Fractionation pressure, definition

Fractionation, by definition, is simply the mass transfer between a liquid phase and a gas phase in contact with each other. A fractionation column is simply a tall, vertical, cylindrical pressure vessel that contains numerous flat internal metal plates called trays. Each tray allows liquid to flow over it, so the liquid flows from tray to tray by the force of gravity. The liquid thus enters the top tray. The liquid portion not vaporized in the column s trays is taken out in the column s bottom liquid accumulation. Gas enters the column s bottom section and flows through each tray to the top section. Entering vapor pressure is its driving force. Gas not absorbed by the liquid exits the column s top section. 

Avogadro s principle states that equal volumes of gases represent equal amounts (moles) of the gases, so the volume mixing ratio is equal to the mole fraction. The definition of partial pressures is... 

A saturated aqueous solution in contact with an excess of a definite solid phase at a given temperature will maintain constant humidity in an enclosed space. Table 11.4 gives a number of salts suitable for this purpose. The aqueous tension (vapor pressure, in millimeters of Hg) of a solution at a given temperature is found by multiplying the decimal fraction of the humidity by the aqueous tension at 100 percent humidity for the specific temperature. For example, the aqueous tension of a saturated solution of NaCl at 20°C is 0.757 X 17.54 = 13.28 mmHg and at 80°C it is 0.764 X 355.1 = 271.3 mmHg. 

From the definition of a partial molar quantity and some thermodynamic substitutions involving exact differentials, it is possible to derive the simple, yet powerful, Duhem data testing relation (2,3,18). Stated in words, the Duhem equation is a mole-fraction-weighted summation of the partial derivatives of a set of partial molar quantities, with respect to the composition of one of the components (2,3). For example, in an / -component system, there are n partial molar quantities, Af, representing any extensive molar property. At a specified temperature and pressure, only n — 1) of these properties are independent. Many experiments, however, measure quantities for every chemical in a multicomponent system. It is this redundance in reported data that makes thermodynamic consistency tests possible. 

To extract a desired component A from a homogeneous liquid solution, one can introduce another liquid phase which is insoluble with the one containing A. In theory, component A is present in low concentrations, and hence, we have a system consisting of two mutually insoluble carrier solutions between which the solute A is distributed. The solution rich in A is referred to as the extract phase, E (usually the solvent layer) the treated solution, lean in A, is called the raffinate, R. In practice, there will be some mutual solubility between the two solvents. Following the definitions provided by Henley and Staffin (1963) (see reference Section C), designating two solvents as B and S, the thermodynamic variables for the system are T, P, x g, x r, Xrr (where P is system pressure, T is temperature, and the a s denote mole fractions).. The concentration of solvent S is not considered to be a variable at any given temperature, T, and pressure, P. As such, we note the following ... 

The activities of the various components 1,2,3. .. of an ideal solution are, according to the definition of an ideal solution, equal to their mole fractions Ni, N2,. . . . The activity, for present purposes, may be taken as the ratio of the partial pressure Pi of the constituent in the solution to the vapor pressure P of the pure constituent i in the liquid state at the same temperature. Although few solutions conform even approximately to ideal behavior at all concentrations, it may be shown that the activity of the solvent must converge to its mole fraction Ni as the concentration of the solute(s) is made sufficiently small. According to the most elementary considerations, at sufficiently high dilutions the activity 2 of the solute must become proportional to its mole fraction, provided merely that it does not dissociate in solution. In other words, the escaping tendency of the solute must be proportional to the number of solute particles present in the solution, if the solution is sufficiently dilute. This assertion is equally plausible for monomeric and polymeric solutes, although the... 

The rate of decomposition of gaseous ethylene oxide (QFUO), to CH4 and CO, has been studied by Mueller and Walters (1951) by determination of the fraction (/A) of oxide (A) reacted after a definite time interval (f) in a constant-volume batch reactor. In a series of experiments, the initial pressure of the oxide (P 0) was varied. Some of the results are as follows ... 

What we would like to do is use these thermodynamic properties to calculate an equilibrium elastic moduli. The bulk modulus is by definition the constant of proportionality that links the infinitesimal pressure change resulting from a fractional change in volume (Section 2.2.1). In colloidal terms this becomes... 

Flash or equilibrium distillation, frequently carried out as a continuous process, consists of vaporising a definite fraction of the liquid feed in such a way that the vapour evolved is in equilibrium with the residual liquid. The feed is usually pumped through a fired heater and enters the still through a valve where the pressure is reduced. The still is essentially a separator in which the liquid and vapour produced by the reduction in pressure have sufficient time to reach equilibrium. The vapour is removed from the top of the separator and is then usually condensed, while the liquid leaves from the bottom. 

Two important ways in which heterogeneously catalyzed reactions differ from homogeneous counterparts are the definition of the rate constant k and the form of its dependence on temperature T. The heterogeneous rate equation relates the rate of decline of the concentration (or partial pressure) c of a reactant to the fraction / of the catalytic surface area that it covers when adsorbed. Thus, for a first-order reaction,... 

Analysis of Defined Fractions. Quantitative infrared analysis was used for those fractional groups that have definitive bands average absorptivities were estimated using model compounds (12, 16, 17). Table I lists the infrared bands and the apparent integrated absorption intensities (B) used. Quantitative IR spectra were measured in methylene chloride with 0.05 cm sodium chloride cells, using a Perkin-Elmer 521 infrared spectrophotometer. Peak area was measured by planimetry. Molecular weights were determined by vapor-pressure osmometry in benzene. 

As before, one can show that the length of dimensionless time required for the pressure decrease during blowdown is that given by Eq. (17) The dimensionless time definition in this case is given by Eq. (19). Hence the mole fraction profile after the pressure decrease is found by integrating Eq. (20) from t = 0 to... 

It is, therefore, not surprising that there exists a definite relationship between Aand the enthalpy of vaporization, Av H, the former constituting a fraction between 0.2 and 0.3 of the latter, as is readily obtained from the data in Tables 3.1 and 3.9. The pressure dependence of the viscosity is also closely related to the free volume of the solvent. The fluidity (O = l/r ) is proportional to the ratio between the free and the occupied volume, the former, as mentioned above, being the difference between the actual molar volume and the intrinsic molar volume (Tables 3.1 and 3. 4) (Hildebrand 1978). In fact, the logarithm of the viscosity of liquids was found (Marcus 1998) to be described well for some 300 liquids by the empirical relationship ... 

One of the most important applications of Equation (6.7) is to the chemical potentials. From their definition in terms of the Gibbs energy we know that they are functions of the temperature, pressure, and the mole fractions. The differential of the chemical potential of the fcth component is then given by... 

The reference state of each component in a system may be defined in many other ways. As an example, we may choose the reference state of each component to be that at some composition with the condition that the composition of the reference state is the same at all temperatures and pressures of interest. For convenience and simplicity, we may choose a single solution of fixed composition to be the reference state for all components, and designate xf to be the mole fraction of the /cth component in this solution. If (Afikx) represents the values of the excess chemical potential based on this reference state, then (A/if x ) [T, P, x ] is zero at all temperatures and pressures at the composition of the reference state. That this definition determines the standard state is seen from Equation (8.71), for then... 

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