Sulfuric activity coefficients

The activity of any ion, a = 7m, where y is the activity coefficient and m is the molaHty (mol solute/kg solvent). Because it is not possible to measure individual ionic activities, a mean ionic activity coefficient, 7, is used to define the activities of all ions in a solution. The convention used in most of the Hterature to report the mean ionic activity coefficients for sulfuric acid is based on the assumption that the acid dissociates completely into hydrogen and sulfate ions. This assumption leads to the foUowing formula for the activity of sulfuric acid. 

The activity coefficients of sulfuric acid have been deterrnined independentiy by measuring three types of physical phenomena cell potentials, vapor pressure, and freeting point. A consistent set of activity coefficients has been reported from 0.1 to 8 at 25°C (14), from 0.1 to 4 and 5 to 55°C (18), and from 0.001 to 0.02 m at 25°C (19). These values are all based on cell potential measurements. The activity coefficients based on vapor pressure measurements (20) agree with those from potential measurements when they are corrected to the same reference activity coefficient. 

To calculate the open circuit voltage of the lead—acid battery, an accurate value for the standard cell potential, which is consistent with the activity coefficients of sulfuric acid, must also be known. The standard cell potential for the double sulfate reaction is 2.048 V at 25 °C. This value is calculated from the standard electrode potentials for the (Pt)H2 H2S04(yw) PbS04 Pb02(Pt) electrode 1.690 V (14), for the Pb(Hg) PbS04 H2S04(yw) H2(Pt) electrode 0.3526 V (19), and for the Pb Pb2+ Pb(Hg) 0.0057 V (21). 

Factors in controlling chemical compositions of gold in equilibrium with the ore fluids are temperature, pH, concentration of aqueous H2S and Cl in the ore fluids, concentration ratio of Au and Ag species in the ore fluids, activity coefficient of Au and Ag components in gold, and so on (Shikazono, 1981). In the Yamizo Mountains, as a result, Ag/Au ratios of gold are correlated with a kind of the host rocks and sulfur isotopic compositions of the deposits. This correlation could be used to interpret Ag/Au ratios of gold. 

From the foregoing discussion we conclude that some sophisticated tools are now available by which the activity coefficient in hydrometal— lurgical systems can be addressed. What is lacking is the actual application of these tools by the industry. The next step in establishing the accuracy of the available approaches lies in providing a broader data base for complex multicomponent systems which can be used for parameter refinement. TTte lack of data is most serious in the weak electrolyte area, but even familiar systems such as those encountered in sulfuric acid leaching need attention. 

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 ... 

The solubility of monoclinic sulfur in CS2 is 22-molal. What is the solubility of rhombic sulfur in the same solvent Assume that the activity coefficient for both forms of dissolved sulfur is 1. 

An experimental check on this assumption about activity coefficients is possible over a limited range of solvent acidity. If the composition of water-sulfuric acid mixtures is varied over the range in which all four species, Al5 A2, A1H +, and A2H+ are present in appreciable concentration, then, since OAlH + / aA2H+ 1S (W definition) constant, a constant ratio [A1][A2H+]/ [A2 [A1H + ] implies that the assumption of the ratio of y s being constant is correct in this range of solvents. Experimentally, for bases that are substituted anilines this test is fairly successful, a result that supports the validity of the method. The question of how similar two compounds must be to be sufficiently close in structure will be considered later. 

The discussion in the previous sections concerning solvated species indicates that a complete knowledge of the chemical reactions that take place in a system is not necessary in order to apply thermodynamics to that system, provided that the assumptions made are applied consistently. The application of thermodynamics to sulfuric acid in aqueous solution affords another illustration of this fact. We choose the reference state of sulfuric acid to be the infinitely dilute solution. However, because we know that sulfuric acid is dissociated in aqueous solution, we must express the chemical potential in terms of the dissociation products rather than the component (Sect. 8.15). Either we can assume that the only solute species present are hydrogen ion and sulfate ion (we choose to designate the acid species as hydrogen rather than hydronium ion), or we can take into account the weak character of the bisulfate ion and assume that the species are hydrogen ion, bisulfate ion, and sulfate ion. With the first assumption, the effect of the weakness of the bisulfate ion is contained in the mean activity coefficient of the sulfuric acid, whereas with the second assumption, the ionization constant of the bisulfate ion is involved indirectly. 

The mean activity coefficient of sulfuric acid is usually calculated in terms of Equation (11.91), where the weakness of the bisulfate ion is ignored. The relationship between the various activity coefficients when the incomplete ionization of the ion is included, and when it is not, is now readily obtained by the combination of the appropriate equations. Thus, when Equations (11.91) and (11.92) are equated,... 

The activity coefficient of the molecular diluted sulfur dioxide is set to 1. The water... 

Free energies of formation and activity coefficients of the relevant sulfur moieties at the prevailing temperature or—alternatively—formal potentials of the corresponding redox couples. 

Strength on activity coefficients, since the activities, rather than the concentrations of the participating species are the quantities that determine the potential due to the redox couple. These criteria are difficult to meet and have led to the skeptical outlook that most Eh measurements are not amenable to quantitative interpretation (2,42,43). Contamination of platinum electrode surfaces by oxygen in aerated waters (, ), by sulfur in anaerobic waters (4 ) and by iron in surface sediments (45) may cause errors in the measured values. Furthermore, many Eh measurements are thought to be mixed potentials ( ). For these reasons, most Eh measurements have been used only in a qualitative sense. 

Figure 15-2 (left) depicts several titration curves of Fe(II) with permanganate. Beyond the end point the experimental curves differ from the theoretical shape, which is nearly flat beyond the end point (5-equivalent reduction). The essential symmetry of the curves suggests that the potential is determined by the Mn(III)-Mn(II) couple beyond the end point. Evidence for this behavior can be seen in solutions containing sulfate or phosphate, which tend to stabilize Mn(III) (Section 17-1). That sulfuric and phosphoric acids have about the same effect before and after the end point is consistent with the similarity of the behavior of the Mn(III)-Mn(II) and the Fe(III)-Fe(II) systems with respect to changes in activity coefficients as well as with respect to hydrolysis and complex formation. 

Problem Assuming to remain constant, calculate the relative change in the mean ionic activity coefficient of 1 molal sulfuric acid solution from 0 to 25 C. 

The E.M.F. of a lead storage battery containing 2.75 molal sulfuric acid was found to be 2.005 volt at 25 C. The aqueous vapor pressure of the acid solution at this temperature is about 20.4 mm., while that of pure water is 23.8 mm. The mean ionic activity coefficient of the sulfuric acid is 0.136. Calculate the standard free energy change of the cell reaction at 25 C and check the values from tabulated free energy data. 

In 1979, the Department of Energy initiated support of a number of fundamental projects in the chemistry of flue gas desulfurization. Five chapters in this book report the initial results of this effort. The topics of fundamental work include thermodynamic properties, activity coefficients in aqueous solutions, sulfur and NOx chemistry, and sulfite oxidation kinetics. The results provide the foundation for quantitative understanding of the FGD processes. 

Stelson and Seinfeld (1981) have shown that solution concentrations of 8-26 M can be expected in wetted atmospheric aerosol. At such concentrations the solutions are strongly nonideal, and appropriate thermodynamic activity coefficients are necessary for thermodynamic calculations. Tang (1980), Stelson and Seinfeld (1982a-c), and Stelson et al. (1984) have developed activity coefficient expressions for aqueous systems of nitrate, sulfate, ammonium, nitric acid, and sulfuric acid at concentrations exceeding 1M. 

---