Electrolytes, solutions

3 Electrolyte Solutions. - The self-association of relatively small hydro-phobic organic components in aqueous mixtures has been investigated by Sacco. He determined the association aparameter A(22), which is essentially obtained from experimental intermolecular dipole-dipole relaxation data of nuclei and from NMR measurements of the self-diffusion coefficients of the organic solvents. The effect of electrolytes and non-electrolytes has been studied. The chemical shifts and relaxation times Ti and T2 of He and Xe nuclei of noble gas atoms as well as those of Li and Cs nuclei of isoelectronic Li and Cs ions have been measured in aqueous solutions by Mazitov et Ruso et al. studied the self-association of weakly selfassociating propranolol hydrochloride in aqueous electrolyte solutions by 

NMR techniques. The same measurements were performed to study the selfaggregation of sodium n-hexyl sulfate in aqueous solution.  

Aqueous electrolyte solutions have been studied from the very beginning of physical chemistry. These solutions have been investigated extensively by both experimental and 

The influence of an ion in an aqueous electrolyte solution on the structure of liquid water can be pictured spatially as a localized perturbation of the tetrahedral configuration shown in Fig. 2.2. In the region of the liquid nearest the ion the water molecules are dominated by SagiZ ectro-stricted mass called the primary solvation shell. In the next outer region, the water molecules intefaCT v ldy with the ion and form a structure known as the secondary solvation shell or second-zone structure. Beyond the second zone, the structure of the liquid is indistinguishable from that in the pure bulk phase. 

study of aqueous electrolyte solutions with the methods listed in Table 2.1 has as its objective the development of a molecular model of the 

The secondary solvation shell about an ion can be studied by neutron diffraction and incoherent neutron scattering.When applied to 5 m LiCl, these methods, indicate that Li does not have a secondary solvation shell. The same result would be expected for larger inorganic monovalent cations. The absence of a secondary solvation shell around monovalent ions is not surprising given the relatively small values of T, and T. quoted 

The number of water molecules in the primary solvation shell of a bivalent cation as determined by diffraction methods is always between six and eight unless either cation size or ion-pair complexes intervene to. produce smaller values. Thus the primary shell can be either an octahedral or cubic complex. Table 2.3 shows how the solvation number and orientation of water molecules in a solvation complex can vary with electrolyte concentration. The variation in 0 with the molality of is striking. Evidently lone-pair interactions between a water molecule and this cation are favored in concentrated solutions but dipolar interactions are favored in dilute solutions. 

Diffraction experiments also give evidence for a secondary solvation shell around bivalent cations.This shell contains about 15 water molecules whose mobility varies with electrolyte concentration. INS data indicate clearly that the self-diffusion coefficient of the water molecules in the second-zone structure approaches the diffusion coefficient of the solvated cation as the molality of the solution decreases. Thus the secondary solvation shell moves as a solvation complex with the cation in dilute solutions. 

The application of FST to electrolyte solutions has received considerable interest. It is generally assumed that the average number of cations surrounding an anion in solution must be such that charge neutrality is obeyed for the local region (Kusalik and Patey 1987). The resulting relationships are known as the electroneutrality conditions and can be written in terms of the KBIs as follows  

A simple substitution of vN = N2 = N+ + N then provides relationships between the distributions obtained using the salt (s), the indistinguishable ion (2), and the individual cation and anion notations (Gee et al. 2011), 

The above expressions do not assume electroneutrality and simply represent an index change. Subsequent application of the electroneutrality conditions leads to a series of relationships between the fluctuating quantities, 

Consequently, there is only one unique or independent fluctuating quantity involving the salt species, the others being related by the above expressions. In practical 

Let us consider a dilute solution of a completely dissociated simple electrolyte. The charges of the ions are denoted by ZaS, where the subscript a refers to the different kinds (cations and anions) of ions, e is the absolute value of the unit electronic charge. Za is a positive or a negative integer. Let ao be the number density of ions of the fl-type, namely the number of ions of the a-type per unit 

The thermodynamic properties of electrolyte solutions differ in significant ways from the properties of mixtures of nonelectrolytes. 

