Activity coefficient mean ionic table

Based on agreement between calculated and experimental values of mean ionic activity coefficients, we can infer that the Debye-Hiickel relationship and the data in Table 10-2 give satisfactory activity coefficients for ionic strengths up to about 0.1 M. Beyond this value, the equation fails, and we must determine mean activity coefficients experimentally. 

It has been emphasized repeatedly that the individual activity coefficients cannot be measured experimentally. However, these values are required for a number of purposes, e.g. for calibration of ion-selective electrodes. Thus, a conventional scale of ionic activities must be defined on the basis of suitably selected standards. In addition, this definition must be consistent with the definition of the conventional activity scale for the oxonium ion, i.e. the definition of the practical pH scale. Similarly, the individual scales for the various ions must be mutually consistent, i.e. they must satisfy the relationship between the experimentally measurable mean activity of the electrolyte and the defined activities of the cation and anion in view of Eq. (1.1.11). Thus, by using galvanic cells without transport, e.g. a sodium-ion-selective glass electrode and a Cl -selective electrode in a NaCl solution, a series of (NaCl) is obtained from which the individual ion activity aNa+ is determined on the basis of the Bates-Guggenheim convention for acr (page 37). Table 6.1 lists three such standard solutions, where pNa = -logflNa+, etc. 

A wide variety of data for mean ionic activity coefficients, osmotic coefficients, vapor pressure depression, and vapor-liquid equilibrium of binary and ternary electrolyte systems have been correlated successfully by the local composition model. Some results are shown in Table 1 to Table 10 and Figure 3 to Figure 7. In each case, the chemical equilibrium between the species has been ignored. That is, complete dissociation of strong electrolytes has been assumed. This assumption is not required by the local composition model but has been made here in order to simplify the systems treated. 

Table 1. Data and Results of Fit for Aqueous Solutions of uni-univalent electrolyte at 298.15°K - Mean Ionic Activity Coefficient Data... 

Sulfuric acid is a 2 1 electrolyte, and so (by using the data in Table 3.1) the ionic strengthlis three times the concentration, i.e.l = 0.03 moldm f Next, from the Debye-Huckel extended law equation (3.15), we can obtain the mean ionic activity coefficient y as follows ... 

Worked Example 3.11. We know the concentration of copper sulfate to be 0.01 mol dm from other experiments, and so we also know (from suitable tables) that the mean ionic activity coefficient of the copper sulfate solution is 0.404. The measured electrode potential was Ec j+ — 0.269 V and = 0.340 V. We will calculate the... 

It can be shown that the virial type of activity coefficient equations and the ionic pairing model are equivalent, provided that the ionic pairing is weak. In these cases, it is in general difficult to distinguish between complex formation and activity coefficient variations unless independent experimental evidence for complex formation is available, e.g., from spectroscopic data, as is the case for the weak uranium(VI) chloride complexes. It should be noted that the ion interaction coefficients evaluated and tabulated by Cia-vatta [10] were obtained from experimental mean activity coefficient data without taking into account complex formation. However, it is known that many of the metal ions listed by Ciavatta form weak complexes with chloride and nitrate ions. This fact is reflected by ion interaction coefficients that are smaller than those for the noncomplexing perchlorate ion (see Table 6.3). This review takes chloride and nitrate complex formation into account when these ions are part of the ionic medium and uses the value of the ion interaction coefficient (m +,cio4) for (M +,ci ) (m +,noj)- Io... 

Substances typical of acids and bases are, respectively, HCl and NaOH. Hydrogen chloride dissolves in water with practically complete dissociation into hydrated protons and hydrated chloride ions. Sodium hydroxide dissolves in water to give a solution containing hydrated sodium ions and hydrated hydroxide ions. Table 3.6 gives values of the mean ionic activity coefficients, y , at different concentrations and indicates the pH values and those expected if the activity coefficients are assumed to be unity. 

Table 3.6 Mean ionic activity coefficients and pH values for some aqueous solutions...

The mean ionic activity coefficients of hydrobromic acid at round molalities (calculated by means of Equation 2) are summarized in Tables XI, XII, and XIII for x = 10, 30, and 50 mass percent monoglyme. Values of —logio 7 at round molalities from 0.005 to 0.1 mol-kg-1 were obtained by interpolating a least squares fit to a power series in m which was derived by means of a computer. These values at 298.15° K are compared in Figure 2 with those for hydrochloric acid in the same mixed solvent (I) and that for hydrobromic acid in water (21). The relative partial molal enthalpy (H2 — Hj>) can be calculated from the change in the activity coefficient with temperature, but we have used instead the following equations ... 

