The Activities of Nonvolatile Solutes

For a nonvolatile substance we must find a way to determine its activity coefficient that does not depend on measuring its vapor pressure. We will discuss three different methods. The first is through integration of the Gibbs-Duhem equation. The second is through a theory due to Debye and Hiickel, which can be applied to electrolyte solutes. The third method for electrolyte solutes is an electrochemical method, which we will discuss in Chapter 8. Published data are available for common electrolytes, and some values are included in Table A. 11 in Appendix A. 

For a two-component solution with a volatile solvent such as water and a nonvolatile solute, values of the activity of the solvent can be determined for several values of the solvent mole fraction between unity and the composition of interest. Integration of the Gibbs-Duhem relation can then give the value of the activity coefficient of the solute. The activity of the solvent is usually determined using the isopiestic method. The solution of interest and a solution of a well-studied nonvolatile reference solute in the same solvent are placed in a closed container at a fixed temperature. A solution of KCl is usually used as the reference solute for aqueous solutions, since accurate water activity coefficient data are available for KCl solutions. The solutions are left undisturbed at constant temperature until enough solvent has evaporated from one solution and condensed into the other solution to equilibrate the solvent in the two solutions. 

At equilibrium, the activity of solvent (substance 1) in the solution of interest (solution B) is equal to the activity of solvent in the reference solution (solution A), so that 

The solutions are analyzed to determine the mole fractions of the solvent in the two solutions, and the activity of the solvent in the reference solution is determined from tabulated values. The activity of the solvent in the unknown solution is equal to this value. The experiment is repeated several times for a range of compositions of solution B beginning with pure solvent and extending to X2 = Xj, the composition at which we want the value of Y2. 

For constant pressure and temperature, the Gibbs-Duhem relation for two components is given by Eq. (4.6-11). When we substitute Eq. (6.3-6) into this equation, we obtain 

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Cesium forms simple alkyl and aryl compounds that are similar to those of the other alkah metals (6). They are colorless, sohd, amorphous, nonvolatile, and insoluble, except by decomposition, in most solvents except diethylzinc. As a result of exceptional reactivity, cesium aryls should be effective in alkylations wherever other alkaline alkyls or Grignard reagents have failed (see Grignard reactions). Cesium reacts with hydrocarbons in which the activity of a C—H link is increased by attachment to the carbon atom of doubly linked or aromatic radicals. A brown, sohd addition product is formed when cesium reacts with ethylene, and a very reactive dark red powder, triphenylmethylcesium [76-83-5] (C H )2CCs, is formed by the reaction of cesium amalgam and a solution of triphenylmethyl chloride in anhydrous ether. 

The activity of a volatile solvent in a solution that contains a nonvolatile solute can be obtained from an experimental technique known as the isopiestic method .19 An apparatus is constructed similar to that shown in Figure 6.17. The mixture in container A is a solution of a nonvolatile solute in a solvent in which A], the activity of the solvent, has been accurately determined in other experiments as a function of concentration. Containers B and C hold solutions of other nonvolatile solutes in the same solvent. These are the solutions for which the activity of the solvent is to be determined. 

The activity of the solvent often can be obtained by an experimental technique known as the isopiestic method [5]. With this method we compare solutions of two different nonvolatile solutes for one of which, the reference solution, the activity of the solvent has been determined previously with high precision. If both solutions are placed in an evacuated container, solvent will evaporate from the solution with higher vapor pressure and condense into the solution with lower vapor pressure until equilibrium is attained. The solute concentration for each solution then is determined by analysis. Once the molality of the reference solution is known, the activity of the solvent in the reference solution can be read from records of previous experiments with reference solutions. As the standard state of the solvent is the same for all solutes, the activity of the solvent is the same in both solutions at equUibrium. Once the activity of the solvent is known as a function of m2 for the new solution, the activity of the new solute can be calculated by the methods discussed previously in this section. 

For a solution of one (nonvolatile) solute in water, whose water activity is known over a concentration range, the activity of the solute can be derived from the Gibbs-Duhem relation, which can for this case be written... 

On integrating, we find that U2jx2 = Kr, where the constant is fixed at a given temperature. Now use Henry s law in the form 02 = P2/P2 whenceP2 = KrP x2, which shows that Kr=, and that under conditions where Raoult s law applies to the solvent, Henry s law holds for the solute. This simple relationship obviously applies only to very dilute solutions. The activity of the nonvolatile component can thus be determined by measuring the vapor pressure of the solvent in its dependence on the composition of the solution and then introducing the Gibbs-Duhem relation. 

Because polyelectrolytes are nonvolatile, the most important thermodynamic property for vapor + liquid phase equilibrium considerations is the vapor pressure of water above the aqueous solution. Instead of the vapor pressure, some directly related other properties are used, e.g., the activity of water a, the osmotic pressure 71, and the osmotic coefficient < . These properties are defined and discussed in Sect. 4. Membrane osmometry, vapor pressure osmometry, and isopiestic experiments are common methods for measuring the osmotic pressure and/or the osmotic coefficient. A few authors also reported experimental results for the activity coefficient y i of the counterions (usually determined using ion-selective electrodes) and for the freezing-point depression of water AT p. The activity coefficient is the ratio of activity to COTicentration ... 

