Experimental data in aqueous solution

The heat of ionization in aqueous solution, AH q, represents the enthalpy change for the following reaction M(+anq) -f- nX -aq) = MXn(aq). Although much AHaq data exist for class (b) metal chlorides, bromides and iodides, few data are available for class (b) fluorides and class (a) halides in general. This is because MXn(aq) in these cases is not a stable species. It is therefore difficult to compare class (a) and (b) halides in aqueous solution in a manner which is entirely consistent with AHion(g). It is easy to show, however, that in aqueous solution most metal ions, which are class (b) by 

From Table 3 it is apparent that Hg has the order MI2 MBr2 MC12, and is therefore clearly a class (b) metal. Sr has the reverse order and is class (a). (It should be pointed out that any consideration of the entropy change for SrX2 S) - SrX2(aq) will only make the class (a) character of Sr more pronounced.) 

The data given in Tables 2 and 3 are, of course, related to one another through a thermochemical cycle. AHi0n(g) and AHaq differ only by the heats of solvation (hydration in aqueous solution) of the reactants and product, and therefore these heats of solvation must affect the absolute bond energies in the gas phases in such a manner as to cause an inversion in the order of stability in cases of class (b) behaviour (see below). 

Qualitatively it can be seen almost immediately that these energy differences AHi0n(g)(MFn — MIn) are affected to a great extent by ionic size or internuclear distance. When we use these absolute energy differences to indicate a property (class character), we may be measuring mainly the differences in re (Z2e2/re [electrostatic energy]). 

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Tab. 4.5 Singlet excitation energies of a small subset of psoralen compounds. Experimental data in aqueous solution given in parentheses [99]. Experimental absorption coefficients are denoted w=weak (<8000), i = intermediate (8000-15000), and s = strong (>15000).

Table 8. Bond lengths species calculated by DFT using the Perdew (1986) exchange cofiinctional (Heasman, unpublished data) compared with experimental data in aqueous solution (in parentheses) and Hartree-Fock results (in brackets).

Figure 16.2 Comparison between electron self-exchange rates of transition-metal complexes calculated by TM-1 and experimental data, in aqueous solutions at room temperature (from ref. [1]).

Figure A2.3.17 Theoretical (HNC) calculations of the osmotic coefficients for the square well model of an electrolyte compared with experimental data for aqueous solutions at 25°C. The parameters for this model are a = r (Pauling)+ r (Pauling), d = d = 0 and d as indicated in the figure.

The prevalence of water in many industrial processes has led to the accumulation of a large body of experimental data on aqueous solutions of both electrolytes and nonelectrolytes. 

We will see in chapter 8 that, in the case of aqueous solutions, it is convenient to adopt the condition of hypothetical 1-molal solution at P = 1 bar and T = 298.15 K as the standard state. Most experimental data on aqueous solutions conform to this reference condition. In this case, the resulting activity coefficient is defined as the practical activity coefficient and must not be confused with the rational activity coefficient of general relation 2.80. 

The second part of this series extends the ideas of free volume to liquids. It is only in the third part that Frank and Evans apply the concept of free volume to aqueous solutions. Examining the experimental data on aqueous solutions of nonelectrolytes, they found striking deviations from the standard behavior. These findings led to the now famous conclusion ... 

Table 3. Solvation effects on calculated frequencies (scaled by 0.893) of acetic acid and acetate compared to experimental values in aqueous solution (Kubicki et al. 1999c). (Note Band assignments based on calculated vibrational modes in these model clusters, not experimental data.)...

In our discussion of halide ion quadrupole relaxation we will follow a path of increasing complexity of the systems. First, we consider in the following subsection the relaxation rates observed for the ions at infinite dilution in water and in connection with this the theoretical treatment of relaxation due to ion-solvent interactions. In Subsection 5.1.3, experimental data for aqueous solutions of alkali halides are considered and in connection with this we outline theoretical attempts to account for effects of ion-ion interactions on the relaxation rates. Apart from alkali halide solutions few inorganic systems, mainly earth alkali halide solutions, have been studied and these are treated in Subsection 5.1.4. Hydrophobic solutes have particularly strong effects on chloride, bromide and iodide relaxation and the explanation to this is considered in Subsection 5.1.5. Long-chain hydrophobic solutes in aqueous systems form various types... 

