Solution equilibrium, phase equilibria

The effect of the medium on the position of equilibrium can be considered from two points of view (a) comparison of the gas-phase and solution equilibrium constants, and (b) comparison of the equilibrium constants for different solvents. Unfortunately, few equilibrium reactions have been studied both in the gas and liquid phases [5, 6j. These are primarily non-ionic reactions where the interaction between reacting molecules and solvent is relatively small e.g. the Diels-Alder dimerization of cyclo-pentadiene). In this chapter, therefore, equilibria which have been examined in solvents of different polarity will be the main topic considered (except for acid-base reactions described in Section 4.2.2). 

Table 4-4. Gas-phase and solution equilibrium constants K-y = [NH]/[OH] of 2- and 4-hydroxypyridine at 25. .. 30 °C unless otherwise stated [65, 67].

IR and UV/Vis [65a], mass spectrometric [65b], photoelectron [65c], microwave [65d], as well as low-temperature matrix-isolation IR spectroscopic measurements [65e] reveal that 2- and 4-hydroxypyridine (as well as 2- and 4-mercaptopyridine [65f]) exist in the gas phase and in inert matrices (N2, Ar) under equilibrium conditions mainly in the lactim (hydroxy or mercapto) form, in contrast to the situation in solution. While in nonpolar solvents such as cyclohexane and chloroform both tautomers exist in comparable amounts, the tautomeric equilibrium is shifted entirely in favour of the lactam (0x0 or thioxo) form in polar solvents such as water, as well as in the crystalUne state [66, 67, 141-145, 251-255], Supercritical-fluid 1,1-difluoroethane can be used to adjust the tautomeric constant Ki = [(llb)]l[(lla)] iso thermally over a continuum from gas-phase values to those measured in polar solvents, simply by increasing the pressure [254]. The gas-phase and solution equilibrium constants of 2- and 4-hydroxypyridine are given in Table 4-4. 

The exceptional basicity of phosphazenes (iminophosphoranes) has been discovered by Schwesinger [83]. The phosphazene derivatives have been proved to be chemically very stable, kinetically active and highly versatile, and the large number of these bases has been synthesized. The gas phase and solution equilibrium basicity measurements for a large number of phosphazenes are conducted by Kaljurand et al. [84], and their PA and pAia values are published in various papers. These measurements show that phosphazenes surpass in their basicity the derivatives of acychc or bicyclic guanidines, amidines and vinamidines (Table 2.11). Extraordinary basicity of phosphazenes was theoretically rationalized by Maksic et al. [85], in terms of effective resonance stabilization of protonated molecules [86]. 

Phase Equilibriums, Chemical Equilibriums and Solutions Thermodynamics, Thermochemistry, and Thermal Properties Nuclear Phenomena... 

When only the total system composition, pressure, and temperature (or enthalpy) are specified, the problem becomes a flash calculation. This type of problem requires simultaneous solution of the material balance as well as the phase-equilibrium relations. 

It follows that, because phase equilibrium requires that the chemical potential p. be the same in the solution as in the gas phase, one may write for the chemical potential in the solution ... 

Electrode processes are a class of heterogeneous chemical reaction that involves the transfer of charge across the interface between a solid and an adjacent solution phase, either in equilibrium or under partial or total kinetic control. A simple type of electrode reaction involves electron transfer between an inert metal electrode and an ion or molecule in solution. Oxidation of an electroactive species corresponds to the transfer of electrons from the solution phase to the electrode (anodic), whereas electron transfer in the opposite direction results in the reduction of the species (cathodic). Electron transfer is only possible when the electroactive material is within molecular distances of the electrode surface thus for a simple electrode reaction involving solution species of the fonn... 

Amount of Cs, solution phase Thus, at equilibrium the 1.0 g of resin removed is ... 

In this chapter we shall consider some thermodynamic properties of solutions in which a polymer is the solute and some low molecular weight species is the solvent. Our special interest is in the application of solution thermodynamics to problems of phase equilibrium. 