Here is an example. Pure HCl (hydrogen chloride) is a gas that is very soluble in water. A plot of the partial pressure of gaseous HCl in equilibrium with aqueous HCl, as a function of the solution molality (Fig. 10.1), shows that the limiting slope at infinite dilution is not finite, but zero. What is the reason for this non-Henry s law behavior It must be because HCl is an electrolyte—it dissociates (ionizes) in the aqueous environment. 

It is customary to use a molality basis for the reference and standard states of electrolyte solutes. This is the only basis used in this chapter, even when not expUcitly indicated for ions. The symbol, for instance, denotes the chemical potential of a cation in a standard state based on molality. 

In dealing with an electrolyte solute, we can refer to the solute (a substance) as a whole and to the individual charged ions that result from dissociation. We can apply the same general definitions of chemical potential, activity coefficient, and activity to these different 

Consider a solution of an electrolyte solute that dissociates completely into a cation species and an anion species. Subscripts - - and — will be used to denote the cation and anion, respectively. The solute molality ms is defined as the amount of solute formula unit divided 

Applications of Thermodynamics to Solutions Containing Electrolyte Solutes 

In the previous chapter, we described the thermodynamic properties of nonelectrolyte solutions. In this chapter, we focus on electrolytes as solutes. Electrolytes behave quite differently in solution than do nonelectrolytes. In Chapter 11, we described the strong electrolyte standard state and summarized relationships between the activity of the solute ai, the mean activity coefficient 7 , and the molality m in Table 11.3. 

The special properties of electrolyte solutions present both advantages and disadvantages as we attempt to describe these mixtures. A disadvantage is that significant deviations from limiting law solution behavior occur at much lower concentrations for electrolyte solutes than for nonelectrolyte solutes. An advantage is that the coulombic attractions and repulsions in the electrolyte solution dominate other types of interactions. The result is that theoretical descriptions of electrolyte solutions can concentrate on the coulombic interactions. 

The Debye-Hiickel theory that we summarized in Chapter 11 is based on this assumption. In that chapter we gave the following equations that apply to limiting law behavior 

In these equations / is the molal-based ionic strength given by 

So far we have discussed the colligative properties of nonelectrolyte solutions. Because electrolytes undergo dissociation when dissolved in water [W Section 4.1], we must consider them separately. Recall, for example, that when NaCl dissolves in water, it dissociates into Na Co ) and C aq). For every mole of NaCl dissolved, we get two moles of ions in solution. Similarly, when a formula unit of CaCL dissolves, we get three ions one Ca ion and two Cl ions. Thus, for every mole of CaCl2 dissolved, we get three moles of ions in solution. Colligative properties depend only on the number of dissolved particle.s—not on the type of particles. This means that a 0.1 m solution of NaCl will exhibit a freezing point depression twice that of a 0.1 m solution of a nonelectrolyte, such as sucrose. Similarly, we expect a 0.1 m solution of CaCL to depress the freezing point of water three times as much as a 0.1 m sucrose solution. To account for this effect, we introduce and define a quantity called the van t Hoff factor (i), which is given by 

i is 1 for aU nonelectrolytes. For strong electrolytes such as NaCl and KNO3, i should be 2, and for strong electrolytes such as Na2S04 and CaCL, i should be 3. Consequently, the equations for colligative properties must be modified as follows  

The amount of vapor-pressue lowering would also be affected by dissociation of an electrolyte. In calculating the mole fraction of solute and solvent, the number of moles of solute would have to be multiplied by the appropriate vant Hoff factor. 

Calculated vant Hoff factors are exact numbers [W Section 1.5], 

Jacobus Henricus van l Hoff (1852-1911). Dutch cbemisL One of the most prominent chemists of his time, van t Hoff did significant work in thermodynamics, molecular structure and optical activity, and solution chemistry, hi 1901 he received the first Nobel Pri2e in Chemistry. 

