Solution chemistry activity coefficients

To be more correct thermodynamically, activities (the activity of a species is its concentration multiplied by a number known as the activity coefficient) should be used instead of concentrations. However, in dilute solutions, the activity coefficients are usually taken to be 1 so concentrations are used instead. Table 5.1 shows the dissociation constants of several common acids, and a more complete list can be found in the CRC Handbook of Chemistry and Physics. Because the strength of an acid is... 

A collection of numerical data covering a relatively large number of quantities used in physical chemistry and thermodynamics, mainly for inorganic species for example acidity constants including those found in non-aqueous solvents, solubility constants and complexation constants. Regarding electrochemistry, you can find the redox potentials for numerous couples, the molar conductivities for the main ions in aqueous solution, the activity coefficients for electrolytes, as well as a small number of kinetic features (exchange current density, and transfer coefficient, etc.). 

It should be noted that, strictly speaking, one should also include activity coefficients in (1) and (3) to account for deviations from ideal behavior in a mixture. This is usually not done in practice—the usual assumption used to justify this is that activity coefficients have a negligible effect in the dilute regime used in typical supramolecular chemistry experiments. Notable exceptions are experiments conducted in aqueous buffer or salt solutions where activity coefficients may have a significant effect on the final outcome. ... 

In dilute solutions it is possible to relate the activity coefficients of ionic species to the composition of the solution, its dielectric properties, the temperature, and certain fundamental constants. Theoretical approaches to the development of such relations trace their origins to the classic papers by Debye and Hiickel (6-8). For detailpd treatments of this subject, refer to standard physical chemistry texts or to treatises on electrolyte solutions [e.g., that by Harned... 

In 1985, the IUPAC Commission of Electroanalytical Chemistry defined the pH for solutions in organic solvents of high permittivity and in water-organic solvent mixtures [15]. According to them, the pH is conceptually defined by Eq. (3.26), where m shows the molality and yrn the activity coefficient ... 

Figure 8-5 Activity coefficient of H in solutions containing 0.010 0 M HCIO and varying amounts of NaCI04. [Data derived from L Pezza, M. Molina, M. de Moraes, C. B. Melios, and J. O. Tognoili, Talanta 1996,43, 1689] The authoritative source on electrolyte solutions is H. S. Harned and B. B. Owen, The Physical Chemistry of Electrolyte Solutions (New York Reinhold, 1958).

Let s find the concentrations of species in a saturated solution of Mg(OH)2, given the following chemistry. For simplicity, we ignore activity coefficients. 

SH Considering just acid-base chemistry, not ion pairing and not activity coefficients, use the systematic treatment of equilibrium to find the pH and concentrations of species in 1.00 L of solution containing 0.100 mol ethylenediamine and 0.035 mol HBr. Compare the pH with that found by the methods of Chapter 11. 

Suppose that 0.050 mol of FeG2 is dissolved in 1.00 L and enough HC1 is added to adjust the pH to 8.50. Use Davies activity coefficients to find the composition of the solution. What fraction of iron is in each of its forms and what fraction of glycine is in each of its forms From the distribution of species, explain the principal chemistry that requires addition of HC1 to obtain a pH of 8.50. 

The dimensionless quantity yj is called the activity coefficient of the substance J (Fig. 9.4). More advanced techniques in chemistry enable us to relate the activity coefficient to the composition. For the dilute solutions that concern us, it will be sufficient to set yj = 1. However, we have to remember that our expressions are then valid only for ideal gases and very dilute solutions. 

In Equation 4.21, the activity of pure water (a) is unity and the activity of the water with the inhibitor (a ) is the product of the water concentration (xw) and the activity coefficient (xw). The water concentration is known and the activity coefficient is easily obtained from colligative properties for the inhibitor, such as the freezing point depression. For instance the activity of water in aqueous sodium chloride solutions may be obtained from Robinson and Stokes (1959, p. 476) or from any of several handbooks of chemistry and physics. 

In this chapter, we introduced the reader to some basic principles of solution chemistry with emphasis on the C02-carbonate acid system. An array of equations necessary for making calculations in this system was developed, which emphasized the relationships between concentrations and activity and the bridging concept of activity coefficients. Because most carbonate sediments and rocks are initially deposited in the marine environment and are bathed by seawater or modified seawater solutions for some or much of their history, the carbonic acid system in seawater was discussed in more detail. An example calculation for seawater saturation state was provided to illustrate how such calculations are made, and to prepare the reader, in particular, for material in Chapter 4. We now investigate the relationships between solutions and sedimentary carbonate minerals in Chapters 2 and 3. 

