Water equilibrium measurements

In the discussion of the relative acidity of carboxylic acids in Chapter 1, the thermodynamic acidity, expressed as the acid dissociation constant, was taken as the measure of acidity. It is straightforward to determine dissociation constants of such adds in aqueous solution by measurement of the titration curve with a pH-sensitive electrode (pH meter). Determination of the acidity of carbon acids is more difficult. Because most are very weak acids, very strong bases are required to cause deprotonation. Water and alcohols are far more acidic than most hydrocarbons and are unsuitable solvents for generation of hydrocarbon anions. Any strong base will deprotonate the solvent rather than the hydrocarbon. For synthetic purposes, aprotic solvents such as ether, tetrahydrofuran (THF), and dimethoxyethane (DME) are used, but for equilibrium measurements solvents that promote dissociation of ion pairs and ion clusters are preferred. Weakly acidic solvents such as DMSO and cyclohexylamine are used in the preparation of strongly basic carbanions. The high polarity and cation-solvating ability of DMSO facilitate dissociation... 

Recently, Engel et al.92 critically discussed these models and concluded by equilibrium measurements in different solvents that bridging of the hydroxy group of hydroxyproline by means of a water molecule must be an unspecific reaction and can be caused as... 

The interfacial shear viscosities are measured by the deep channel viscous traction surface viscometer (5) at the Illinois Institute of Technology. The oil-water equilibrium tensions are measured by either the spinning drop or the du Nouy ring (6) method. 

When is equilibrium reached is an important follow-up, timescale question. The water activity measurement involves two interrelated time-scales. The first timescale is related to the nonequilibrium nature of most... 

Wilding, W.V., Adams, K.L., Carmichael, A.E., Hull, J.B., Jarman, T.C., Jenkins, K.P., Marshall, T.L., and Wilson, H.L. Vapor-liquid equilibrium measurements on three binary mixtures difluoromethane/hydrogen chloride, c/s-1,3-dichloropropene/frans-dichloropropene, and pyrrole/water, /. Chem. Eng. Data, 47(4) 748-756, 2002. 

Bennett and Barter (1997) discuss the effect of partitioning-dissolution in an aqueous phase of alkylphenol. Specifically, they show that the depletion of this crude oil component affects the chemical composition of the original pollutant. Partitioning at equilibrium can be considered the maximum dissolution value of a compound under optimal solvation conditions. Partitioning-dissolution is obtained by washing the crude oil with saline water at variable temperature and pressure conditions, similar to those in the subsurface. The data reported were obtained using a partition device able to simulate the natural environmental conditions of a crude oil reservoir. The alkylphenol partition coefficients between crude oil and saline subsurface water were measured as a function of variation in pressure, temperature, and water salinity. Preliminary trials proved that the experimental device did not allow alkylphenol losses due to volatilization. 

You can measure the equilibria in this system by effectively titrating the acidic hydrogens on these waters, and the equilibrium measurements show—I don t want to get involved in the details of the measurements—but they show that starting with approximately a 0.01 M ion concentration, gives comparable quantities of what must be the sum of these two isomers. This is what titration determines. Their combined concentrations must be roughly equal to the trichloro species and the concentration of the diaquo species will be very small. 

Water isotherms determined at 35°C. are shown in Figure 3. The amount of water sorbed by the Pittsburgh coal is about twice the amount taken up by Pocahontas coal. These isotherms represent equilibrium measurements. Hysteresis loops that do not close at relative pressures less than 0.3 are characteristic of water adsorption on coal. 

A linear relation was found28 to exist between the logarithm of the equilibrium constant for the addition of water and other nucleophiles to quinazoline and the y-value of Sander and Jencks. The latter is an equilibrium measure of the avidity of a nucleophile to add across the carbonyl bond in aldehydes.29... 

Smith, PR. 1971. The determination of equilibrium relative humidity or water activity in foods A literature review. The British Food Manufacturing Industries Research Association, U.K. Stekelenburg, F.K. and Labots, H. 1991. Measurement of water activity with an electric hygrometer. Ini. J. Food Sci. Technol. 26 111-116. Stoloff, L. 1978. Calibration of water activity measuring instruments and devices Collaborative study. J. AOAC 61 1166-1178. 

Theoretically this is possible, and — 150-atm. tension has been demonstrated experimentally on water in Berthelot (3) tubes. However, negative pressures in Town-end s experiments with dilute solution were less than 1 atm. and it is felt that more basic research on liquid tensions is necessary before schemes A and B of Table I can be considered for solutions as concentrated as sea water. Townend measured only equilibrium and had no need for rapid vapor transfer. 

Equilibrium measurements of the solid hydrate phase have been previously avoided due to experimental difficulties such as water occlusion, solid phase inhomogeneity, and measurements of solid phase concentrations. Instead, researchers have traditionally measured fluid phase properties (i.e., pressure, temperature, gas phase composition, and aqueous inhibitor concentrations) and predicted hydrate formation conditions of the solid phase using a modified van der Waals and Platteeuw (1959) theory, specified in Chapter 5. 

