Concentration of solute in liquid phase

C concentration of solute in liquid phase, moles/liter... 

Concentration of solute in liquid phase Concentration of solute in gas phase... 

Cl = solute concentration in liquid leaving bottom of column, lb moles/cu ft C2 = solute concentration in liquid fed to top of cohmm, lb moles/cu ft c = solute concentration in main body of liquid, lb moles/cu ft = concentration of solute in liquid phase in equilibrium with main bocty of gas, lb moles/cu ft... 

Concentration of solute in mobile phase Cm Diffusion coefficient, liquid film Dt... 

Flow parameter (Norton Co.) = F = FP Concentration of solute in liquid, lb mol solute/lb mol solute free solvent (or stream) Concentration of solute in liquid, in equiUbri-um -with the gas, lb mol solute/lb mol solvent Concentration of solute in liquid, mole fraction, or mol fraction of more volatile component in liquid phase Curve fit coefficients for C2, Table 9-32 Curve fit coefficients for Cg, Table 9-32 Concentration of solute in liquid in equilibrium -with gas, mol fracdon Concentradon of solute in gas, lb mol solute/lb mol solute free (solvent) (stream) Capacity parameter (Norton)... 

The upper curve shows the adsorption isotherm that normally occurs in liquid chromatography separations where the concentration of solute in the system is very low. The isotherm is linear and thus the distribution coefficient is constant at all concentrations of solute in either phase. It follows that as the peak velocity is inversely related to the distribution coefficient, all solute concentrations travel at the same velocity through the column and the peak is symmetrical. 

Reference concentration in equation 11.30 Concentration of solute in solution at column base Concentration of solute in solution at column top Reference concentration equations 11.25 and 11.26 Mol fraction of component in vapour phase Mol fraction of component A in a binary mixture Mol fraction of component B in a binary mixture Equilibrium concentration Mol fraction of component i Concentration driving force in the gas phase Log mean concentration driving force Concentration of solute in gas phase at column base Concentration of solute in gas phase at column top Height of packing Liquid hold-up on plate Length of liquid path... 

In gas absorption operations the equilibrium of interest is that between a relatively nonvolatile absorbing liquid (solvent) and a solute gas (usually the pollutant). As described earlier, the solute is ordinarily removed from a relatively large amount of a carrier gas that does not dissolve in the absorbing liquid. Temperature, pressure, and the concentration of solute in one phase are independently variable. The equilibrium relationship of importance is a plot (or data) of x, the mole fraction of solute in the liquid, against y, the mole fraction in the vapor in equilibrium with x. For cases that follow Henry s law, Henry s law constant m, can be defined by the equation... 

The rate of adsorpfion of solute A present in the fluid phase in contact with the surface of the adsorbent is proportional to the number of molecules of A (partial pressure of A in gas phase or concentration of A in liquid phase) in the fluid phase and the number of free acfive sifes on the surface. Define as rate of adsorption of A on to the surface S. rja... 

The lower isotherm represents the overload condition that can occur in liquid/liquid or gas/liquid systems under somewhat unique circumstances. If the interactions between solute molecules with themselves is stronger than the interactions between the solute molecules and the stationary phase molecules, then, as the concentration of solute molecules increases, the distribution coefficient of the solute with respect to the stationary phase also increases. This is because the solute molecules interact more strongly with a solution of themselves in the stationary phase than the stationary phase alone. Thus, the higher concentrations of solute in the chromatographic... 

The development of a scientific understanding of diffusion in liquid-phase polymeric systems has been largely due to Duda et al. (1982), Ju et al. (1981), and Vrentas and Duda (1977a,b, 1979) whose work in this area has been signal. In their most recent work, Duda et al. (1982) have developed a theory which successfiilly predicts the strong dependence of the diffusion coefficient on temperature and concentration in polymeric solutions. The parameters in this theory are relatively easy to obtain, and in view of its predictive capability this theory would seem to be most appropriate for incorporating concentration-dependent diffusion coefficients in the diffusion equation. 

In CCC, there are nothing else but mobile and stationary phases inside the column. Since it is possible to work with very high concentrations of solutes in CCC, the technique is mainly used in the preparative conditions. If fhe liquid nafure of fhe sfafionary phase is fhe main advanfage of CCC, if is also ifs main problem. Two frifs at both ends of fhe colunm are what is needed to maintain a solid stationary phase. A liquid stationary phase, without any support, is difficult to maintain really stationary. 

Figure 1.9. The dependence of the boundary profile on the form of the partition isotherm. (Courtesy of John Wiley-Interscience. ) c=concentration (cm 5/mole) of solute in gas phase q=concentration in liquid or adsorbed phase t=time for band to emerge from column (1) se1f-sharpening profile (2) diffuse profile (3) gaussian profile.