In addition to the rather scattered data reported in the previous survey (76AHCSl,p. 510), a few new studies appeared on purine-6- and -2-thiones. Tire MO calculations of solvent effects (AMl-SMl and AM1-SM2) on the tautomerism of 6-thiopurine indicated that l//,9//-tautomer 7a is greatly stabilized in aqueous solution [94THE(309)137].Tlie same results were obtained experimentally from UV and and NMR studies (75JA3215, 75JA4627,75JA4636). 

A criterion for the presence of associated ion pairs was suggested by Bjerrum. This at first appeared to be somewhat arbitrary. An investigation by Fuoss,2 however, threw light on the details of the problem and set up a criterion that was the same as that suggested by Bjerrum. According to this criterion, atomic ions and small molecular ions will not behave as strong electrolytes in any solvent that has a dielectric constant less than about 40. Furthermore, di-divalent solutes will not behave as strong electrolytes even in aqueous solution.2 Both these predictions are borne out by the experimental data. 

In the two sets of results plotted in Fig. 34 no maximum is observed in either case within the range of temperature covered by the experiments nevertheless, in both cases the values appear to be tending toward a maximum lying just outside the experimental range, namely, at — 5.4°C for chloracetic acid, and at 53.9 for glycine. In 1934, Harned and Embree, surveying all the data (in Table 9) that had been obtained up to that time in aqueous solution, found a remarkable uniformity in... 

If any equilibrium constants show this linearity, this behavior is most likely to be found among proton transfers of type (118) and type (120). The expressions for log K given in Table 11 show this linearity they represent, within the experimental error, the accurate data obtained by measurements on three proton transfers in aqueous solution. All three are of the type (120). 

When interpreting proton transfers in Chapter 7, we found that the experimental data showed that for most solute species in aqueous solution the values of J lay between 0.25 and 1.0 electron-volts. We shall now be interested in the values of L that are necessary to account for the observed solubilities of solids in water. We may expect the range of values of L to be rather similar the main difference is that in the solution of a crystal the value of Aq in (8G) is never less than 2, whereas in most of the proton transfers discussed in Chapter 7 the value of Aq was either unity or zero. 

Activity Coefficients. Turning now to the experimental data on activity coefficients, Fig. 70 shows the results for lithium bromide in aqueous solution at 25°C, plotted against the square root of the concentration. 

As a final example of numerical simulations, consider the base-catalyzed decomposition of ozone in aqueous solution. This multistep reaction is controversial in that contradictory mechanisms have been suggested.33 34 The set of reactions that appears to be the most consistent with the experimental data is shown in Table 5-1, with a set of rate constants. Most of these values were reported in the literature, but several were refined to give agreement with experiments that measured the decline in concentration O3. 

The available experimental data, because of their paucity and their inaccuracy, do not permit the extensive testing of these figures. The directly determined susceptibilities for helium, neon, and argon are in gratifying agreement with the theoretical ones (Table YI). From the mole refraction results we may expect ions in solution to have values of % near those for gaseous ions. KoenigsbergerJ has made determinations of % for seven alkali halides in aqueous solution, in... 

Calculation of the Solvation Energy from Experimental Data The solvation energies of individual ions can be calculated from experimental data for the solvation energies of electrolytes when certain assumptions are made. If it is assumed that an ion s solvation energy depends only on its crystal radius (as assumed in Bom s model), these energies should be the same for ions K+ and F , which have similar values of these radii (0.133 0.002nm). It follows that in aqueous solutions, K+ = F- = = 414.0 kJ/mol. With the aid of these values we can now determine... 

The data in Table 2.1 suggest that the O-benzylated adduct cannot be isolated since it is less stable than reactants. The N3-benzylated adduct should be generated faster, but it should also decompose under mild conditions into free reactants, because the activation free energy in aqueous solution for the decomposition into free QM and methylcytosine is only 21.4 kcal/mol.14 In other words, these data suggested that the QM-N3-cytosine conjugate could act as QM-carrier, few years before the experimental data related to the stability of QM-conjugates became available.4... 

Despite the importance of the oxidative polymerization of 5,6-dihydroxyin-dole, in the biosynthesis of pigments, little experimental data are known on the oxidation chemistry of the oligomers of 1. For such reasons, three major dimers of 1, such as 2-4 (Scheme 2.9), have been computationally investigated at PBEO/ 6-31+G(d,p) level of theory both in gas and in aqueous solution (by PCM solvation model) to clarify the quinone methide/o-quinone tautomeric distribution. 

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