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12 Kerrick, D.M. and Jacobs, G.K. 1981. A modified Redlich–Kwong equation for H2O, CO2 and H2O–CO2 mixtures at elevated pressures and temperatures. American Journal of Science 281: 735–67.
13 Morel, F.M.M. and Hering, J.G. 1993. Principles and Applications of Aquatic Chemistry, 2nd edn. New York, John Wiley and Sons, Ltd.
14 Nordstrom, D.K. and Munoz, J.L. 1986. Geochemical Thermodynamics. Palo Alto, Blackwell Scientific.
15 Saxena, S.K., Chaterjee, N., Fei, Y. and Shen, G. 1993. Thermodynamic Data on Oxides and Silicates. Berlin, Springer Verlag.
PROBLEMS
1 Consider the following minerals:anhydrite:CaSO4bassanite:CaSO4.½H2O(plaster of Paris)gypsum:CaSO4.2H2OIf water vapor is the only phase of pure water in the system, how many phases are there in this system and how many components are there?How many phases are present at invariant points in such a system? How many univariant reactions are possible? Write all univariant reactions, labeling each according the phase that does not participate in the reaction.
2 Consider a system consisting of olivine of variable composition ((Mg,Fe)2SiO4) and orthopyroxene of variable composition ((Mg,Fe)SiO3). What is the minimum number of components needed to describe this system?
3 In section 3.2.1.3, we showed that a system containing , and OH– could be described in terms of components , H+, and OH–. Find a different set of components that describe the system equally well. Show that each of the species in the system is an algebraic sum of your chosen components.
4 Use the data in Table 2.2 to construct a temperature–pressure phase diagram that showing the stability fields of calcite and aragonite.
5 Consider the following hypothetical gaseous solution: gases 1 and 2 form an ideal binary solution; at 1000 K, the free energies of formation from the elements are −50 kJ/mol for species 1 and −60 kJ/mol for species 2.Calculate ΔGmixing for the solution at 0.1 increments of X2. Plot your results.Calculate for an ideal solution at 0.1 increments of X2. Plot your results.Using the method of intercepts, find μ1 and μ2 in the solution at X2 = 0.2
6 Using the thermodynamic data in Table 2.2, determine which side of this reaction is stable at 600°C and 400 MPa.:
7 The following analysis of water is from the Rhine River as it leaves the Swiss Alps:Ca2+40.7 ppmHCO3–113.5 ppmMg2+7.2 ppmSO42–36.0 ppmNa+1.4 ppmNO3–1.9 ppmK+1.2 ppmCl−1.1 ppmCalculate the ionic strength of this water. (Recall that concentrations in ppm are equal to concentrations in mmol kg−1 multiplied by formula weight.)Using the Debye–Hückel equation and the data in Table 3.2, calculate the practical activity coefficients for each of these species at 25°C.
8 Seawater has the following composition:Na+0.481 MCl−0.560 MMg2+0.0544 MSO42–0.0283 MCa2+0.0105 MHCO3–0.00238 MK+0.0105 MCalculate the ionic strength.Using the Davies equation and the data in Table 3.2, calculate the practical activity coefficients for each of these species at 25°C.
9 The following is an analysis of Acqua di Nepi, a spring water from the Italian province of Viterbo:Ca2+82 ppmHCO3–451 ppmK+50 ppmSO42–38 ppmMg2+27 ppmCl−20 ppmNa+28 ppmNO3–9 ppmF–1.3 ppmCalculate the ionic strength of this water.Using the Debye–Hückel equation and the data in Table 3.1, calculate the practical activity coefficients for each of these species at 25°C.
10 Water from Thonon, France, has the following composition:Anionsmg/lCationsmg/lHCO3–332Ca2+103.2SO42_14Mg2+16.1NO3–14K+1.4Cl–8.2Na+5.1What is the ionic strength of this water?What are the activity coefficients for and in this water?Assuming an equilibrium constant for the dissociation of bicarbonate:of 4.68 × 10–11 and a pH of 7.3, what is the equilibrium concentration of in this water?