Values of the mean ionic activity coefficients for several electrolyte in water at 25°C are given in the following table ... 

It will be found in the Table 8 that the mean activity coefficient of NaOH or rather the activity coefficient of hydroxyl ions in solutions of pure sodium hydroxide with an ionic strength fx = 6.28 (equal to the value of the molality, in this case) will be ... 

Table VI. Mean Ionic Activity Coefficients (Molality Scale) of HBr in H20/NMA Solvent Mixtures at 25°C...

It is evident that smoothed values of the mean ionic activity coefficient of HBr (yHBr), scale of molality, can be derived by Equation 1 A and B are given in Table I, and a is 5.2 A. Values of ft (the slope of the E° vs. molality plot divided by — 2k) are listed in Table VI, along with yHBr at molalities from 0.005-0.1 for each solvent mixture at 25°C. For comparison, the corresponding values of the activity coefficient in pure water are listed (19). 

It is an interesting fact that the activation energy for electrolytic conductance is almost identical with that for the viscous flow of water, viz., 3.8 kcal. at 25 hence, it is probable that ionic conductance is related to the viscosity of the medium. Quite apart from any question of mechanism, however, equality of the so-called activation energies means that the positive temperature coefficient of ion conductance is roughly equal to the negative temperature coefficient of viscosity. In other words, the product of the conductance of a given ion and the viscosity of water at a series of temperatures should be approximately constant. The results in Table XVI give the product of the conductance of the acetate ion at... 

Table 2-2. As a justification of his procedure the values of mean activity coefficients calculated for various electrolytes from the individual ionic values are in satisfactory agreement with the experimental values up to an ionic strength of about 0.1.

Utilize the mean ionic activity coefficients for solutions up to 0.05 molal in Table XXXIII to determine by a graphical procedure the mean ionic diameter d of hydrochloric acid. 

The mean ion activity coefficients of several salts taken from tables in Robinson and Stokes (1970) are plotted against ionic strength in Fig. 4.1. For reasons discussed later in this chapter, y ... 

Values of/x = Ac/A may be calculated from Kohlrausch s measurements of electrical conductivity of hydrochloric acid solutions. /h and fci can be evaluated from the potentiometric measurements on hydrochloric acid solutions performed by Scatchaed. These data are very reliable since the concentration chain was so arranged as to eliminate diffusion potentials. In this way, ScATCHARD determined the mean activity coefficient V/h/ci instead of the individual ion activities. If we assume that in a potassium chloride solution/ = /ci— which is plausible when we recall that both ions have the same structure—and that fci is the same in hydrochloric acid solutions and potassium chloride solutions of the same concentration, then we can calculate/h and fci in hydrochloric acid solutions. Naturally these values are not strictly correct since the effect of the potassium ions on the activity of the chloride ions probably is different from that of the hydrogen ions at the same ionic strength. In the succeeding table are given values of /x, /h, and fci calculated by the above method. 

According to Table 2.3, K x 700 L mol 1. Moreover, m = 0.025 mol L 1 and y was calculated at 0.36, which then yields a. — 0.48. This would mean that only about half of the salt is in the dissociated form. That implies that the ionic strength is far smaller than supposed, so that the ion activity coefficient is higher than calculated and the calculation of a. thus was incorrect. An iterative calculation, inserting adapted values of y or a until agreement is reached between both parameters, would be needed. This yields about a — 0.37, leading to 1x31 mmolar. 

Here the standard state for the ionic species is a 1-molal ideal solution the enthalpies and Gibbs energies of formation for some ions in this standard state at 25 C are given in Table 13.1-4. In Eq. 13.1-27 the standard state for the undissodated molecule has also been chosen to be the ideal 1-molal solution (see Eq. 9.7-20), although the pure component state could have been used as well (with appropriate changes in AfG, b aA B ). Finally, we have used the mean molal activity coefficient, y , of Eq. 9.10-11. Also remember that for the 1-molal standard state, y ° 1 as the solution becomes veiy dilute in the component. 

Fig. 17.4. Stoichiometric mean ionic activity of HCl (a ,Hci) versus molality of HCl. Crosses are data points from Table 17.2 dotted line is Henry s Law, having an activity of 1.0 at 1.0 molal HCl. The stoichiometric mean ionic activity coefficient at muci =0J sxy/xz = 0.772.

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