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THE GEOCHEMISTRY OF NATURAL WATERS CHEMICAL EQUILIBRIUM CHAPTER 2c - Kehew (2001) 1 LEARNING OBJECTIVES Learn to use some tools of thermodynamics. Become acquainted with equilibrium and the equilibrium constant. Become acquainted with activity and activity coefficients. Learn to calculate and use IAP and SI. Learn to calculate variation of the equilibrium constant with temperature. See and be able to calculate the effect of activity coefficients on mineral solubility. See and be able to calculate the effect of complexation on mineral solubility. 2 IONIC STRENGTH - I Recall that activity and concentration are related through the activity coefficient according to: ai = i·Mi Activity coefficients different from unity arise because of the interaction of ions as concentration rises. The degree of ion interaction depends on ionic charge as well as concentration. 3 IONIC STRENGTH - II Ionic strength (I ) is a quantity that is required to estimate activity coefficients. It takes into account both concentration and charge: I 1 2 M z 2 i i The calculation of ionic strength must take into account all major ions: I 1 [ M Na 4 M Ca 2 4 M Mg 2 M HCO M Cl 4 M SO2 ] 2 3 4 4 DEBYE-HÜCKEL EQUATION Az I 2 log i i 1 Ba o I Used to calculate activity coefficients for ions at ionic strengths < 0.1 mol L-1. A, B are functions of temperature and pressure and are given in Table 2-1 of the text. ao is the distance of closest approach and it is a property of the specific ion. 5 DEBYE-HÜCKEL PARAMETERS T(C) A B(108) 0 0.4883 0.3241 5 0.4921 0.3249 10 0.4960 0.3258 15 0.5000 0.3262 20 0.5042 0.3273 25 0.5085 0.3281 30 0.5130 0.3290 40 0.5221 0.3305 50 0.5319 0.3321 60 0.5425 0.3338 6 DISTANCES OF CLOSEST APPROACH FOR SELECTED IONS Ion a0 (10-8) Ion a0 (10-8) Ca2+ 5.0 HCO3-, CO32- 5.4 Mg2+ 5.5 NH4+ 2.5 Na+ 4.0 Sr2+, Ba2+ 5.0 K+, Cl- 3.5 Fe2+, Mn2+, Li+ 6.0 SO42- 5.0 H+, Al3+, Fe3+ 9.0 7 THE DAVIES EQUATION I log i Az 2 i 1 I 0.2 I Used to calculate activity coefficients for ions at ionic strengths < 0.5 mol L-1. The value of A is the same as the one employed in the Debye-Hückel equation. The advantage over the D-H equation is that the only ion-dependent parameter is the ionic charge, zi. 8 ACTIVITY COEFFICIENTS 1.2 + H HCO3- 1.0 + Na Activity coefficient, K+, Cl- 0.8 0.6 0.4 2+ 2- Mg , CO3 Ca2+, SO42- 0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Ionic strength (I) 9 NEUTRAL SPECIES Deviations from ideal behavior are least important for neutral solutions, e.g., H2CO30. In other words, their activity coefficients will not be greatly different from unity. A useful approximation for neutral species is: 10 0.1I 10 EFFECT OF ACTIVITY COEFFICIENTS ON GYPSUM SOLUBILITY Question: what is the solubility of gypsum in water at 25°C and 1 bar? For the equilibrium: CaSO4·2H2O(s) Ca2+ + SO42- + 2H2O(l) we can calculate log KSP = -4.41. We can also see that, if gypsum dissolves in pure water, then the stoichiometry of the reaction is such that the molarity of calcium should equal the molarity of sulfate. Thus, solubility of gypsum = MCa2+. So what’s the problem? Catch 22! We don’t know the concentrations, so we can’t calculate the ionic strength, so we can’t calculate the activity coefficients, so we can’t calculate the concentrations! 11 WHAT TO DO? We start by making an initial assumption that the activity coefficients are equal to 1 and solve the problem by iteration. We write: K aCa 2 aSO2 Ca 2 M Ca 2 SO2 M SO2 10 4.41 4 4 4 but because we assume activity coefficients are equal to 1, we write: K M 2 M 2 M 2 2 104.41 Ca SO4 Ca or M Ca 2 102.205 6.24 103 This is what the solubility would be if we ignored activity coefficients altogether. 12 THE NEXT STEP Now, having the concentration of Ca2+ and SO42-, we can calculate the ionic strength according to: I 1 2 46.24 10 46.24 10 2.5 10 3 3 2 mol L1 Applying the Debye-Hückel formula we get: Ca SO 0.548 2 2 4 which are about half the originally assumed values. We calculate a new estimate for the molality of Ca2+: 4.41 10 3 M Ca 2 11.40 10 0.548 0.548 This is used to calculate a new ionic strength and the whole process is repeated until convergence. 13 RESULTS OF ITERATIONS Iteration MCa2+ I 1 1 6.2410-3 2.5010-2 2 0.548 11.4010-3 4.5610-2 3 0.476 13.1110-3 5.2410-2 4 0.460 13.5610-3 5.4210-2 5 0.454 13.7510-3 5.5010-2 6 0.452 13.7810-3 5.5110-2 7 0.453 13.7810-3 5.5110-2 14 FINAL ANSWER The final calculated molarity of Ca2+ is 13.7810-3. This is 2.21 times the calculated molarity of Ca2+ assuming activity coefficients are unity. We see that activity coefficient corrections are very important for this solution. It is customary to express solubility in g L-1 of gypsum: (13.7810-3 mol L-1)(172.1 g mol-1) = 2.37 g L-1 15

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posted: | 10/28/2011 |

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