram. The Widom test particle method [7] of the previous paragraph or any other suitable method [10] can be used to obtain the chemical potentials. Corrections to the chemical potential of the liquid and vapor phases can be made, using standard thermodynamic relationships, for deviations... 

In contrast to the Gibbs ensemble discussed later in this chapter, a number of simulations are required per coexistence point, but the number can be quite small, especially for vapor-liquid equilibrium calculations away from the critical point. For example, for a one-component system near the triple point, the density of the dense liquid can be obtained from a single NPT simulation at zero pressure. The chemical potential of the liquid, in turn, determines the density of the (near-ideal) vapor phase so that only one simulation is required. The method has been extended to mixtures [12, 13]. Significantly lower statistical uncertainties were obtained in [13] compared to earlier Gibbs ensemble calculations of the same Lennard-Jones binary mixtures, but the NPT + test particle method calculations were based on longer simulations. 

The most fundamental manner of demonstrating the relationship between sorbed water vapor and a solid is the water sorption-desorption isotherm. The water sorption-desorption isotherm describes the relationship between the equilibrium amount of water vapor sorbed to a solid (usually expressed as amount per unit mass or per unit surface area of solid) and the thermodynamic quantity, water activity (aw), at constant temperature and pressure. At equilibrium the chemical potential of water sorbed to the solid must equal the chemical potential of water in the vapor phase. Water activity in the vapor phase is related to chemical potential by... 

We can equate the chemical potential of the solute to the chemical potential of the vapor in equilibrium with it. Assume the vapor is an ideal gas ... 

Equation 29 implies that is the chemical potential of a hypothetical solution in which XA = 1, but the vapor pressure over the solution still obeys Henry s law as extrapolated from infinite dilution. Thus the standard state is a hypothetical Henry s law solution of unit mole fraction. 

Because the chemical potentials of water distributed in two phases (i.e., solution and vapor) must be equal, the water activity of a food can be measured by bringing the food into equilibrium with the air above it. At equilibrium, under conditions of constant temperature and pressure, the aw values of the aqueous phase of a food (aw l) and of the air (aw v) are equal and can be estimated from the ratio of the partial vapor pressure of water above the food (pv) to the vapor pressure of pure water (p") at the same temperature (Walstra, 2003) ... 

As is customary we select the ideal vapor at unit pressure, P°, as the standard state. The partial molar free energy (chemical potential) of the vapor, p,(v), is... 

Here a°(c) is the standard state chemical potential of condensed fluid in equilibrium with the vapor at the vapor pressure P, and the temperature of the measurement. 

SPMD sample extracts, e.g., certain organochlorine pesticides (OCPs), are known to inhibit cholinesterase activity. Therefore, these results were not unexpected. However, it was surprising that a similar response was not observed with brain cholinesterase activity. It is possible that brain cells can more readily metabolize the chemicals, that the chemicals did not pass the brain blood barrier or that the effects occurred earlier in the exposure period, effectively allowing the activity to recover. Considering the numerous neurotoxic chemicals potentially entering aquatic ecosystems or present as airborne vapor phase chemicals, the neurotoxic mode of action related to exposure to contaminants is of increasing interest. Evidence presented in this work demonstrate that SPMDs concentrate members of this class of toxicants. 

The vapor embryo, or bubble, is in unstable equilibrium and will either collapse or grow. We are only interested in those that follow the latter path. The chemical criteria of equilibrium between the bubble and liquid state that the temperature and chemical potential of the material in the bubble are equal to those in the superheated liquid, i.e.. 

Chemical equilibrium corresponds to zero water flux and uniform chemical potential of water in the membrane interior and in the external vapor phase. 

Two other conventions exist for the choice of standard states for components of a solution. One convention chooses the pure component at 1 bar of pressure, for conformance with the usual standard state for pure components. This choice has the disadvantage that it requires aterm for the effect of pressure in the relation between the chemical potentials of the pure component and of the component in solution. The other convention chooses the pure component at the vapor pressure of the solution. This choice has the disadvantage of having different standard states for each composition of solution. 

Solvent in Solution. We shall use the pure substance at the same temperature as the solution and at its equilibrium vapor pressure as the reference state for the component of a solution designated as the solvent. This choice of standard state is consistent with the limiting law for the activity of solvent given in Equation (16.2), where the limiting process leads to the solvent at its equilibrium vapor pressure. To relate the standard chemical potential of solvent in solution to the state that we defined for the pure liquid solvent, we need to use the relationship... 

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