Molar Volumes in Aqueous Solutions

5 Ionic Molar Volumes in Aqueous Solutions The densities, p, of electrolyte solutions, as dependent on their concentrations at constant temperatures and pressures, are measurable with high accuracy. In a solution made up from moles of water and moles of electrolyte, the total volume of the solution is V=Mlp, where The apparent molar volume of an electrolyte, Vg, is the 

Here V is the molar volume of pure water, disregarding any effect due to the ions. In an electrolyte solution of molality or concentration c and density p, the 

The second version of Equation 2.21 is preferred, because of the square root dependence of Vg on in dilute solutions. Extrapolation of or of Vg to infinite dilution yields the standard partial molar volume of the electrolyte = V. It is 

At infinite dilution, the standard molar volumes of the cations and anions are additive and conventional values V, , based on V ( , aq) =0cm -mol at all temperatures, have been listed by Millero [78] at several temperatures (0,25, 50, and 75°C). Some of the 25°C values have since been revised [55]. The absolute standard partial ionic molar volumes are V (1, aq) = V aq) and the tempera- 

Values of the ionic standard partial molar volumes of the hydrogen, alkali metal, alkaline earth metal, and anunonium cations and hydroxide, hahde, nitrate, perchlorate, and sulfate anions from 0 to 200°C at 25°C intervals have been reported by Marcus in Refs. 79-81. Conventional values V for these ions (except CIO ) and also for HCOj and HS are reported by Tanger and Helgeson [84] from 0 to 350°C at 25°C intervals. 

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TABLE 18.3. Partial Molar Volumes in Aqueous Solutions of Glycine... 

Careful consideration was taken in the parameterization process to insure that the parameters were deemed reasonable for the atom types, using the OPLS-AA force field atom types as a comparison. As one of the goals of this project was to ensure that robustness was achieved in many different calculated properties of the newly developed model, several sets of simulations were also performed to ensure that the parameters could achieve a reasonable agreement with experiment. Some of the properties calculated included the gas phase density, the partial molar volume in aqueous solution, and the bulk solvent structure as well. The calculation of the solubility was discussed in the previous section for the parameterization process and the viewing of these results, the solubility will be reported in log S values, as many of the literature values are reported as log S values, and therefore, the comparison would not lose any sensitivity due to rounding error from the log value. 

Partial molar volume in aqueous solution at infinite dilution (at 25 °C)... 

Thus, if the partial molar volume of solute in aqueous solution is greater than the molar volume of solid solute, an increase in pressure will increase the chemical potential of solute in solution relative to that in the solid phase solute will then leave the solution phase until a lower, equilibrium solubility is attained. Conversely, if the partial molar volume in the solution is less than that in the solid, the solubility will increase with pressure. 

Fig. 1.2 Plots of the molar volume of aqueous solutions of acetonitrile (AcN) and methanol (MeOH) against their mole fraction in solution.

FIGURE 9.3 Variations of Krichevskii function, for various small solutes in water (a) for high solvent densities, (b) for lower densities. Symbols for data, lines for Equation 9.25. (Reprinted with permission from J. P. O Connell, A. V. Sharygin, and R. H. Wood, 1996, Infinite Dilution Partial Molar Volumes of Aqueous Solutes over Wide Ranges of Conditions, Industrial and Engineering Chemistry Research, 35, 2808. With permission from ACS Publishing.)... 

The molar volumes of electrolytes Y = [QlAJI] at infinite dilution, or do not depend on ion-ion, but only on ion-solvent interactions and therefore should be additively composed of the ionic quantities (i.e., + v y ). The partition of the values into their ionic parts can be executed with the help of extrathermodynamic assumptions (see Section II.C). The assumption that the ratio of the molar ionic volumes in aqueous solutions, of Ph4AsBPh4 equals the ra-... 

Fig. 5.1. Reduced viscosity /]red as a function of the concentration c for poly(acrylamide) (PAAm) of different molar masses in aqueous solution.The mass average molar masses Mw are given for each data set.The value of 1/10 of the critical concentration c i] of the viscosimetry (at which already 10% of the solution volume is filled with polymer coils) is shown to demonstrate that deviations from the linear relation between the reduced viscosity / red and the concentration c are caused by intermolecular interactions between the polymer coils. Data from [89]...

