Activity coefficients aqueous solutes

M6. Meissner, H.P. and N.A. Peppas, "Activity Coefficients - Aqueous Solutions of Polybasic Acids and Their Salts", AIChE J., 19, 806 (1973)... 

The most important factor in determining KQW is the aqueous-phase activity coefficient (aqueous solubility) of the organic solute. The observed partition coefficients are less than the ideal partition coefficients (K w) as result from 1) the incompatibility of the solute in water-saturated octanol and, to a lesser degree,... 

Table XVI gives recent values of the thermionic work functions for several clean metals and also (for discussion later) the accepted values of the standard electrode potential of the metal in contact with an activity molar aqueous solution of one of its salts, where the concentration is such that the activity coefficient multiplied by the molarity is unity.

Many nonionizable organic solutes in water are described thermodynamically on the mole fraction scale, although their solubilities may commonly be reported in practical units, for example, molality. [Refer to Schwarzenbach et al. (1993) and Klotz (1964) for detailed discussion of such aqueous solutions.] Here, the standard state is the pure liquid state of the organic solute, that is, Xj = 1. The reference state is Xi - 1, that is, a solution in which the organic solute molecules interact with one another entirely. Activity coefficients of solute molecules in dilute aqueous solutions are generally much greater than unity for this reference state choice, jc, 1. For example, with this reference state, aqueous benzene has an experimental infinitely dilute solution activity coefficient, T nzeno of 2400 for an infinite dilution reference state, jc, - 0, the activity coefficient would be approximately 1 (Tanford, 1991). 

The determination of the activity coefficients of species that exist dominantly as neutral molecules, such as Si02(ag), H2S(ag) and C02(ag), is much simpler. In these cases it is usually possible to establish a two-phase equilibrium between the substance in its pure state (solid or gaseous) and the substance in its aqueous or dissolved state. This leads to a simple and rigorous determination of the activity coefficient in solutions of varying composition. 

Volatilizational loss of chemicals from water to air is an important fate process for chemicals with low aqueous solubility and low polarity. Many chemicals, despite their low vapor pressure, can volatilize rapidly owing to their high activity coefficients in solution. Volatilizational loss from surfaces is a significant transport process. Volatilization of organic chemicals from the soil surface is complicated by other variables. There is no simple laboratory... 

Assume that an aqueous solute adsorbs at the mercury-water interface according to the Langmuir equation x/xm = bc/( + be), where Xm is the maximum possible amount and x/x = 0.5 at C = 0.3Af. Neglecting activity coefficient effects, estimate the value of the mercury-solution interfacial tension when C is Q.IM. The limiting molecular area of the solute is 20 A per molecule. The temperature is 25°C. 

The following data (for 25°C) were obtained at the pzc for the Hg-aqueous NaF interface. Estimate and plot it as a function of the mole fraction of salt in solution. In the table,/ is mean activity coefficient such that a = f m , where m is mean molality. 

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. 

Henry s law is useful for handling equiUbria associated with gas absorption (qv) and stripping problems. Henry s law coefficients are useful for estimating terminal activity coefficients and have been tabulated for many compounds in dilute aqueous solutions (27). 

Many additional consistency tests can be derived from phase equiUbrium constraints. From thermodynamics, the activity coefficient is known to be the fundamental basis of many properties and parameters of engineering interest. Therefore, data for such quantities as Henry s constant, octanol—water partition coefficient, aqueous solubiUty, and solubiUty of water in chemicals are related to solution activity coefficients and other properties through fundamental equiUbrium relationships (10,23,24). Accurate, consistent data should be expected to satisfy these and other thermodynamic requirements. Furthermore, equiUbrium models may permit a missing property value to be calculated from those values that are known (2). 

There is a third experimental design often used for studies in electrolyte solutions, particularly aqueous solutions. In this design the reaction rate is studied as a function of ionic strength, and a rate variation is called a salt effect. In Chapter 5 we derived this relationship between the observed rate constant k and the activity coefficients of reactants l YA, yB) and transition state (y ) ... 

Select now a second neutral indicator base C that is weaker than B by roughly an order of magnitude thus, a solvent can be found of such acidity that a significant fraction of both B and C will be protonated, but this will no longer be a dilute aqueous solution, so the individual activity coefficients will in general deviate from unity. For this solution containing low concentrations of both B and C,... 

Examples of Values of L and AF°. As a first example we may evaluate both L and AF° for a moderately soluble salt in aqueous solution. At 25° a saturated solution of potassium perchlorate has a concentration of 0.148 mole of KCIO4 in a 1000 grams of water that is to say, y+ = y = 0.148/55.5. The activity coefficient in the saturated solution has been taken1 to be 0.70 + 0.05. Using this value, we can estimate the work required to take a pair of ions from the crystal surface to mutually distant points, when the crystal is in contact with pure solvent at 25°C ... 

As another example we may discuss silver iodide. As mentioned in Sec. 49 a saturated aqueous solution of this salt at 25°C contains only 9.08 X 10-9 mole in 1000 grams of water. At this low concentration the activity coefficient does not differ appreciably from unity we have then... 

The Change of Solubility with Temperature. The solubilities of various salts have been measured in aqueous solution at various temperatures. But from these measurements we cannot derive values of L as a function of temperature, until the activity coefficients in the various saturated solutions have been accurately measured. In dilute solutions... 

Lithium Carbonate in Aqueous Solution. As an illustration, we shall evaluate the conventional AF° and AS0 for lithium carbonate in aqueous solution. At 25°C the concentration of the saturated solution is 0.169 molal.1 In this solution the molality of the Li+ ion is of course 0.338. The activity coefficient of the Li2CO.t in the saturated solution is not accurately known, but its value is not far from y,at = 0.59. Substituting in (186) we have then... 

As an example, take the molecule aminoazobenzene, one of the solutes listed in Table 39. When colorimetric measurements were made at room temperature on very dilute aqueous solutions of HC1, containing a trace of this substance, it was found that neutral molecules and (BH)+ ions were present in equal numbers when the concentration of the HCl was 0.0016 molal.1 At this low concentration the activity coefficient of the HCl is very near unity, and we may use (216) to find how far the vacant proton level provided by the aminoazobenzene molecule in aque-... 

Fui. 70. Activity coefficient of lithium bromide in aqueous solution at 25°C. 

Activity Coefficients. Turning now to the experimental data on activity coefficients, Fig. 70 shows the results for lithium bromide in aqueous solution at 25°C, plotted against the square root of the concentration. 

Fig. 73. Activity coefficients of alkali hydroxides in aqueous solution at 2S°C.

The activity coefficient ya of the undissociated acid is approximately unity in dilute aqueous solution. Expression (24) thus becomes ... 

Ise, N. The Mean Activity Coefficient of Polyelectrolytes in Aqueous Solutions and Its Related Properties. Vol. 7, pp. 536—593. 

If the activity coefficients are estimated from the Debye-Huckel theory in dilute regions of simple electrolyte systems, we have for aqueous solutions at 25 °C,... 

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