Liquid partial pressure

As pointed out in Volume 1, the fraction of any one component that flashes to gas at any stage in a process is a function of the temperature, pressure, and composition of the fluid at that stage. For a given temperature this tendency to flash can be visualized by the partial pressure of the component in the gas phase that is in equilibrium with the liquid. Partial pressure is defined as ... 

Equation (9.1) is the preferred method of describing membrane performance because it separates the two contributions to the membrane flux the membrane contribution, P /C and the driving force contribution, (pio — p,r). Normalizing membrane performance to a membrane permeability allows results obtained under different operating conditions to be compared with the effect of the operating condition removed. To calculate the membrane permeabilities using Equation (9.1), it is necessary to know the partial vapor pressure of the components on both sides of the membrane. The partial pressures on the permeate side of the membrane, p,e and pje, are easily obtained from the total permeate pressure and the permeate composition. However, the partial vapor pressures of components i and j in the feed liquid are less accessible. In the past, such data for common, simple mixtures would have to be found in published tables or calculated from an appropriate equation of state. Now, commercial computer process simulation programs calculate partial pressures automatically for even complex mixtures with reasonable reliability. This makes determination of the feed liquid partial pressures a trivial exercise. 

FIGURE 14J3 Schematic diagram of evaporation in a porous network (a) geometry of pore and boundary layer, (b) liquid partial pressure proMe, and (c) temperature profile. Taken from Castro et ol. [5]. Reprinted by pennissian of the American Ceramic Socieiy. 

In a pure liquid, there is a tendency for some of the molecules of solvent to escape from the liquid and pass into the vapour phase. That is, the molecules form an atmosphere of gas above the liquid. Eventually equilibrium will be reached, with molecules evaporating from the surface at a rate equal to the rate at which they are condensing back into the liquid. This equilibrium pressure of the vapour above the liquid (partial pressure, see Section 4.5.7) is called the vapour pressure. Each solvent will have its own vapour pressure, which will increase with temperature. If the liquid is a mixture, both components contribute to the vapour pressure depending on their relative concentrations, and the total vapour pressure will be the sum of the two. 

Mole Fraction Acetone in Liquid, Partial Pressure of Acetone in Vapor, (mm Hg)... 

Henry s law states that when a liquid and a gas are in contact, the weight of the gas that is dissolved in a given quantity of liquid is proportional to the pressure of the gas above the liquid (partial pressure). The value of the constant of proportionality is called the Henry s law constant (H) and is dependant on the solute-solvent pair, temperature and pressure. Henry s law constant is a measure of a chemical s volatility from a solvent (in this chapter it is water) the larger a compound s H value, the more volatile it is, and it is also easier to be transferred from the aqueous phase into air. 

Vapor pressure is the partial pressure of a gas above its liquid. Partial pressure increases with increasing temperature. 

Component Vapor Pressure at 150°F, Psia Concentrating Mol% In Liquid, % Partial Pressure, Psia... 

Component Vapor pressure at 150°F, psia Concentrating mol% in liquid, % Partial pressure, psIa... 

In the Nernst equation, we make the usual substitutions into Q a = 1 for the activities of pure solids and liquids, partial pressures (bar) for the activities of gases, and molarities for the activities of solution components. Example 19-9 demonstrates that the Nernst equation makes it possible to calculate EceU for any chosen concentrations, not just for standard conditions. 

At pressures to a few bars, the vapor phase is at a relatively low density, i.e., on the average, the molecules interact with one another less strongly than do the molecules in the much denser liquid phase. It is therefore a common simplification to assume that all the nonideality in vapor-liquid systems exist in the liquid phase and that the vapor phase can be treated as an ideal gas. This leads to the simple result that the fugacity of component i is given by its partial pressure, i.e. the product of y, the mole fraction of i in the vapor, and P, the total pressure. A somewhat less restrictive simplification is the Lewis fugacity rule which sets the fugacity of i in the vapor mixture proportional to its mole fraction in the vapor phase the constant of proportionality is the fugacity of pure i vapor at the temperature and pressure of the mixture. These simplifications are attractive because they make the calculation of vapor-liquid equilibria much easier the K factors = i i ... 

In the phase equilibrium between a pure solid (or a liquid) and its vapour, the addition of other gases, as long as they are insoluble in the solid or liquid, has negligible effect on the partial pressure of the vapour. 

Steam Distillation. Distillation of a Pair of Immiscible Liquids. Steam distillation is a method for the isolation and purification of substances. It is applicable to liquids which are usually regarded as completely immiscible or to liquids which are miscible to only a very limited extent. In the following discussion it will be assumed that the liquids are completely immiscible. The saturated vapours of such completely immiscible liquids follow Dalton s law of partial pressures (1801), which may be stated when two or more gases or vapoms which do not react chemically with one another are mixed at constant temperature each gas exerts the same pressure as if it alone were present and that... 

The composition of the vapour can easily be calculated as follows — Assuming that the gas laws are applicable, it follows that the number of molecules of each component in the vapour wdll be proportional to its partial pressure, i.e., to the vapour pressure of the pure liquid at that temperature. If and p are the vapour pressures of the two liquids A and B at the boiling point of the mixture, then the total pressure P is given by ... 