11 The equilibrium constant for the dissolution of galena:is 9.12 × 10−7 at 80°C. Using = 0.11 and = 1.77, calculate the equilibrium concentration of Pb2+ in aqueous solution at this temperature and at pHs of 6, 5 and 4. Assume the dissolution of galena is the only source of Pb and H2S in the solution, and that there is no significant dissociation of H2S. Hint: Mass balance requires that [H2S] = [Pb2+].
12 The dissociation constant for hydrofluoric acid (HF) is 10−3.2 at 25°C. What would be the pH of a 0.1 M solution of HF? You may assume ideal behavior. (Hint: Ask yourself what addition constraints are imposed on the system. Your final answer will require solving a quadratic equation.)
13 The first dissociation constant for H2S is K1 = 9.1 × 10−3. Neglecting the second dissociation and assuming ideality (i.e., activity equals concentration), what is the pH of 1 liter of pure water if you dissolve 0.01 moles of H2S in it? What fraction of H2S has dissociated?(HINT: Assume that the concentration of OH− is negligible (in other words, no autodissociation of water) and use the quadratic equation for your final solution.)
14 Given the following analysis of biotite and assuming a mixing-on-site model for all sites, calculate the activities of the following components:SiteIonIons per siteTetrahedralSi2.773Al1.227OctahedralAl0.414Ti0.136Fe3+0.085Fe2+1.399Mg0.850InterlayerCa0.013Na0.063K0.894AnionOH1.687F0.037Hint: Check your result by making sure the activity of phlogopite in pure phlogopite is 1.
15 Given the following analysis of a pyroxene, use the mixing-on-site model of ideal activities to calculate the activity of jadeite (NaAlSi2O6) and diopside (CaMgSi2O6) in this mineral:SiteIonIons per siteTetrahedralSi1.96Al0.04Octahedral M1Al0.12Mg0.88Octahedral M2Fe2+0.06Ca0.82Na0.12
16 Write the equilibrium constant expression for the reaction:assuming the solids are pure crystalline phases and that the gas is ideal.
17 Assuming ideal solution behavior for the following:Show that the boiling point of a substance is increased when another substance is dissolved in it, assuming the concentration of the solute in the vapor is small.By how much will the boiling point of water be elevated when 10% salt is dissolved in it?
18 Find for the reaction:Which side of the reaction is favored?(Hint: Use the data in Table 3.3.)
19 What is the for the reaction:What is the pε° for this reaction?
20 Consider a stream with a pH of 6.7 and a total dissolved Fe concentration of 1 mg/l. Assume ideal behavior for this problem.If the stream water is in equilibrium with the atmospheric O2 (partial pressure of 0.2 MPa), what is the pε of the water?Assuming they are the only species of Fe in the water, what are the concentrations of Fe3+ and Fe2+? Use the pε you determined in part a.
21 Write reactions for the oxidation of nitrogen gas to aqueous nitrite and nitrate ions that contain the electron and hydrogen ion (i.e., reactions suitable for a pε–pH diagram). Write the log equilibrium constant expression for these reactions. Using the data below, calculate the log equilibrium constant for these reactions under standard state conditions). Calculate pε° and for these reactions.SpeciesH2O−237.19N2 (gas)0−111.3−32.2Standard state is 25°C and 0.1 MPa. R = 8.314 J/mol-K.Hint: remember, in the standard state, all reactants and products have activities of 1.
22 Construct a pε–pH diagram for the following species of sulfur: , , H2S, HS–, and S2– at 25°C and 0.1 MPa. The following free energies of formation should provide sufficient information to complete this task.SpeciesSpeciesS2− (aq)+85.81H2O−237.19HS− (aq)+12.09H+0H2S (aq)−27.82H2 (g)0 (aq)−744.54O2 (g)0HSO4– (aq)−755.92Values are in kJ/mol, standard state is 25°C and 0.1 MPa. R = 8.314 J/mol-K.
23 Construct a pε–pH diagram for dissolved species of uranium, and , and the two solid phases UO2 and U3O8 at 25°C