Solutions equilibria Liquids

In the upper part of Fig. 9.11, which represents a typical binary mixture, the enthalpies of saturated vapors at their dew points have been plotted vs. y and those of the saturated liquids at their bubble points vs. x. The vertical distances between the two curves at x = 0 and 1 represent, respectively, the molar latent heats of B and A. The heat required for complete vaporization of solution C is Hq — H(2 energy/mole solution. Equilibrium liquids and vapors may be joined by tie lines, of which line EF is typical. The relation between this equilibrium phase diagram and the xy plot is shown in the lower part of Fig. 9.11. Here the point G represents the tie line EF, located on the lower plot in the manner shown. Other tie lines, when projected to the xy plot, produce the complete equilibrium-distribution curve. 

This description of the dynamics of solute equilibrium is oversimplified, but is sufficiently accurate for the reader to understand the basic principles of solute distribution between two phases. For a more detailed explanation of dynamic equilibrium between immiscible phases the reader is referred to the kinetic theory of gases and liquids. 

X = concentration of solute in liquid in equilibrium with the gas, lb mol solute/lb mol solvent... 

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 most widely used reference electrode, due to its ease of preparation and constancy of potential, is the calomel electrode. A calomel half-cell is one in which mercury and calomel [mercury(I) chloride] are covered with potassium chloride solution of definite concentration this may be 0.1 M, 1M, or saturated. These electrodes are referred to as the decimolar, the molar and the saturated calomel electrode (S.C.E.) and have the potentials, relative to the standard hydrogen electrode at 25 °C, of 0.3358,0.2824 and 0.2444 volt. Of these electrodes the S.C.E. is most commonly used, largely because of the suppressive effect of saturated potassium chloride solution on liquid junction potentials. However, this electrode suffers from the drawback that its potential varies rapidly with alteration in temperature owing to changes in the solubility of potassium chloride, and restoration of a stable potential may be slow owing to the disturbance of the calomel-potassium chloride equilibrium. The potentials of the decimolar and molar electrodes are less affected by change in temperature and are to be preferred in cases where accurate values of electrode potentials are required. The electrode reaction is... 

If the coexisting liquid or solid phases are not pure, but solutions, equilibrium will be established when the chemical potential... 

Unfortunately, the system selected was not in physico-chemical equilibrium uranium carbide was gradually going into solution in liquid uranium, and intergranular penetration and erosion of UC occurred to an extent which increased with temperature that was varied between 1180° and 1720 °C. No wonder then, that the 6 observed in different tests was as low as 37° and as high as 110°. Also for the surface tension 7 of liquid uranium values from 780 to 1510 dyne/cm have been obtained at a constant temperature of 1600 °C. The ys of UC in argon was estimated to be approximately 730 erg/cm2 at 1325 °C, and 7si (at the boundary U — UC) appeared to be near 140 erg/cm2 at 1100 °C. 

For the molecular solute, equilibrium between the vapor phase and the liquid phase is given by ... 

Other references in Table in discuss applications in precipitation of metal.compounds, gaseous reduction of metals from solution, equilibrium of copper in solvent extraction, electrolyte purification and solid-liquid equilibria in concentrated salt solutions. The papers by Cognet and Renon (25) and Vega and Funk (59) stand out as recent studies in which rational approaches have been used for estimating ionic activity coefficients. In general, however, few of the studies are based on the more recent developments in ionic activity coefficients. 

To reestablish equilibrium, p g must be decreased also. This decrease in p can be accomplished by decreasing the temperature. The chemical potential of the liquid solvent is decreased by the drop in temperature as well as by the addition of solute. Equilibrium is reestablished if... 

The hydrotropic action of a dicarboxylic acid is discussed against the general features of hydro-tropic action the liquid crystal/isotropic solution equilibrium. It is shown that the hydrotropic action of the dicarboxylic acid in question, 8-[5(6)-carboxy-4-hexyl-cyclohex-2-enyl] octanoic acid, depends on its conformation at an interface. 