An electrolyte is a substance that conducts electric current as a result of its dissociation into positively and negatively charged ions in solutions or melts. Ions with a positive charge are called cations, ions with negative charge anions, respectively. The most typical electrolytes are acids, bases, and salts dissolved in a solvent, very often in water. But molten electrolytes and solid electrolytes in the absence of any solvent are also possible, for example, molten sodium chloride or solid silver iodide. 

The product of the elementary charge e and the Avogadro number is the Faraday constant 

In a macroscopic solution, the total number of charges becomes zero, since the solution is always neutral, otherwise there would be an electric current  

For electrolyte solutions, the particular ions are formed by dissociation reactions like 

Chemical Thermodynamics for Process Simulation, First Edition. 

In the following section we discuss the problems of activities of ionic species. Following that we discuss the conventions used to obtain numerical values for the state variables of individual ions, and we discuss the theory underlying the two major approaches to systematizing the data on electrolytes, the HKF and the Pitzer models. Because these are essentially equations of state, we introduced them in Chapter 13 ( 13.6.2 and 13.6.3). 

Activity coefficient models offer an alternative approach to equations of state for the calculation of fugacities in liquid solutions (Prausnitz ct al. 1986 Tas-sios, 1993). These models are also mechanistic and contain adjustable parameters to enhance their correlational ability. The parameters are estimated by matching the thermodynamic model to available equilibrium data. In this chapter, vve consider the estimation of parameters in activity coefficient models for electrolyte and non-electrolyte solutions. 

We consider Pitzer s model for the calculation of activity coefficients in aqueous electrolyte solutions (Pitzer, 1991). It is the most widely used thermodynamic model for electrolyte solutions. 

1 Pitzer s Model Parameters for Aqueous NajSiOj Solutions 

Osmotic coefficient data measured by Park (Park and Englezos, 1998 Park, 1999) are used for the estimation of the model parameters. There are 16 osmotic coefficient data available for the Na2Si03 aqueous solution. The data are given in Table 15.1. Based on these measurements the following parameters in Pitzer s 

Molality Osmotic Coefficient ( pexp) Standard Deviation (op) 

mol = 10000, 9 wt% hydroxypropyl content, Fluka AG, Bucks, Switzerland water H2O 

Type of data cloud points (LCST behavior) 

Wilhelm Ostwald was born to a German family in 1853 in Riga, Latvia, where he grew up and attended school. In 1872 he entered Dorpat University (now Tartu University in Estonia) 

Hayamizu and Price presented a new type of sample tube for reducing convection effects in PGSE-NMR measurements of self-diffusion coefficients of liquid samples. The performance of this tube was demonstrated by conducting measurements on an electrochemically important system. 

Hayamizu and Akiba measured self-diffusion coefficients of lithium ion, anion and solvent in the electrolytes for lithium batteries. The self-association of some anions is discussed. Sekhon et u/. investigated the diffusive motion of cations and anions in polyethylene oxide based polymer electrolytes. Translational motion was found above Tg. 

Sample Problem 13.8 demonstrates the experimental determination of a van t Hoff factor. 

TABLE 13.3 Calculated and Measured and I lofT Factors of 0.0500. V/ Electroh tc Solutions at 25°C 

TABLE 13.4 Expenmentalh Measured wan t Hoff Factors of Sucrose and NaCl Solutions at 25T 

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The discussion focuses on two broad aspects of electrical phenomena at interfaces in the first we determine the consequences of the presence of electrical charges at an interface with an electrolyte solution, and in the second we explore the nature of the potential occurring at phase boundaries. Even within these areas, frequent reference will be made to various specialized treatises dealing with such subjects rather than attempting to cover the general literature. One important application, namely, to the treatment of long-range forces between surfaces, is developed in the next chapter. 