When the concentration of dissolved coal exceeds about 5% of the solution by weight, the extracted material resembles the parent coal in composition and some properties. The extract consists of the smaller molecules within the range of the parent coal. Recovered extract is relatively nonvolatile and high melting. A kinetic study of coal dissolution indicated increasing heats of activation for increasing amounts of dissolved coal (69). 

Field desorption (FD) was introduced by Beckey in 1969 [76]. FD was the first soft ionization method that could generate intact ions from nonvolatile compounds, such as small peptides [77]. The principal difference between FD and FI is the sample injection. Rather than being in the gas phase as in FI, analytes in FD are placed onto the emitter and desorbed from its surface. Application of the analyte onto the emitter can be performed by just dipping the activated emitter in a solution. The emitter is then introduced into the ion source of the spectrometer. The positioning of the emitter is cmcial for a successful experiment, and so is the temperature setting. In general, FI and FD are now replaced by more efficient ionization methods, such as MALDI and ESI. For a description of FD (and FI), see Reference 78. 

The production of cocamidopropyl betaine has traditionally been based on two feedstocks coconut oil and topped or stripped (C-8 and 10 removed) coconut fatty acid or methyl ester. These products are still widely used but, to achieve better colors and odors, hydrogenated feedstocks are now very frequently used, either fully hydrogenated coconut oil triglyceride or stripped, hydrogenated, distilled coconut fatty acid. These products are most frequently sold as aqueous solutions with 35% nonvolatile matter. If made from triglyceride, the betaine surfactant will contain about 2.5% glycerin by-product and 5% sodium chloride by-product in addition to the active surfactant. Products made from fatty acid or methyl ester are approximately 30% active product and slightly more than 5% sodium chloride. 

The fractionation of citrus oil is an important subject in perfume industry. Citrus oil consists of terpenes (over 95 %), oxygenated compounds (less than 5 %), waxes, and pigments. Terpenes must be removed to stabilize the products and to dissolve it in aqueous solution. Terpenes are conventionally removed by distillation or solvent extraction, which involves higher temperature process resulting in thermal degradation of essential oil. Furthermore, nonvolatils such as waxes and pigments must be eliminated because of turbidity in the oil and phototoxic activity [1-2]. 

A study of the acid-base properties of solutes in nonaqueous solvents must include consideration of hydrogen ion activities and in particular a comparison of their activities in different solvents. Attempting to transpose interpretations and methods of approach from aqueous to nonaqueous systems may lead to diflSculty. The usual standard state (Section 2-2) for a nonvolatile solute is arbitrarily defined in terms of a reference condition with activity equal to concentration at infinite dilution. Comparisons of activities are unsatisfactory when applied to different solvents, because different standard states are then necessarily involved. For such comparisons it would be gratifying if the standard state could be defined solely with reference to the properties of the pure solute, as it is for volatile nonelectrolytes (Section 2-7). Unfortunately, for ionic solutes a different standard state is defined for every solvent and every temperature. 

Show that if the vapor cannot be treated as an ideal gas, equation (38.4) for the activity coefficient of a volatile solute would become 7n = (/2/ni)/(pJ/nJ), assuming the solvent to be nonvolatile so that p, represents virtually zero total pressure hence, suggest a possible procedure for determining 7n in a case of this type. 

Digestion is usually performed in a solution at specified conditions of pH, temperature, and buffer (see T able 1) and in a denaturing environment to ensure complete endpoint digestion. Volatile buffers such as ammonium carbonate and ammonium bicarbonate are preferred because they can be easily removed by lyophilization. A practical method for the removal of a nonvolatile buffer and salts is to use solid-phase extraction (SPE) cartridges prior to mass spectrometry analysis. One can also use immobilized trypsin packed into a small-diameter PEEK (polyetheretherketone) column or covalently attached to an activated MALDI probe for on-probe digestion.15... 

In practice, determination of the activity coefficients of a solvent in a solution is easy, if the solute is nonvolatile. The vapor pressure of the solution and the pure solvent are measured and aA = PJP (Equation (166) applies). However, if the solute is volatile, then the partial pressure of both the solute and the solvent should be determined. 

The main part of the HLLW is aqueous raffinate from the Purex cycle. It contains 99.9% of the nonvolatile FPs, <0.5% of the uranium, <0.2% of the plutonium, and some corrosion products. For each ton of uranium reprocessed about 5 m of HLLW is produced. This is usually concentrated to 0.5-1 m for interim tank storage specific activity is in the range 10 GBq m. The amounts of various elements in the waste and their concentration in 0.5 m solution is shown in Table 21.9. The HNO3 concentration may vary within a factor of 2 depending on the concentration procedure. The metal salt concentration is 0.5 M it is not possible to keep the salt in solution except at high acidity. The amounts of corrosion products, phosphate, and gadolinium (or other neutron poison added) also may vary considerably. Wastes from the HTGR and FBR cycles are expected to be rather similar. 

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