In-solution Equilibrium Calculations

No cychc zwitterion formation is possible due to steric reasons for the structurally rigid, coplanar amino acids, such as 3- and 4-carboxylic pyridine. Dimeric form with two intermolecular hydrogen bonds is also unlikely mainly for the 4-COOH isomer. For these amino acids the zwitterion is not stable in methanol and tetrahydrofuran [49], but both forms are present in mixed aqueous solvents. 

The partitioning mechanism from the aqueous solution to a lipophilic phase, which could be modeled by a two-phase system, is still unknown. 

In contrast, Nagy pointed out [13] that the zwitterionic P-alanine ( H3N-CH2-CH2-C00 ), which forms an intramolecular hydrogen bond in its favorable NCCC gauche conformation in aqueous solution (note the difference with GABA upon one less CH2 group in the linker), transforms to the intramolecularly hydrogen-bonded neutral species in chloroform with an anti -COOH group. This is an important consequence of the solvent effect on the amino acid tautomeric forms in different media. 

In cases of asymmetrically substituted heterocycles (see, e.g., [25,30,31,50,51]), the proton relocation modifies the dipole moment of the system, while the neutrality of the solute is preserved. Partition of the solute into a shghtly polar phase is generally more favorable with a smaller dipole moment. Thus, for a given molecule, the free energy changes in a solution through possible tau-tomeric/conformational transformations could be explored theoretically. Such studies would allow for the estimation of the tautomeric/conformational equilibrium constant in the selected solvents or miscible mixtures. However, from the point of view of the partition mechanism between the aqueous solution and a nonmixing solvent model of the lipophilic phase, interface studies are required, as mentioned above. 

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As a further test of the approach to equilibrium, we use the observed ajir-/aci- ratio in solution to calculate the expected slope on plots of log K vs x, if at equilibrium. Equilibrium is indicated by close agreement in calculated and observed slopes. 

Similarly, for the system of iron/calcium/phosphate, the percentage distribution of various complexes can also be calculated using solution equilibrium calculations as shown in Fig. 6.26. It follows that depending on solution pH, the dominant complexes is CaPO at pH= 10, whereas CaHP04(aq) and CaH2P04are dominant at pH = 8. 

More refined continuum models—for example, the well-known Fumi-Tosi potential with a soft core and a term for attractive van der Waals interactions [172]—have received little attention in phase equilibrium calculations [51]. Refined potentials are, however, vital when specific ion-ion or ion-solvent interactions in electrolyte solutions affect the phase stability. One can retain the continuum picture in these cases by using modified solvent-averaged potentials—for example, the so-called Friedman-Gumey potentials [81, 168, 173]. Specific interactions are then represented by additional terms in (pap(r) that modify the ion distribution in the desired way. Finally, there are models that account for the discrete molecular nature of the solvent—for example, by modeling the solvent as dipolar hard spheres [174, 175]. 

Make sure you aren t getting mixed up about the changing concentrations of the buffer constituents and the signs in the A column. The change in concentration that occurs because of the addition of strong acid or base takes place in a separate reaction to the one in the equilibrium calculation table. The effects of these changes are reflected in the different amounts in the start row of the table. The other events shown in the table only describe the equilibrium of the acetic acid solution, which will always increase the concentration of acetate ion. 

While H" exists as a hydrated species in water, c does not. As we shall see, pe is related to the equilibrium redox potential (volts, hydrogen scale). The electron, as discussed here and used as a component in our equilibrium calculations, is different from the solvated electron, which is a transient reactant in photolyzed solutions. 

Because reactions among ionic species in solution are rapid, thermo-d5mamic calculations are used to constrain the activities of dissolved chemical species at equilibrium. Garrels and Thompson (1962) were the first to calculate the speciation of the major ions in seawater by determining the extent to which each species is involved in ion pairing with each counter-ion. This information is necessary to establish the percentages of free major ions available in chemical equilibrium calculations. This section presents an example of how such multiple equilibrium systems can be constrained. 

