Vapor-liquid equilibrium solutions

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). 

These are general equations that do not depend on the particular mixing rules adopted for the composition dependence of a and b. The mixing rules given by Eqs. (4-221) and (4-222) can certainly be employed with these equations. However, for purposes of vapor/liquid equilibrium calculations, a special pair of mixing rules is far more appropriate, and will be introduced when these calculations are treated. Solution of Eq. (4-232) for fugacity coefficient at given T and P reqmres prior solution of Eq. (4-231) for V, from which is found Z = PV/RT. 

Vapor/liquid equilibrium (XT E) relationships (as well as other interphase equihbrium relationships) are needed in the solution of many engineering problems. The required data can be found by experiment, but such measurements are seldom easy, even for binaiy systems, and they become rapidly more difficult as the number of constituent species increases. This is the incentive for application of thermodynamics to the calculation of phase-equilibrium relationships. 

Gmehhng and Onken (op. cit.) give the activity coefficient of acetone in water at infinite dilution as 6.74 at 25 C, depending on which set of vapor-liquid equilibrium data is correlated. From Eqs. (15-1) and (15-7) the partition ratio at infinite dilution of solute can he calculated as follows ... 

In the case of vapor-liquid equilibrium, the vapor and liquid fugacities are equal for all components at the same temperature and pressure, but how can this solution be found In any phase equilibrium calculation, some of the conditions will be fixed. For example, the temperature, pressure and overall composition might be fixed. The task is to find values for the unknown conditions that satisfy the equilibrium relationships. However, this cannot be achieved directly. First, values of the unknown variables must be guessed and checked to see if the equilibrium relationships are satisfied. If not, then the estimates must be modified in the light of the discrepancy in the equilibrium, and iteration continued until the estimates of the unknown variables satisfy the requirements of equilibrium. 

There are two main issues concerning the chemistry of the reaction and the separation. One is how to separate the hydriodic acid and sulfuric acid produced by the Bunsen reaction. The other is how to carry out the hydrogen iodide (HI) decomposition section, where the presence of azeotrope in the vapor-liquid equilibrium of the hydriodic acid makes the energy-efficient separation of HI from its aqueous solution difficult, and also, the unfavorable reaction equilibrium limits the attainable conversion ratio of HI to a low level, around 20%. 

The solution requires the concentration of the heptane and toluene in the vapor phase. Assuming that the composition of the liquid does not change as it evaporates (the quantity is large), the vapor composition is computed using standard vapor-liquid equilibrium calculations. Assuming that Raoult s and Dalton s laws apply to this system under these conditions, the vapor composition is determined directly from the saturation vapor pressures of the pure components. Himmelblau6 provided the following data at the specified temperature ... 

In general, the formulation of the problem of vapor-liquid equilibria in these systems is not difficult. One has the mass balances, dissociation equilibria in the solution, the equation of electroneutrality and the expressions for the vapor-liquid equilibrium of each molecular species (equality of activities). The result is a system of non-linear equations which must be solved. The main thermodynamic problem is the relation of the activities of the species to be measurable properties, such as pressure and composition. In order to do this a model is needed and the parameters in the model are usually obtained from experimental data on the mixtures involved. Calculations of this type are well-known in geological systems O) where the vapor-liquid equilibria are usually neglected. 

To test the validity of the extended Pitzer equation, correlations of vapor-liquid equilibrium data were carried out for three systems. Since the extended Pitzer equation reduces to the Pitzer equation for aqueous strong electrolyte systems, and is consistent with the Setschenow equation for molecular non-electrolytes in aqueous electrolyte systems, the main interest here is aqueous systems with weak electrolytes or partially dissociated electrolytes. The three systems considered are the hydrochloric acid aqueous solution at 298.15°K and concentrations up to 18 molal the NH3-CO2 aqueous solution at 293.15°K and the K2CO3-CO2 aqueous solution of the Hot Carbonate Process. In each case, the chemical equilibrium between all species has been taken into account directly as liquid phase constraints. Significant parameters in the model for each system were identified by a preliminary order of magnitude analysis and adjusted in the vapor-liquid equilibrium data correlation. Detailed discusions and values of physical constants, such as Henry s constants and chemical equilibrium constants, are given in Chen et al. (11). 