Extensive measurements of heats of formation of carbocations in the gas phase exist and there have been more limited measurements in solution for nonhydroxylic solvents.39 For comparison with equilibrium measurements in water, however, the most appropriate measurement would appear to be free energies of formation in aqueous solution. It is fortunate therefore that a convenient compilation of values of AGf(aq) at 25°C has been provided by Guthrie.38 This allows us for example to derive a value of AGf(aq) for a carbocation from a measurement of its pXR value, provided that the free energy of formation of the corresponding alcohol [R OH in Equation (1)] is known. 

In practice, extrapolations of p fR in water have usually used the older acidity function based method, for example, for trityl,61,62 benzhydryl,63 or cyclopropenyl (6) cations.66,67 These older data include studies of protonation of aromatic molecules, such as pKSi = —1.70 for the azulenium ion 3,59 and Kresge s extensive measurements of the protonation of hydroxy- and methoxy-substituted benzenes.68 Some of these data have been replotted as p fR or pKa against XQ with only minor changes in values.25,52 However, for more unstable carbocations such as 2,4,6-trimethylbenzyl, there is a long extrapolation from concentrated acid solutions to water and the discrepancy is greater use of an acidity function in this case gives pA 2° = —17.5,61 compared with —16.3 (and m = 1.8) based on X0. Indeed because of limitations to the acidity of concentrated solutions of perchloric or sulfuric acid pICs of more weakly nucleophilic carbocations are not accessible from equilibrium measurements in these media. 

However, note that the values of pAR in Scheme 29 were measured in 50-50 v v TFE-water mixtures rather than water. In general, for anionic nucleophiles pAR is expected to be highly sensitive to solvent. Results of Pham and McClelland222 indicate that pAR pA 1 increases by 8 log units between water and 2% aqueous acetonitrile. The effect of a change from water to TFE-water will be much less than this, but a comparison for the /)-mcthoxybcn/yi cation shows that pAR decreases by 1 log unit.223 Thus neglecting any difference between pAR values in the two solvents the estimate of pAR for the a-trifluoromethyl-substituted /7-methoxybenzyl cation is increased to —22.5. This value has been considered at some length because equilibrium measurements for the ions summarized as 58 are relevant to the effects of a-trifluoromethyl substituents on reactivity discussed later in the chapter (p. 80). 

There have been more equilibrium measurements for reactions of carbocations with azide than halide ions. Regrettably, there is little thermodynamic data on which to base estimates of relative values of pARz and pAR using counterparts of Equations (17) and (18) with N3 replacing Cl. Nevertheless, a number of comparisons in water or TFE-H20 mixtures have been made87,106,226,230 and Ritchie and Virtanen have reported measurements in methanol.195 The measurements recorded below are for TFE-H20 and show that whereas pA" 1 is typically 4 log units more positive than pA R. pA Rz is eight units more negative. The difference should be less in water, perhaps by 2 log units, but it is clear that azide ion has about a 1010-fold greater equilibrium affinity for carbocations than does chloride (or bromide) ion. 

The brackets indicate the molar concentrations of the various molecular species. The empirical quantity a is defined by pH = —log a. In sea water, pH measurements do not yield a thermodynamic hydrogen ion activity due to liquid junction and asymmetry potentials a only approximates the hydrogen activity an+. For sea water of 33%>o salinity at 20 °C and at pH 8, 87% of the inorganic phosphate exist as HPO4-, 12% as PO4-, and 1% as H2POj. Of the PO - species 99.6% is complexed with cations other than Na+. The equilibrium relationship for the system is shown in Fig. 15. 

In this, the most common method, air is bubbled at a known rate into a volume of water containing the solute, so that the exit air achieves equilibrium with the water. By measuring the decrease in water concentration, KAW can be deduced from a mass balance. No air phase concentrations are measured. This method is ideal for fairly volatile chemicals, i.e., when Kaw exceeds 1(F3 but can be applied down to about 1(H. Yin and Hassett (1986) modified the method for less volatile chemicals the air phase solute concentration is measured by trapping solute from the exit air stream. Hovorka and Dohnal (1997) have refined the test conditions to achieve greater accuracy. 

The rate at which C02 comes into equilibrium with H2C03 and its dissociation products when passed into water is measurably slow, and this indeed is what has made possible an analytical distinction between H2C03 and the loosely hydrated C02 (aq). This slowness is of great importance physiologically and in biological (e.g., carbonic anhydrase catalyzed hydration), analytical, and industrial chemistry. 

Marriott, R.A., E. Fitzpatrick, F. Bernard, H.H. Wan, K.L. Lesage, P.M. Davis, and P.D. Clark. 2009. Equilibrium water content measurements for acid gas mixtures. First International Acid Gas Injection Symposium, Calgary, AB. 

Water equilibrium across the plant-air interface occurs when the water potential in the leaf cells equals that of the surrounding atmosphere. (This presupposes that the leaf and the air are at the same temperature, an aspect that we will reconsider in Chapter 8.) To measure vFleaf, the leaf can be placed in a closed chamber and the relative humidity adjusted until the leaf does not gain or lose water. Such a determination is experimentally difficult because small changes in relative humidity have large effects on VPVW, as we will show next. 

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