Another method for the estimation of the intrinsic volumes of electrolytes, independent of values of the ionic radii, was proposed by Pedersen et al. [53], who employed the molar volume of the molten alkali metal halides, extrapolated to ambient temperatures, as a measure of their intrinsic volumes in aqueous solutions, but the extrapolation is quite long. A variant of this idea is to use the molar volumes of molten hydrated salts, proposed by Marcus [54], where the temperature extrapolation to 25°C is much shorter. It is then necessary to subtract the volume of the water of hydration, which is n times the molar volume of electrostricted water, 15.2 cm mok at 25°C [55], from the extrapolated molar volume of the undercooled molten hydrated salt containing n water molecules per formula unit of the salt. A cogent method, applicable to highly soluble salts, was proposed by Marcus [56]. The volumes considered, applied to aqueous solutions, are intrinsic, so they should be independent of the concentration c and to a certain extent also of the temperature T. The partial molar volume of an electrolyte, V c, T), describes the volume that it actually occupies in the solution and does not include the volume of the water. Therefore, a fairly short extrapolation of the hnear 25°C) from c = 3M to such high concentrations at which all of the solvent is as closely packed as possible (completely electrostricted) is equivalent to considering the electrolyte as an undercooled molten hydrated salt... 

This chapter presents new information about the physical properties of humic acid fractions from the Okefenokee Swamp, Georgia. Specialized techniques of fluorescence depolarization spectroscopy and phase-shift fluorometry allow the nondestructive determination of molar volume and shape in aqueous solutions. The techniques also provide sufficient data to make a reliable estimate of the number of different fluorophores in the molecule their respective excitation and emission spectra, and their phase-resolved emission spectra. These measurements are possible even in instances where two fluorophores have nearly identical emission specta. The general theoretical background of each method is presented first, followed by the specific results of our measurements. Parts of the theoretical treatment of depolarization and phase-shift fluorometry given here are more fully expanded upon in (5,9-ll). Recent work and reviews of these techniques are given by Warner and McGown (72). 

The quantitative aspects of acid-base chemistry obey the principles Introduced earlier in this chapter. The common acid-base reactions that are important in general chemistry take place in aqueous solution, so acid-base stoichiometry uses molarities and volumes extensively. Example Illustrates the essential features of aqueous acid-base stoichiometry. 

In aqueous solutions, concentrations are sometimes expressed in terms of normality (gram equivalents per liter), so that if C is concentration, then V = 103/C and a = 103 K/C. To calculate C, it is necessary to know the formula of the solute in solution. For example, a one molar solution of Fe2(S04)3 would contain 6 1CT3 equivalents cm-3. It is now clear as to why A is preferred. The derivation provided herein clearly brings out the fact that A is the measure of the electrolytic conductance of the ions which make up 1 g-equiv. of electrolyte of a particular concentration - thereby setting conductance measurements on a common basis. Sometimes the molar conductance am is preferred to the equivalent conductance this is the conductance of that volume of the electrolyte which contains one gram molecule (mole) of the ions taking part in the electrolysis and which is held between parallel electrodes 1 cm apart. 

As in aqueous solution, the lanthanide contraction favors a change from nine-coordination for the light lanthanides to eight-coordination for the light lanthanides such that [Ln(DMF)8]3+ is the major species when Ln3+ = Ce3+-Nd3+, and that this becomes the only detected species when Ln3+ = Tb3+-Lu3+ in dimethylformamide perchlorate solution (11, 92, 93, 321-323). Thus, Nd3+ is characterized by AH° = -14.9 kJ mol-1, AS0 = -69.1 J K"1 mol-1, and AV° = - 9.8 cm3 mol-1 for the equilibrium shown in Eq. (25) (93). The molar volume of DMF is 72 cm3 mol- and it therefore appears that the substantially smaller magnitude of AV° is a consequence of significant... 