Each of the rate terms, k+ and k, in Eq. (9.16) is related to concentrations in a way that one would predict if the probability of reaction were dependent on the collision of randomly moving particles the rate is proportional to the product of the number of entities involved in the reaction. All other factors that determine the reaction rate (energy barriers, temperature dependence, the effect of other species in solution, catalysis, etc.) are represented in the rate constant, k, which has units necessary to balance the left- and right-hand sides of the rate expression. Because ion interaction effects that are accounted for by activity coefficients in chemical equilibrium calculations (Chapter 3) are all incorporated into the rate constant, concentrations and not activities are used on the right-hand side of the reaction rate equation. 

Behavior of Binary Liquid Solutions Property changes of mixing and excess properties find greatest application in the description of liquid mixtures at low reduced temperatures, i.e., at temperatures well below the critical temperature of each constituent species. The properties of interest to the chemical engineer are V (= AV), (= AH), S, AS, G, and AC. The activity coefficient is also of special importance because of its application in phase equilibrium calculations. 

Do not waste time starting the algebra in an equilibrium calculation until you are absolutely sure that you have enough independent equations to make the solution feasible. 

In this formulation the solution task consist in identifying the species composition vector Ueq that minimizes G, for fixed T and p. The governing equations to be solved in the equilibrium calculations can be derived from the total differential of the state function. Assuming G = G T,p,n), the total differential of the Gibbs function can be expressed like ... 

Nuclear magnetic resonance spectroscopy gives precise information on complexation in solution. Equilibrium is rapidly established on an NMR time scale, hence only an average spectrum is observed and it is difficult to determine the spectrum of a pure complex. When complexation of a sugar or polyol with a diamagnetic ion occurs, all of the signals shift downfield. Equation (11.1) allows the variation of the shielding constant Ao- of the proton to be calculated when the nucleus is subjected to an electric field E whose projection on the C-H bond is... 

Periodic boundary conditions are not always used in computer simulations. Some systems, such as liquid droplets or van der Waals clusters, inherently contain a boundary. Periodic botmdary conditions may also cause difficulties when simulating inhomogeneous systems or systems that are not at equilibrium. In other cases the use of periodic boundary conditions would require a prohibitive number of atoms to be included in the simulation. This particularly arises in the study of the structural and conformational behaviour of macromolecules such as proteins and protein-ligand complexes. The first simulations of such s) tems ignored all solvent molecules due to the limited computational resources then available. This corresponds to the unrealistic situation of simulating an isolated protein in vacuo and then comparing the results with experimental data obtained in solution. Vacuum calculations can lead to significant problems. A vacuum boundary tends to minimise the surface area and so may distort the shape of the system if it is non-spherical. Small molecules may adopt more compact conformations when simulated in vacuo due to favourable intramolecular electrostatic and van der Waals interactions, which would be dampened in the presence of a solvent. 

In making equilibrium calculations for redox reactions it is often necessary to make use of the electron balance. The equation is analogous to the proton balance and is based on the principle that electrons are conserved. For example, when Cl a is added to a solution, the following half-reactions take place ... 

In applying equilibrium calculations to problems of chemical composition, that is, what species are present and in what concentrations, it is vital to be clear about the respective roles of the concentration of a species, [A], and its activity, a. For example, let us take 0.01 M HCl. In this solution of... 

In phase equilibrium calculations, three unknowns, namely the polymer concentration in the dilute phase Xg, the polymer concentration in the concentrated phase Xg, and the temperature T, occur. Specifying one of the unknowns, the two other ones can be calculated by solving Eq. (10.15) simultaneously. In order to find suitable initial values, the spinodal and/or the critical solution point can be helpful. The spinodal (see Figure 10.2) separates the metastable from the unstable region in the phase diagram and can be calculated with the help of the stability theory, where the necessary condition reads... 

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