Two activity coefficient models have been developed for vapor-liquid equilibrium of electrolyte systems. The first model is an extension of the Pitzer equation and is applicable to aqueous electrolyte systems containing any number of molecular and ionic solutes. The validity of the model has been shown by data correlation studies on three aqueous electrolyte systems of industrial interest. The second model is based on the local composition concept and is designed to be applicable to all kinds of electrolyte systems. Preliminary data correlation results on many binary and ternary electrolyte systems suggest the validity of the local composition model. 

Chen, C., H. I. Britt, J. F. Boston, and L. B. Evans, "Extension and Application of the Pitzer equation for Vapor-Liquid Equilibrium of Aqueous Electrolyte Systems with Molecular Solutes," AIChE J., 1979, 25, 820. 

The solubility of gaseous weak electrolytes in aqueous solutions is encountered in many chemical and petrochemical processes. In comparison to vapory-liquid equilibria in non reacting systems the solubility of gaseous weak electrolytes like ammonia, carbondioxide, hydrogen sulfide and sulfur dioxide in water results not only from physical (vapor-liquid) equilibrium but also from chemical equilibrium in the liquid phase. 

To calculate the multicomponent vapor-liquid equilibrium, equilibrium constants for chemical reactions 1-9 are taken from literature in comparison to the original publication, in the present work different numerical values for the second dissociations of hydrogen sulfide and sulfur dioxide were chosen (cf. Appendix III). Henry s constants are evaluated from single solute solubility data without neglecting Poynting corrections ... 

The NaHSOg was analyzed by iodine titration and was typically 97-98% of the expected SO2 content. Several of the solutions used for vapor/liquid equilibrium experiments were analyzed for total SO2 and found to contain 5 to 10% less than the nominal concentration. Nominal concentrations were used in presenting and analyzing the data, unless noted otherwise. Therefore, correlated values of Pgc may he 5 to 10% low for a given solution composition. 

Optimized steam requirement is relatively insensitive to solution pH. Solution capacity for SO2 absorption can reasonably vary from 0.1 to 0.4 g-moles S02/liter. The SO2 gas sensing electrode is an effective tool for vapor/liquid equilibrium at room temperature. 

The analysis providing interaction second virial coefficients from chromatography rests upon three principal assumptions 1) vapor-liquid equilibrium exists in the column 2) the solute (component 1) is soluble in both the carrier gas (component 2) and the stationary liquid phase (component 3) 3) the carrier gas and stationary liquid are insoluble. Under assumption 1, we can write... 

Silverman [2] has presented an analogous analysis of the vapor-liquid equilibrium for an ideal solution. 

In Figure 1 we compare our numerical solutions with the molecular dynamics computer simulations of Thompson, et al. (7). In this comparison we use liquid and vapor densities obtained from the simulation studies. In the next section we obtain the required boundary values by approximate evaluation of vapor-liquid equilibrium for a small system. 

Tang, I. N., H. R. Munkelwitz, and J. H. Lee, Vapor-Liquid Equilibrium Measurements for Dilute Nitric Acid Solutions, Atmos. Environ., 22, 2579-2585 (1988). 

The use of a dissolved salt in place of a liquid component as the separating agent in extractive distillation has strong advantages in certain systems with respect to both increased separation efficiency and reduced energy requirements. A principal reason why such a technique has not undergone more intensive development or seen more than specialized industrial use is that the solution thermodynamics of salt effect in vapor-liquid equilibrium are complex, and are still not well understood. However, even small amounts of certain salts present in the liquid phase of certain systems can exert profound effects on equilibrium vapor composition, hence on relative volatility, and on azeotropic behavior. Also extractive and azeotropic distillation is not the only important application for the effects of salts on vapor-liquid equilibrium while used as examples, other potential applications of equal importance exist as well. 

