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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   104.41
                          Ca   SO4        Ca
                               or
                 M Ca 2  102.205  6.24  103
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   46.24 10   46.24 10   2.5 10
                       3                3        2
                                                        mol L1


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     6.2410-3    2.5010-2
    2       0.548   11.4010-3   4.5610-2
    3       0.476   13.1110-3   5.2410-2
    4       0.460   13.5610-3   5.4210-2
    5       0.454   13.7510-3   5.5010-2
    6       0.452   13.7810-3   5.5110-2
    7       0.453   13.7810-3   5.5110-2

                                        14
           FINAL ANSWER
 The final calculated molarity of Ca2+ is
   13.7810-3.
 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:
  (13.7810-3 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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