Phase equilibrium solute concentration

Adsorption isotherms are used to quantitatively describe adsorption at the solid/ liquid interface (Hinz, 2001). They represent the distribution of the solute species between the liquid solvent phase and solid sorbent phase at a constant temperature under equilibrium conditions. While adsorbed amounts as a function of equilibrium solute concentration quantify the process, the shape of the isotherm can provide qualitative information on the nature of solute-surface interactions. Giles et al. (1974) distinguished four types of isotherms high affinity (H), Langmuir (L), constant partition (C), and sigmoidal-shaped (S) they are represented schematically in Figure 3.3. 

An extractor with hollow fibres of polypropylene could operate with the aqueous phase inside the fibers at a pressure slightly greater than the pressure of the organic phase on the outside. The pores of the membrane would fill with the organic solvent, and the liquid-liquid interface would be at the pore mouths. The concentration gradients are sketched in Fig. 26.14 for an example where the equilibrium solute concentration is much higher in the organic phase. The overall resistance for this case is... 

Figure 12 Comparison of simulated concentration profiles with experimental data for a system with partially miscible solvents, x - solute concentration in heavy phase, y - solute concentration in light phase, xb - concentration of light solvent in heavy phase, yf - concentration of heavy solvent in light phase. Broken lines equilibrium values.

Figure 11.1 Phase diagram, phase equilibriums, and concentration profile in a binary multiphase system a and fS are solid solutions 1, 2, 3 are stable and 4 is a metastable intermediate phase.

Reaction Conditions. Alcoholysis commonly takes place in one Hquid phase, sometimes with one of the reactants being only partially soluble and going into solution gradually as the reaction proceeds. Unless an excess of one of the reactants is used, or unless one of the products is withdrawn from the reaction phase by vaporization or precipitation, the reaction does not proceed to completion but comes to a standstill with substantial proportions of both alcohols and both esters in equilibrium. The concentrations present at equilibrium depend on the characteristics of the alcohols and esters involved, but in most practical uses of the reaction, one or both of the devices mentioned are used to force the reaction toward completion. 

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. 

Classical Adiabatic Design Method The classical adiabatic method assumes that the heat of solution serves only to heat up the liquid stream and that there is no vaporization of solvent. This assumption makes it feasible to relate increases in the hquid-phase temperature to the solute concentration x by a simple eutnalpy balance. The equihbrium curve can then be adjusted to account For the corresponding temperature rise on an xy diagram. The adjusted equilibrium curve will become more concave upward as the concentration increases, tending to decrease the driving forces near the bottom of the tower, as illustrated in Fig. 14-8 in Example 6. 

Ternary-phase equilibrium data can be tabulated as in Table 15-1 and then worked into an electronic spreadsheet as in Table 15-2 to be presented as a right-triangular diagram as shown in Fig. 15-7. The weight-fraction solute is on the horizontal axis and the weight-fraciion extraciion-solvent is on the veriical axis. The tie-lines connect the points that are in equilibrium. For low-solute concentrations the horizontal scale can be expanded. The water-acetic acid-methylisobutylketone ternary is a Type I system where only one of the binary pairs, water-MIBK, is immiscible. In a Type II system two of the binary pairs are immiscible, i.e. the solute is not totally miscible in one of the liquids. 

The working capacity of a sorbent depends on fluid concentrations and temperatures. Graphical depiction of soration equilibrium for single component adsorption or binary ion exchange (monovariance) is usually in the form of isotherms [n = /i,(cd or at constant T] or isosteres = pi(T) at constant /ij. Representative forms are shown in Fig. I6-I. An important dimensionless group dependent on adsorption equihbrium is the partition ratio (see Eq. 16-125), which is a measure of the relative affinities of the sorbea and fluid phases for solute. 

Now, as equilibrium is maintained in the plate (p) by definition, the mass (dm) will bfe distributed between the two phases, resulting in a solute concentration change of dXm(p) in the mobile phase and dXs(p) in the stationary phase. Then,... 

A third method, or phenomenon, capable of generating a pseudo reaction order is exemplified by a first-order solution reaction of a substance in the presence of its solid phase. Then if the dissolution rate of the solid is greater than the reaction rate of the dissolved solute, the solute concentration is maintained constant by the solubility equilibrium and the first-order reaction becomes a pseudo-zero-order reaction. 

Raoulfs law. Adding a solute lowers the concentration of solvent molecules in the liquid phase. To maintain equilibrium, the concentration of solvent molecules in the gas phase must decrease, thereby lowering the solvent vapor pressure. 

It is essentially a phase diagram which consists of a family of isotherms that relate the equilibrium pressure of hydrogen to the H content of the metal. Initially the isotherm ascends steeply as hydrogen dissolves in the metal to form a solid solution, which by convention is designated as the a phase. At low concentrations the behaviour is ideal and the isotherm obeys Sievert s Law, i.e.,... 

The parameters which characterize the thermodynamic equilibrium of the gel, viz. the swelling degree, swelling pressure, as well as other characteristics of the gel like the elastic modulus, can be substantially changed due to changes in external conditions, i.e., temperature, composition of the solution, pressure and some other factors. The changes in the state of the gel which are visually observed as volume changes can be both continuous and discontinuous [96], In principle, the latter is a transition between the phases of different concentration of the network polymer one of which corresponds to the swollen gel and the other to the collapsed one. 

Baviere et al. [41] determined the adsorption of C18 AOS onto kaolinite by agitating tubes containing 2 g of kaolinite per 10 g of surfactant solution for 4 h in a thermostat. Solids were separated from the liquid phase by centrifugation and the supernatant liquid titrated for sulfonate. The amount of AOS adsorbed is the difference between initial solution concentration and supernatant solution concentration at equilibrium. 

The penetration theory has been used to calculate the rate of mass transfer across an interface for conditions where the concentration CAi of solute A in the interfacial layers (y = 0) remained constant throughout the process. When there is no resistance to mass transfer in the other phase, for instance when this consists of pure solute A, there will be no concentration gradient in that phase and the composition at the interface will therefore at all Limes lie the same as the bulk composition. Since the composition of the interfacial layers of the penetration phase is determined by the phase equilibrium relationship, it, too. will remain constant anil the conditions necessary for the penetration theory to apply will hold. If, however, the other phase offers a significant resistance to transfer this condition will not, in general, be fulfilled. 

Values of p can be determined, in principle, from any phase equilibrium data. A small table of p 2 values is available in reference (2). However, one of the most straightforward ways of determining pf values is to fit phase equilibrium data for solvent sorption in concentrated polymer solutions. To do this, equations (2) and (13) are combined to solve for p utilizing experimental partial pressure data. 

There are relatively few phase equilibrium data relating to concentrated polymer solutions containing several solvents. Nevertheless, In polymer devolatilization, such cases are often of prime Interest. One of the complicating features of such cases Is that. In many Instances, one of the solvents preferentially solvates the polymer molecules, partially excluding the other solvents from Interaction directly with the polymer molecules. This phenomenon Is known as "gathering". 

---