The coordination numbers of the Ln3+ ions in water are now well established from different experimental techniques (214-221). The lighter La3+-Nd3+ ions are predominantly nine-coordinate, Pm3+ Eu3+ exist in equilibria between nine- and eight-coordinate states and the heavier Gd3+-Lu3+ are predominantly eight-coordinate. The change in coordination number is also reflected in the absolute partial molar volumes, U°bs, of several Ln3+ ions determined in aqueous solutions (222,223). 

A thermodynamic parameter (dV/dnB)T,F,n g which describes how the volume of component S in a multicomponent system depends on the change in its amount expressed in mol. Hpiland recently summarized the partial molar volumes of numerous biochemical compounds in aqueous solution. See Dalton s Law of Partial Pressures Concentrations Molecular Crowding... 

J.M. Corkill, J.F. Goodman and T. Walker, Partial molar volumes of surface-active agents in aqueous solution, Trans. Faraday Soc. 63 (1967) 786-772. 

For binary solutions, this is just the slope of the plot at constant T and P of the volume of the solution versus its molality. This is illustrated in Fig. 1 for an aqueous MgS04 solution. Note that at low concentration, the partial molar volume of MgS04 in aqueous solution is negative. 

Calculation of A//e -quantities from the dependence of AG on temperature is less reliable than direct calorimetric measurements (Franks and Reid, 1973 Frank, 1973 Reid et al., 1969). However, disagreement between published A//-functions for apolar solutes in aqueous solutions may also stem from practical problems associated with low solubilities (Gill et al., 1975). Calorimetric data have the advantage that, as theory shows, the standard partial molar enthalpy H3 for a solute in solution is equal to the partial molar enthalpy in the infinitely dilute solution, i.e. x3 - 0. A similar identity between X3 and X3 (x3 - 0) occurs for the volumes and heat capacities but not for the chemical potentials and entropies. The design of a flow system for the measurement of the heat capacity of solutions (Picker et al., 1971) has provided valuable information on aqueous solutions. 

Example The partial molar volume of Na2S04 in aqueous solution may be denoted V(Na2S04, aq), in order to distinguish it from the volume of the solution K(Na2S04, aq). 

The question of coordination in aqueous solutions is not as clear as in solid state. Sped-ding s work [53] on the partial molar volumes of aquo ions of lanthanides and the irregular trends of these quantities in the lanthanides has been taken as evidence for change in coordination number in the lanthanide series [54]. The change in coordination from 9 to 8 in the lanthanide series has been confirmed by X-ray and neutron diffraction studies of LnCb solutions [55], The coordination numbers of lanthanides determined in aqueous solutions by various techniques along with the coordination numbers obtained are given below ... 

For predicting the diffusivity of small molecules (with molecular weights less than about 1000 or molar volumes less than about 0.500 m3/kg) in aqueous solution, we may use the Wilke-Chang correlation to estimate the diffusivity in m2/s... 

The two primary reference works on inorganic thermochemistry in aqueous solution are the National Bureau of Standards tables (323) and Bard, Parsons, and Jordan s revision (30) (referred to herein as Standard Potentials) of Latimer s Oxidation Potentials (195). These two works have rather little to say about free radicals. Most inorganic free radicals are transient species in aqueous solution. Assignment of thermodynamic properties to these species requires, nevertheless, that they have sufficient lifetimes to be vibrationally at equilibrium with the solvent. Such equilibration occurs rapidly enough that, on the time scale at which these species are usually observed (nanoseconds to milliseconds), it is appropriate to discuss their thermodynamics. The field is still in its infancy of the various thermodynamic parameters, experiments have primarily yielded free energies and reduction potentials. Enthalpies, entropies, molar volumes, and their derivative functions are available if at all in only a very small subset. 

Molarity, the most common measure of concentration used by chemists, is introduced in Section 11.1 and nsed to solve problems involving numbers of moles and volumes. The concentrations of individual ions in aqueous solutions of ionic snbstances are discnssed in Section 11.2. The technique of titration, nsed to determine experimentally the nnknown concentrations of solutions or unknown nnmbers of moles of a snbstance, is presented in Section 11.3. 

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