Deliquescence and efflorescence. A substance is said to deliquesce (Latin to become liquid) when it forms a solution or liquid phase upon standing in the air. The essential condition is that the vapour pressure of the saturated solution of the highest hydrate at the ordinary temperature should be less than the partial pressure of the aqueous vapour in the atmosphere. Water will be absorbed by the substance, which gradually liquefies to a saturated solution water vapour will continue to be absorbed by the latter until an unsaturated solution, having the same vapour pressure as the partial pressure of water vapour in the air, is formed. In order that the vapour pressure of the saturated solution may be sufficiently low, the substance must be extremely soluble in water, and it is only such substances (e.g., calcium chloride, zinc chloride and potassium hydroxide) that deliquesce. 

The first term, AG°, is the change in Gibb s free energy under standard-state conditions defined as a temperature of 298 K, all gases with partial pressures of 1 atm, all solids and liquids pure, and all solutes present with 1 M concentrations. The second term, which includes the reaction quotient, Q, accounts for nonstandard-state pressures or concentrations. Eor reaction 6.1 the reaction quotient is... 

Condition in which solids and liquids are in pure form, gases have partial pressures of 1 atm, solutes have concentrations of 1 M, and the temperature is 298 K. 

Significant disciepancies in fomialdehyde partial pressures above aqueous solutions (22,23) can occur due to nonequilibrium conditions in the liquid phase. However, these problems have been overcome and consistent results obtained (8,18,22,24—26). 

A tabulation of the partial pressures of sulfuric acid, water, and sulfur trioxide for sulfuric acid solutions can be found in Reference 80 from data reported in Reference 81. Figure 13 is a plot of total vapor pressure for 0—100% H2SO4 vs temperature. References 81 and 82 present thermodynamic modeling studies for vapor-phase chemical equilibrium and liquid-phase enthalpy concentration behavior for the sulfuric acid—water system. Vapor pressure, enthalpy, and dew poiat data are iacluded. An excellent study of vapor—liquid equilibrium data are available (79). 

The H in solubility tables (2-121 to 2-144) is the proportionahty constant for the expression of Henry s law, p = Hx, mere x = mole fraction of the solute in the liqiiid phase p = partial pressure of the solute in the gas phase, expressed in atmospheres and H = a. proportionality constant expressed in units of atmospheres of solute pressure in the gas phase per unit concentration of the solute in the hquid phase. (The unit of concentration of the solute in the liquid phase is moles solute per mole solution.)... 

D. Rectification in vertical wetted wall column with turbulent vapor flow, Johnstone and Pigford correlation =0.0.328(Wi) Wi P>vP 3000 < NL < 40,000, 0.5 < Ns. < 3 N=, v,.gi = gas velocity relative to R. liquid film = — in film -1 2 " [E] Use logarithmic mean driving force at two ends of column. Based on four systems with gas-side resistance only, = logarithmic mean partial pressure of nondiffusing species B in binary mixture. p = total pressure Modified form is used for structured packings (See Table 5-28-H). 

T. Single liquid drops in gas, gas side coefficient =2 + ANiS,Ni [E] Used for spray drying (arithmetic partial pressure difference). [88] p. 489... 

On the other hand, when evolved vapor is purged from the dryer environment by using a second (inert) gas, the temperature at which vaporization occurs will depend on the concentration of vapor in the surrounding gas. In effect, the liquid must be heated to a temperature at which its vapor pressure equ s or exceeds the partial pressure of vapor in the purge gas. In the reverse situation, condensation will occur. 

In order to define completely the solubility of a gas in a liquid, it generally is necessary to state the temperature, the equilibrium partial pressure of the solute gas in the gas phase, and the concentration of the solute gas in the liquid phase. Stric tly speaking, the total pressure on the system also should be stated, but for low total pressures, less than about 507 kPa (5 atm), the solubihty for a particular partial pressure of solute gas normally will be relatively independent of the total pressure of the system. 

For dilute concentrations of manv gases and over a fairly wide range for some gases, the equihbrium relationship is given by Henry s law, which relates the partial pressure developed by a dissolved solute A in a liquid solvent B by one of the following equations ... 

Pure-component vapor pressures can be used for predicting solu-bihties for systems in which RaoiilFs law is valid. For such systems Pa = Pa a, where p° is the pure-component vapor pressure of the solute andp is its partial pressure. Extreme care should be exercised when attempting to use pure-component vapor pressures to predict gas-absorption behavior. Both liquid-phase and vapor-phase nonidealities can cause significant deviations from the behavior predicted from pure-component vapor pressures in combination with Raoult s law. Vapor-pressure data are available in Sec. 3 for a variety of materials. 

Ga.s-Lic(uid Ma.s.s Tran.sfer Gas-liqiiid mass transfer norrnallv is correlated bv means of the mass-transfer coefficient K a ersiis powder le el at arioiis superficial gas elocities. The superficial gas clocitv is the ohirne of gas at the a erage temperature and pressure at the midpoint in the tank di ided bv the area of the essel. In order to obtain the partial-pressure dri ing force, an assumption must be made of the partial pressure in equilibrium wdth the concentration of gas in the liquid, Manv times this must be assumed, but if Fig, 18-26 is obtained in the pilot plant and the same assumption principle is used in e ahiating the mixer in the full-scale tank, the error from the assumption is limited. 

T = temperature, °F p = partial pressure, atm L = liquid-flow rate, lb/(h-fF)... 

In order to allow integration of countercurrent relations like Eq. (23-93), point values of the mass-transfer coefficients and eqiiilibrium data are needed, over ranges of partial pressure and liquid-phase compositions. The same data are needed for the design of stirred tank performance. Then the conditions vary with time instead of position. Because of limited solubihty, gas/liquid reactions in stirred tanks usually are operated in semibatch fashion, with the liquid phase charged at once, then the gas phase introduced gradually over a period of time. CSTR operation rarely is feasible with such systems. 

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