These are the criteria of phase equilibrium apphed in the solution of practical problems. 

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. 

The N equations represented by Eq. (4-282) in conjunction with Eq. (4-284) may be used to solve for N unspecified phase-equilibrium variables. For a multicomponent system the calculation is formidable, but well suited to computer solution. The types of problems encountered for nonelectrolyte systems at low to moderate pressures (well below the critical pressure) are discussed by Smith, Van Ness, and Abbott (Introduction to Chemical Engineering Thermodynamics, 5th ed., McGraw-Hill, New York, 1996). 

Availability of large digital computers has made possible rigorous solutions of equilibrium-stage models for multicomponent, multistage distillation-type columns to an exactness limited only by the accuracy of the phase equilibrium and enthalpy data utilized. Time and cost requirements for obtaining such solutions are very low compared with the cost of manual solutions. Methods are available that can accurately solve almost any type of distillation-type problem quickly and efficiently. The material presented here covers, in some... 

The weight fraction of solute in the extract phase y divided by the weight fraction of solute in the raffinate phase x at equilibrium is called the partition ratio, K [Eq. (15-1)]. 

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. 

Solute equilibrium parameters (X5,S for RPC and (Xz,Z for lEC Solute retention factor for initial mobile phase A ... 

Y = Mol fraction of one component (solute) at any point in the gas phase Y = Mol fraction gas phase composition in equilibrium with a liquid composition, X... 

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. 

Whenever die rich and the lean phases are not in equilibrium, an interphase concentration gradient and a mass-transfer driving force develop leading to a net transfer of the solute from the rich phase to the lean phase. A common method of describing the rates of interphase mass transfer involves the use of overall mass-transfer coefficients which are based on the difference between the bulk concentration of the solute in one phase and its equilibrium concentration in the other phase. Suppose that the bulk concentradons of a pollutant in the rich and the lean phases are yi and Xj, respectively. For die case of linear equilibrium, the pollutant concnetration in the lean phase which is in equilibrium with y is given by... 

Particular attention has been given to the study of thermal rearrangements of N-substituted benzotriazoles. N-(N, N -Dialkylaminomethyl) benzotriazoles exist in the solid state solely as the isomers 37a, but in the liquid, solution, melt, and argon matrix phases they form equilibrium mixtures of the tautomers 37a and 3 (Scheme 19) [76JCS(P2)741 ... 

Raoult s Law. The molar composition of a liquid phase (ideal solution) in equilibrium with its vapor at any temperature T is given by... 

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. 

There is one other three-phase equilibrium involving clathrates which is of considerable practical importance, namely that between a solution of Q, the clathrate, and gaseous A. For this equilibrium the previous formulas and many of the following conclusions also hold when replacing fiQa by fiQL, the chemical potential of Q in the liquid phase. But a complication then arises since yqL and the difference are not only... 

Let us first consider the three-phase equilibrium ( -clathrate-gas, for which the values of P and x = 3/( +3) were determined at 25°C. When the temperature is raised the argon content in the clathrate diminishes according to Eq. 27, while the pressure can be calculated from Eq. 38 by taking yA values following from Eq. 27 and the same force constants as used in the calculation of Table III. It is seen that the experimental results at 60°C and 120°C fall on the line so calculated. At a certain temperature and pressure, solid Qa will also be able to coexist with a solution of argon in liquid hydroquinone at this point (R) the three-phase line -clathrate-gas is intersected by the three-phase line -liquid-gas. At the quadruple point R solid a-hydroquinone (Qa), a hydroquinone-rich liquid (L), the clathrate (C), and a gas phase are in equilibrium the composition of the latter lies outside the part of the F-x projection drawn in Fig. 3. The slope of the three-phase line AR must be very steep, because of the low solubility of argon in liquid hydroquinone. 

---