Because K, depends on concentrations and the product KyKx is concentration independent, Kx must also depend on concentration. This shows that the simple equilibrium calculations usually carried out in first courses in chemistry are approximations. Actually such calculations are often rather poor approximations when applied to solutions of ionic species, where deviations from ideality are quite large. We shall see that calculations using Eq. (47) can present some computational difficulties. Concentrations are needed in order to obtain activity coefficients, but activity coefficients are needed before an equilibrium constant for calculating concentrations can be obtained. Such problems are usually handled by the method of successive approximations, whereby concentrations are initially calculated assuming ideal behavior and these concentrations are used for a first estimate of activity coefficients, which are then used for a better estimate of concentrations, and so forth. A G is calculated with the standard state used to define the activity. If molality-based activity coefficients are used, the relevant equation is... 

Feb. 22,1879, Varde, Denmark - Dec. 17,1947, Copenhagen, Denmark) Ph.D. Copenhagen 1908, since 1908 Professor of Chemistry (the 3rd chair, i.e., the chair of Physical Chemistry at the Univ. of Copenhagen). 1926/27 visiting Professor at Yale Univ., New Haven, Connecticut, USA. Famous for his work on chemical reaction kinetics, chemical affinity, indicators, and thermodynamics of solutions. He could explain the effect of activity coefficients on reaction rates in solutions. In 1923 he developed independently of - Lowry, and - Bjerrum a new -> acid-base theory, the so-called Bronsted acid-base theory. 

Schnitzer M (1986) Binding of humic substances by soil mineral colloids. In Interactions of soil Minerals With Natural Organics and Microbes. In HUANG P M, SCHNITZER M (Eds).-Soil. Sci. Soc. Am. Publ. No. 17, Madison, WI Sigg L, Stumm W (1994) Aquatische Chemie.-B G Teubner Verlag Stuttgart Silvester KS, Pitzer KS (1978) Thermodynamics of electrolytes. X. Enthalpy and the effect of temperature on the activity coefficients.-Jour, of Solution Chemistry, 7 pp 327-337 Sparks DL (1986) Soil Physical Chemistry.- CRC Press Inc., Boca Raton FL Stumm W, Morgan JJ (1996) Aquatic Chemistry, 3rd edition.-John Wiley Sons New York... 

Worked example 5.7 — soil solution chemistry ionic strength and activity coefficients... 

In this section, we derive PDT expressions for activity coefficients and standard state chemical potentials that are conventional in physical chemistry and chemical engineering thermodynamics. We assume here a single homogeneous solution phase composed of several components, and write the following conventional expression for the chemical potential of component a in this multicomponent solution ... 

It should be noted that the complexity and ill definition of carbonate salts in highly saline solutions is documented in literature by the complete absence of single salt osmotic and activity coefficient data. This situation requires the use of this less than satisfying technique to define heavy metal chemistry in brines. 

In saline soils and soils contaminated with geothermal brines, the ionic strengths of the soil solution may exceed 0.5 M. This fact poses the necessity of using equations which have been developed to describe the activity coefficients of ions in concentrated, multicomponent electrolyte solutions. As part of a study on the chemistry of ore-forming fluids, Helgeson (50) has proposed that the true individual ion activity coefficients for ions present in small concentrations in multicomponent electrolyte solution having sodium chloride as the dominant component be approximated by a modified form of the Stokes-Robinson equation. The equation proposed is ... 

It would be difficult to find more comprehensive or more detailed studies on the physical chemistry of seawater than those done at the University of Miami (Millero, 2001). Several programs were developed for calculation of activity coefficients and speciation of both major ions and trace elements in seawater. The activity coefficient models have been influenced strongly by the Pitzer method but are best described as hybrid because of the need to use ion-pair formation constants (Millero and Schreiber, 1982). The current model is based on Quick Basic computes activity coefficients for 12 major cations and anions, 7 neutral solutes, and more than 36 minor or trace ions. At 25 °C the ionic strength range is 0-6 m. For major components, the temperature range has been extended to 0-50 °C, and in many cases the temperature dependence is reasonably estimated to 75 °C. Details of the model and the parameters and their sources can be found in Millero and Roy (1997) and Millero and Pierrot (1998). Comparison of some individual-ion activity coefficients and some speciation for seawater computed with the Miami model is shown in Section 5.02.8.6 on model reliability. 

The TLM (Davis and Leckie, 1978) is the most complex model described in Figure 4. It is an example of an SCM. These models describe sorption within a framework similar to that used to describe reactions between metals and ligands in solutions (Kentef fll., 1988 Davis and Kent, 1990 Stumm, 1992). Reactions involving surface sites and solution species are postulated based on experimental data and theoretical principles. Mass balance, charge balance, and mass action laws are used to predict sorption as a function of solution chemistry. Different SCMs incorporate different assumptions about the nature of the solid - solution interface. These include the number of distinct surface planes where cations and anions can attach (double layer versus triple layer) and the relations between surface charge, electrical capacitance, and activity coefficients of surface species. 

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