Solvent extraction rarely involves gases, so that other cases should now be considered. Most liquid organic solutes are completely miscible with, or at least highly soluble in, most organic solvents. The case of a liquid solute that forms a solute-rich liquid phase that contains an appreciable concentration of the solvent is related to the mutual solubility of two solvents, and has been discussed in section 2.2. This leaves solid solutes that are in equilibrium with their saturated solution. It is expedient to discuss organic, nonelectrolytic solutes separately from salts or other ionic solutes. 

LIQUID-PHASE BEHAVIOR. The liquid phase contains dissolved substances and contacts the solid phase. For our purposes, the liquid phase is used synonymously with aqueous phase , and all processes discussed in this section take place in aqueous solutions. The dissolved monomers of the solid phase are formed in equilibrium with their uncomplexed components. Such components may be uncomplexed ions (which are charged atoms or molecules) free in solution or ionic complexes in equilibrium with dissociated ions. Concentrations of the uncomplexed ions, therefore, depend upon the concentrations of all chemical substances competing for binding interactions with them. Each complex-ation reaction is defined by either a solution equilibrium constant ... 

In solutions and liquid mixtures, activities are defined in various ways and somewhat different conventions are adopted for standard states. For a detailed discussion, the reader is referred to Denbigh [3] and Bett et al. [4]. Tabulated values of activities in many solutions are available [14, 15] and these can be used to calculate equilibrium constants using eqn. (26). 

Vapor-liquid equilibrium experiments were performed with an improved Othmer recirculation still as modified by Johnson and Furter (2). Temperatures were measured with Fisher thermometers calibrated against boiling points of known solutions. Equilibrium compositions were determined with a vapor fractometer using a type W column and a thermal conductivity detector. The liquid samples were distilled to remove the salt before analysis with the gas chromatograph the amount of salt present was calculated from the molality and the amount of solvent 2 present. Temperature measurements were accurate to 0.2°C while compositions were found to be accurate to 1% over most of the composition range. The system pressure was maintained at 1 atm. 1 mm... 

Assuming ideal gas behavior, the equilibrium partial pressure, ph of a compound above a liquid solution or liquid mixture is a direct measure of the fugacity, fu, of that compound in the liquid phase (see Fig. 3.9 and Eq. 3-33). 

Horizontal separators normally are more efficient at handling large volumes of gas than vertical types since liquid droplets fall perpendicular to the gas flow in the gravity settling section, and are more easily settled out of the gas continuous phase. Also, since interface area is larger in a horizontal separator, it is easier for gas bubbles, which come out of solution as liquid approaches equilibrium, to reach the vapor space. 

Distillation of Ammonium Bicarbonate Solutions. Vapor-liquid equilibrium data for ammonium bicarbonate solutions at the boil are apparently not available in the literature. The data in the literature, however, do indicate that when the temperature of such a solution is increased, or the pressure on it decreased, the gas that is evolved is predominantly carbon dioxide. Thus, it appears that such a distillation would be two consecutive processes first, a steam stripping of the carbon dioxide in the solution, followed by a distillation of ammonia from an ammonia-water mixture containing perhaps some carbon dioxide. Possibly the ammonia, carbon dioxide, and water in the distillate product would recombine completely in the condenser to form an ammonium bicarbonate solution. Perhaps an absorption tower would be necessary to effect the recombination. 

Adsorption equilibria for the systems phenol-p-toluene sulfonate, phenol-p-bromophenol and phenol-dodecyl benzene sulfonate are shown in Figures 5, 6 and 7. In these figures, the ratio of the observed equilibrium values and computed values from equation (14) are plotted against the equilibrium liquid phase concentration of the solute in the mixture. It is seen that most of the data points are well within a deviation of 20%. The results for these diverse solute systems indicate that equation (14) is suitable for correlating binary equilibrium data for use in multicomponent rate models. 

The solute equilibrium concentration C is normally always greater in the solvent liquid phase than in the feed-raffinate phase on the same tie-line. Note the slope of the tie-lines (the dotted lines). 

It is interesting to consider a simple model for noble gas solution in liquids. From the Boltzmann distribution theorem, the ratios of equilibrium concentrations of solute molecules in two phases (here we consider liquid and gas phases) can be written as... 

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