Fig. V-1. Variation of m / o and n /wo with distance for = 51.38 mV and 0.01 M uni-univalent electrolyte solution at 23°C. The areas under the full lines give an excess of 0.90 X 10 mol of anions in a column of solution of 1-cm cross section and a deficiency of 0.32 x 10 mol of cations. There is, correspondingly, a compensating positive surface charge of 1.22 x 10 " mol of electronic charge per cm. The dashed line indicates the effect of recognizing a finite ion size.

It has long been known that the form of a curved surface of mercury in contact with an electrolyte solution depends on its state of electrification [108, 109], and the earliest comprehensive investigation of the electrocapillary effect was made by Lippmann in 1875 [110]. A sketch of his apparatus is shown in Fig. V-10. 

Streaming potential measurements are to be made using a glass capillary tube and a particular electrolyte solution, for example, O.OIM sodium acetate in water. Discuss whether the streaming potential should or should not vary appreciably with temperature. 

H. S. Hamed and B. B. Owen, The Physical Chemistry of Electrolyte Solutions, Reinhold, New York, 1950. 

Rehbinder and co-workers were pioneers in the study of environmental effects on the strength of solids [144], As discussed by Frumkin and others [143-145], the measured hardness of a metal immersed in an electrolyte solution varies with applied potential in the manner of an electrocapillary curve (see Section V-7). A dramatic demonstration of this so-called Rehbinder effect is the easy deformation of single crystals of tin and of zinc if the surface is coated with an oleic acid monolayer [144]. 

Here, x denotes film thickness and x is that corresponding to F . An equation similar to Eq. X-42 is given by Zorin et al. [188]. Also, film pressure may be estimated from potential changes [189]. Equation X-43 has been used to calculate contact angles in dilute electrolyte solutions on quartz results are in accord with DLVO theory (see Section VI-4B) [190]. Finally, the x term may be especially important in the case of liquid-liquid-solid systems [191]. 

Finally, if the sliding surfaces are in contact with an electrolyte solution, an analysis indicates that the coefficient of friction should depend on the applied potential [41]. 

Fig. XIII-10. Properties of colloidal electrolyte solutions—sodium dodecyl sulfate. (From Ref. 102a.)...

Itaya K 1998 In situ scanning tunneling microscopy in electrolyte solutions Prog. Surf. Sc/. 58 121... 

The situation for electrolyte solutions is more complex theory confimis the limiting expressions (originally from Debye-Htickel theory), but, because of the long-range interactions, the resulting equations are non-analytic rather than simple power series.) It is evident that electrolyte solutions are ideally dilute only at extremely low concentrations. Further details about these activity coefficients will be found in other articles. 

Were the FlCl in its standard state, AC would equal where is the standard emf for the reaction. In general, for any reversible chemical cell without transference, i.e. one with a single electrolyte solution, not one with any kind of junction between two solutions. 

We conclude this section by discussing an expression for the excess chemical potential in temrs of the pair correlation fimction and a parameter X, which couples the interactions of one particle with the rest. The idea of a coupling parameter was mtrodiiced by Onsager [20] and Kirkwood [Hj. The choice of X depends on the system considered. In an electrolyte solution it could be the charge, but in general it is some variable that characterizes the pair potential. The potential energy of the system... 

The Debye-Htickel limiting law predicts a square-root dependence on the ionic strength/= MTLcz of the logarithm of the mean activity coefficient (log y ), tire heat of dilution (E /VI) and the excess volume it is considered to be an exact expression for the behaviour of an electrolyte at infinite dilution. Some experimental results for the activity coefficients and heats of dilution are shown in figure A2.3.11 for aqueous solutions of NaCl and ZnSO at 25°C the results are typical of the observations for 1-1 (e.g.NaCl) and 2-2 (e.g. ZnSO ) aqueous electrolyte solutions at this temperature. 

Jacob J, Kumar A, Anisimov M A, Povodyrev A A. and Sengers J V 1998 Crossover from Ising to mean-field critical behavior in an aqueous electrolyte solution Phys. Rev. E 58 2188... 

Card D N and Valleau J 1970 Monte Carlo study of the thermodynamics of electrolyte solutions J. Chem. Phys. 52 6232... 

