Excess Volume Comparison

2 Calculation of the Thermodynamic Properties of Strong Electrolyte Solutes The Debye-Hiickel Theory 

Solutions containing strong electrolyte solutes differ from those containing nonelectrolyte solutes in that deviations from Henry s law become important at much lower concentrations for the electrolyte solute than for the nonelectrolyte 

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Excess Volume Comparison Figure 7.5 compares V for the three systems for which we have compared H, G, and 5, plus the (cyclohexane + decane) system.5 The comparatively large negative for the (ethanol + water) system curve (4) can be attributed to the decrease in volume resulting from the formation of hydrogen-bonded complexes in those mixtures. The negative for the (hexane + decane) system curve (3) reflects an increased packing... 

Fig. 4. Qualitative comparison between the experimental excess volumes and the APM predictions. White circles Vs > 0, black circles vB < 0 (x = 0.5).

Prepare the titration reaction mix in each reaction tube as shown in the following tables. Add all the components except the main counterion that would mediate folding (Mg2-1- for Mg titration and K+ for K titrations). For each reaction mix, prepare a reference solution of slightly excess volume but with identical reagent concentrations, for blank absorbance measurements. [Note For K+ titrations, prepare two tubes with 10 mM MgCl2 for comparison of the final states of the RNA in highest K+ concentration and in 10 mM Mg2 1.]... 

Table 1. Comparison of the destabilization parameter for different metal hydrides. A large positive value of T] indicates that the enthalpy of formation of the hydride is reduced by the introduction of deformed regions while a negative value shows that introducing regions of excess volume would increase the heat released upon the hydriding reaction.

In comparison, ab initio calculations of the electronic stmcture of Fe-S and Fe-Si compounds by Sherman (1997) indicate that due to large excess volumes of mixing as little as 2-8 wt.% of sulfur is enough to account for the density deficit in the core. Alfe et al. (1999b) estimated that 9-11 wt.% oxygen is required to explain the density deficit. 

The quantity A Ff = of expressed in J per m2 is the excess (in comparison with the bulk) of free energy per unit area of film2. Consequently, pressure IT can be also viewed as the excessive density per unit volume of the film free energy, in J m 3. 

There are about 850 newly published referenees containing about 150 new vapor-liquid equilibrium data sets and some new tables containing classical Henry s coefficients, about 600 new liquid-liquid equilibrium data sets and some new high-pressure fluid phase equilibrium data, 10 new enthalpic data sets, 20 new data sets describing PVT-properties of polymers, and 120 new data sets with densities or excess volumes. There are also new results on second osmotic virial coefficients of about 45 polymers in aqueous solution. So, in comparison to the original handbook, the new supplementary volume contains even a larger amoimt of data and will be a useful as well as necessary completion of the origirral handbook. 

Comparison with (6.4.6) reveals that these contributions are proportional to I he excess volume. We may write (6.5.8) in the form... 

Procedure. Dissolve a weighed portion of the substance in which the amount of iron is to be determined in a suitable acid, and evaporate nearly to dryness to expel excess of acid. Dilute slightly with water, oxidise the iron to the iron(III) state with dilute potassium permanganate solution or with a little bromine water, and make up the liquid to 500 mL or other suitable volume. Take 40 mL of this solution and place in a 50 mL graduated flask, add 5 mL of the thiocyanate solution and 3 mL of AM nitric acid. Add de-ionised water to dilute to the mark. Prepare a blank using the same quantities of reagents. Measure the absorbance of the sample solution in a spectrophotometer at 480 nm (blue-green filter). Determine the concentration of this solution by comparison with values on a reference curve obtained in the same way from different concentrations of the standard iron solution. 

Figure 7.5 Comparison of excess molar volumes for four mixtures as follows Curve 1 . y,C 0H22 +. y2c-C6H,2 at 7=313.15 K.

An attempt was made to improve on the analysis by employing a pingle column of approximately the same volume. The details of this are shown in Figure 5 as Column A, and a comparison is made with the three-column style designated as B. The niimber of theoretical plates (TTP) and the number of theoretical plates per foot (TPPF) are higher for Column A. However, the separation is much poorer as a result of excessive tailing of the polymer when Colxamn A was run at 1 ml/minute. Slowing the flow rate to O.U ml/minute for Column A did not improve the situation. 

Figure 3. Time course of Na+ binding to the exterior surface ( , gill and body combined) of 10 g rainbow trout compared with uptake into the entire plasma volume (O) or whole livers ( ) of the fish. Na+ uptake into the liver is also normalised to 0.325 g of fresh liver weight (A) to enable a direct comparison with the blood volume of the 10 g fish (0.325 ml, see Gingerich and Pityer [87]). Fish were dipped in 500 ml fresh water containing 0.2 mmol l 1Na+ and 10 p,Ci of 22Na+ (see [30] for other water-quality details), and then rinsed in 30 1 of unlabelled freshwater for 15 s to remove excess radio-isotope. Data are means S.E. (n = 6 fish). Note that Na+ measurements in/on tissues are absolute amounts in nmoles, not concentration units...

Tanaka et al. have studied the surface molecular motions of PS films coated on a solid substrate by lateral force microscopy and revealed that the Tg at the surface was much lower than the corresponding bulk one [148]. Possible reasons for this included an excess free volume induced by localized chain ends, a reduced cooperativity for of-relaxation process, a reduced entanglement, and a unique chain conformation at the surface. For comparison, they examined surface relaxation behavior of high-density PMMA brushes. 

A direct quantitative comparison between AG theory and measurements requires the resolution of two issues. First, the excess entropy Sexc must be normahzed by the molar volume. We suggest that the lack of this normalization is partly responsible for previous claims [15, 49] that AG theory breaks down for small molecule fluids. Second, the vibrational contribution to which is absent in s, must be subtracted reliably. While the first correction can readily be introduced, the inclusion of the second correction requires further investigation [63, 240]. 

An iron deficiency could be accommodated by a defect structure in two ways either iron vacancies, giving the formula Fe] /D, or alternatively, there could be an excess of oxygen in interstitial positions, with the formula FeOi+ f. A comparison of the theoretical and measured densities of the crystal distinguishes between the alternatives. The easiest method of measuring the density of a crystal is the flotation method. Liquids of differing densities which dissolve in each other, are mixed together until a mixture is found that will just suspend the crystal so that it neither floats nor sinks. The density of that liquid mixture must then be the same as that of the crystal, and it can be found by weighing an accurately measured volume. 

In the nested case-control study of Carpenter et al. (1988) (described in more detail in the monograph on toluene in this volume), there was a hint of excess risk of central nervous system cancer among workers exposed to toluene, xylene and methyl ethyl ketone (evaluated as one chemical group) at two nuclear facilities located in Tennessee (United States). The relative risk was 2.0 (95% confidence interval (CI), 0.7-5.5 n = 28) in comparison with unexposed workers. [The Working Group noted that no separate... 

FIGURE 3.6 Comparison of surface excess free energy (AGs) and volume excess free energy (AGv) as functions of cluster size. (Reproduced and modified from Larson, M.A., Garside, J., Chem. Eng. Sci., 41, 1285 (1986). With permission from Elsevier.)... 

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