A procedure is presented for correlating the effect of non-volatile salts on the vapor-liquid equilibrium properties of binary solvents. The procedure is based on estimating the influence of salt concentration on the infinite dilution activity coefficients of both components in a pseudo-binary solution. The procedure is tested on experimental data for five different salts in methanol-water solutions. With this technique and Wilson parameters determined from the infinite dilution activity coefficients, precise estimates of bubble point temperatures and vapor phase compositions may be obtained over a range of salt and solvent compositions. 

Therefore, the objectives of this study were to investigate the influence of salt concentration on the vapor-liquid equilibrium behavior of aqueous solutions of methyl alcohol and to develop a fundamentally sound approach to correlating the influence of salt on the behavior. 

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... 

Isothermal vapor-liquid equilibrium data at 75°, 50° and 25° C for the system of 2-propanol-water-lithium perchlorate were obtained by using a modified Othmer still. In the 2-propanol-rich region 2-propanol was salted out from the aqueous solution by addition of lithium perchlorate, but in the water-rich region 2-propanol was salted in. It is suggested from the experimental data that the simple electrostatic theory cannot account for the salt effect parameter of this system. 

The salt effects of potassium bromide and a series office symmetrical tetraalkylammonium bromides on vapor-liquid equilibrium at constant pressure in various ethanol-water mixtures were determined. For these systems, the composition of the binary solvent was held constant while the dependence of the equilibrium vapor composition on salt concentration was investigated these studies were done at various fixed compositions of the mixed solvent. Good agreement with the equation of Furter and Johnson was observed for the salts exhibiting either mainly electrostrictive or mainly hydrophobic behavior however, the correlation was unsatisfactory in the case of the one salt (tetraethylammonium bromide) where these two types of solute-solvent interactions were in close competition. The transition from salting out of the ethanol to salting in, observed as the tetraalkylammonium salt series is ascended, was interpreted in terms of the solute-solvent interactions as related to physical properties of the system components, particularly solubilities and surface tensions. 

The data in Tables I-XVI (see Appendix for all tables) show the isobaric vapor-liquid equilibrium results at the boiling point for potassium, ammonium, tetramethylammonium, tetraethylammonium, tetra-n-propylammonium, and tetra-n-butylammonium bromides in various ethanol-water mixtures at fixed liquid composition ratios. The temperature, t, is the boiling temperature for all solutions in these tables. In all cases, the ethanol-water composition was held constant between 0.20 and 0.35 mole fraction ethanol since it is in this range that the most dramatic salt effects on vapor-liquid equilibrium in this particular system should be observed. That is, previous data (12-15,38) have demonstrated that a maximum displacement of the vapor-liquid equilibrium curve by salts frequently occurs in this region. In the results presented here, it should be noted that Equation 1 has been modified to... 

In this system, C = 2. If we choose a point which does not fall on the vapor-liquid equilibrium line, then all three variables must be known to describe the system. However, by choosing a point on the vapor-liquid line phases, P=2 and thus, degrees of freedom F = 2-2+2 =2. In other words, only two of the three degrees of freedom (variables) must be known. Referring to Figure 2.3b, if we have a 50/50 mole fraction solution of A and B, the mixture boils at 92°C and the vapor contains 78 mole % of B. In Figure 2.3a the dotted lines indicate the partial pressure of each of the components, that is, the equation of each line defines Raoult s law ... 

In the usual distillation problem, the operating pressure, the feed composition and thermal condition, and the desired product compositions are specified. Then the relations between the reflux rates and the number of trays above and below the feed can be found by solution of the material and energy balance equations together with a vapor-liquid equilibrium relation, which may be written in the general form... 

The performance of a given column or the equipment requirements for a given separation are established by solution of certain mathematical relations. These relations comprise, at every tray, heat and material balances, vapor-liquid equilibrium relations, and mol fraction constraints. In a later section, these equations will be stated in detail. For now, it can be said that for a separation of C components in a column of n trays, there still remain a number, C + 6, of variables besides those involved in the dted equations. These must be fixed in order to define the separation problem completely. Several different combinations of these C + 6 variables may be feasible, but the ones commonly fixed in column operation are the following ... 

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. 

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