Friedman H L and Dale W T 1977 Electrolyte solutions at equilibrium Statistical Mechanics part A, Equilibrium Techniques ed B J Berne (New York Plenum)... 

Outhwaite C W 1974 Equilibrium theories of electrolyte solutions Specialist Periodical Report (London Chemical Society)... 

Rasaiah J C 1987 Theories of electrolyte solutions The Liquid State and its Electrical Properties (NATO Advanced Science Institute Series Vol 193) ed E E Kunhardt, L G Christophous and L H Luessen (New York Plenum)... 

Rasaiah J C 1973 A view of electrolyte solutions J. Solution Chem. 2 301... 

Ionic conductors arise whenever there are mobile ions present. In electrolyte solutions, such ions are nonually fonued by the dissolution of an ionic solid. Provided the dissolution leads to the complete separation of the ionic components to fonu essentially independent anions and cations, the electrolyte is tenued strong. By contrast, weak electrolytes, such as organic carboxylic acids, are present mainly in the undissociated fonu in solution, with the total ionic concentration orders of magnitude lower than the fonual concentration of the solute. Ionic conductivity will be treated in some detail below, but we initially concentrate on the equilibrium stmcture of liquids and ionic solutions. 

For an electrolyte solution containing both anions and cations, with the tennmal velocity of the cations being and the number of ions of charge z Cq per unit volume being Et, the product corresponds just... 

The integral equation approach has also been explored in detail for electrolyte solutions, with the PY equation proving less usefiil than the HNC equation. This is partly because the latter model reduces cleanly to the MSA model for small h 2) since... 

In principle, simulation teclmiques can be used, and Monte Carlo simulations of the primitive model of electrolyte solutions have appeared since the 1960s. Results for the osmotic coefficients are given for comparison in table A2.4.4 together with results from the MSA, PY and HNC approaches. The primitive model is clearly deficient for values of r. close to the closest distance of approach of the ions. Many years ago, Gurney [H] noted that when two ions are close enough together for their solvation sheaths to overlap, some solvent molecules become freed from ionic attraction and are effectively returned to the bulk [12]. 

In addition to the case of a metal in contact with its ions in solution there are other cases in which a Galvani potential difference between two phases may be found. One case is the innnersion of an inert electrode, such as platinum metal, into an electrolyte solution containing a substance S that can exist m either an oxidized or reduced fomi tlirough the loss or gain of electrons from the electrode. In the sunplest case, we have... 

Robinson R A and Stokes R H 1959 Electrolyte Solutions (London ButtenA/orth)... 

Martynov G A and Salem R R 1983 Electrical Double Layer at a Metal-Dilute Electrolyte Solution Inteiface (Berlin Springer)... 

One potentially powerfiil approach to chemical imaging of oxides is to capitalize on the tip-surface interactions caused by the surface charge induced under electrolyte solutions [189]. The sign and the amount of the charge induced on, for example, an oxide surface under an aqueous solution is detenuined by the pH and ionic strength of the solution, as well as by the isoelectric point (lEP) of the sample. At pH values above the lEP, the charge is negative below this value. 

Protems can be physisorbed or covalently attached to mica. Another method is to innnobilise and orient them by specific binding to receptor-fiinctionalized planar lipid bilayers supported on the mica sheets [15]. These surfaces are then brought into contact in an aqueous electrolyte solution, while the pH and the ionic strength are varied. Corresponding variations in the force-versus-distance curve allow conclusions about protein confomiation and interaction to be drawn [99]. The local electrostatic potential of protein-covered surfaces can hence be detemiined with an accuracy of 5 mV. 

Simonson J M and Mesmer R E 1994 Electrolyte solutions at high temperatures and pressures Solution Calorimetry, Experimental Thermodynamics yo IV, ed K N Marsh and PAG O Hare (Oxford Blackwell)... 

Figure Bl.28.6. (a) Convection within the electrolyte solution, due to rotation of the electrode (b) Nemst diflfiision model for steady state.

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