The problem to be solved in this paragraph is to determine the rate of spread of the chromatogram under the following conditions. The gas and liquid phases flow in the annular space between two coaxial cylinders of radii ro and r2, the interface being a cylinder with the same axis and radius rx (0 r0 < r < r2). Both phases may be in motion with linear velocity a function of radial distance from the axis, r, and the solute diffuses in both phases with a diffusion coefficient which may also be a function of r. At equilibrium the concentration of solute in the liquid, c2, is a constant multiple of that in the gas, ci(c2 = acj) and at any instant the rate of transfer across the interface is proportional to the distance from equilibrium there, i.e. the value of (c2 - aci). The dispersion of the solute is due to three processes (i) the combined effect of diffusion and convection in the gas phase, (ii) the finite rate of transfer at the interface, (iii) the combined effect of diffusion and convection in the liquid phase. In what follows the equations will often be in sets of five, labelled (a),..., (e) the differential equations expression the three processes (i), (ii) (iii) above are always (b), (c) and (d), respectively equations (a) and (e) represent the condition that there is no flow over the boundaries at r = r0 and r = r2. 

The initial concentration of solute in the liquid phase is C] and zero in the solid phase. The surface concentration on the solid phase is an unknown function of time, and the flux at the center of the particle at all times is zero. 

The separation of compounds by their differential partition between two immiscible phases is the basis for partition chromatography. The system consists of a stationary liquid phase coated on an inert solid support, and an immiscible mobile phase. Chromatographic separations are based on the different equilibrium distributions of the samples between these two phases. The greater the quantity of substance in the stationary phase at equilibrium the dower is the migration. For analyses, this equilibrium must remain constant over a suitable concentration range. Thus an increase in the concentration of solute results in a linear increase in the concentration of solute in the mobile and stationary phase, respectively. Under these conditions, the retention time, tR, is independent of the amount of sample chromatographed and a symmetrical peak (gaussian band) is observed. 

Recently, considerable attention has been paid to the use of compressed gases and liquids as solvents for extraction processes (Schneider et al., 1980 Dain-ton and Paul, 1981 Bright and McNally, 1992 Kiran and Brennecke, 1992), although the law of partial pressures indicates that when a gas is in contact with a material of low volatility, the concentration of solute in the gas phase should be minimal and decrease with increased pressure. Nevertheless, deviations from this law occur at temperatures near the critical temperature of the gas, and the concentration of solute in the gas may actually be enhanced as well as increased with pressure. 

Here, Bn and B(a> are the initial and final concentrations of solute in the liquid phase. ksa, can be obtained from a plot of... 

The plot between the concentration of the solute in the liquid phase and that in the gas phase is called the operating line. Consider an absorption operation in a tower and let G be the mole flow rate of solute-free gas phase (carrier gas) carrying solute at a concentration [F] mole units per unit mole of the gas phase solute-free carrier gas. The corresponding quantities for the liquid phase are L and [X], where L is the mole flow rate of solute-free liquid phase (carrier liquid) and [X] is the mole of solute per unit mole of the solute-free liquid carrier. 

An adaptation of the distribution constant defined in Equation (23-3) could be made for solutes in chromatojp-aphy. As in liquid-liquid extraction, however, solutes may be present in several chemical forms, and therefore a quantity analogous to the distribution ratio (Section 23-1), called the partition ratio, is preferred. The partition ratio must be a somewhat more broadly defined term than the distribution ratio in liquid-liquid extraction for two reasons. First, in chromatography, concentrations of solute in the two phases are usually unknown and may be unmeasurable, as when adsorption is important. Second, instead of the two phases being merely an aqueous phase and an immiscible organic solvent, in chromatography they can be any one of innumerable combinations of solid or liquid stationary phases and liquid or gas... 

Q is the solute saturation concentration in equilibrium with the gas phase and Ci is the acutal bulk concentration of solute in the liquid phase. Thus, for absorption, where Ci > Q, J is positive because the mass transfer is from the gas phase to the liquid phase however, for stripping, where Q < Q, J is negative and the mass transfer is from the liquid to the gas phase. A correlation for kL a is given in Bakker et al. (1994). 

If a solution is placed in contact with a solvent in which it is immiscible, the solute will distribute itself between the two liquid phases. If the solute is in the same form in both liquids, then the ratio of concentration of solute in the two phases will be essentially constant and independent of the total concentration ... 

An equilibrium or theoretical stage in liquid-liquid extraction, as defined earlier, is routinely utilized in laboratory procedures. A feed solution is contacted with a solvent to remove one or more of the solutes from the feed. This can be carried out in a separating funnel or, preferably, in an agitated vessel that can produce droplets about 1 mm in diameter. After agitation has stopped and the phases separate, the two clear liquid layers are isolated by decantation. The partition ratio can then be determined directly by measuring the concentration of solute in the extract and raffinate layers. (Additional discussion is given in Liquid-Liquid Equilibrium Experimental Meth-... 

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