1. Activity Coefficients
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2. EFFECT OF ELECTROLYTES ON CHEMICAL EQUILIBRIA
H3AsO4 + 3I- + 2H+  H3AsO3 + I3- + H2O
The position of most solution equilibria depends on the electrolyte concentration of the medium, even when the added electrolyte contains no ion in common with those involved in the equilibrium. KI
KCl
H3AsO4 + 3I- + 2H+  H3AsO3 + I3- + H2O
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3. Effect of Ions concentration on Solubility of Potassium tartarate
↑ concentration with addition of an “inert” ion
“neutral” species
K2C4H4O6
↓ concentration with addition of common ion
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4. Chemical Equilibrium Electrolyte Effects
Electrolytes: producing ions
1-Common 2-no common
Can electrolytes affect chemicalequilibria?
(A) “Common Ion Effect”
Decreases solubility of BaSO4 with BaCl2
Ba2+ is the “common ion”
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5. Predicted effect of excess barium ion on solubility of BaSO4.
©Gary Christian, Analytical Chemistry, 6th Ed. (Wiley)
Predicted effect of excess barium ion on solubility of BaSO4.
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6. “inert electrolyte effect”or “diverse ion effect”
(B) No common ion:
“inert electrolyte effect”or
“diverse ion effect”
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7. The Salt Effect
Adding an “inert” salt to a sparingly soluble salt increases the solubility of the sparingly soluble salt.
“inert” salt = a salt whose ions do not react with (e.g., chelate, or precipitate) the compound of interest
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8. Increases solubility of BaSO4 Why???
Predicted effect of presense of Na2SO4 on solubility of BaSO4.
Increases solubility of BaSO4 Why???
shielding of dissociated ion species
©Gary Christian, Analytical Chemistry, 6th Ed. (Wiley)
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9. How? Consider: BaSO4 Ba2+ + SO42-
NO3-
Na+
Consider: BaSO4 Ba2+ + SO42-
BaSO4 (Ksp = 1.1x10-10) as the sparingly soluble salt and NaNO3 → Na+ + NO3- as the “inert” salt.
The cation (Ba2+) is surrounded by anions (SO42-, NO3-)
net positive charge is reduced
The anion (SO42-) is surrounded by cations (Ba2+, Na+)
net negative charge is reduced
attraction between oppositely charged ions (Ba2+, SO42-) is decreased Solubility is increased
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10. Concentration v.s. Activity
For many substances the active mass per unit volume is directly proportional to the concentration. ai≈Ci
...but the approximation of activity being equal to concentration will not accurately reflect the actual behavior of matter under all conditions.
ai=Ci :is a reasonably valid approximation for an
u< 10-2 M
Only an approximation of the equilibrium condition.
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11. Activity Coefficients
The activity coefficient accounts for available ‘acid’ species in solution at high concentrations
Activity
Activity Coefficient
Concentration
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12. Activity Coefficient Effective concentration of decreases
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13. Ionic Strength
Ionic strength, , is a measure of the total ionic charges in solutions
where ci is the concentration of the iones species and zi is the associated charge.
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14. Ionic Strength Find the ionic strength of a KCl solution:
At 0.10 M KCl…
At M KCl…
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15. Ionic Strength Find the ionic strength of a CaCl2 solution:
At 0.10 M CaCl2 …
At M CaCl2 …
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17. Calculation of Activity Coefficients
Requires the Debye-Hückel equation:
z is the charge of the ion
a is the effective hydrated radius of the ion (in nm)
m is the ionic strength of the solution
(Valid at 25°C for   0.1M)
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18. Calculating Activity Coefficients
Calculate the activity coefficients of
Ca2+ and F- in M NaClO4
(Ca2+= nm, F- = nm)
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19. Activity of the ion in a solution depends on its hydrated radius not the size of the bare ion.
α → g 
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20. Z → g  α → g  920116......34 slides http:\\asadipour.kmu.ac.ir

21. Activity Coefficients
Z,α→ g 
 approaches 1 in very dilute solution at which approaches 0.
The effect of  on  is greater for larger z and small .
Note that if m >0.1 M it is necessary to experimentally determine g,
otherwise use referenceTable as an approximation
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22. As ionic strength increases, the activity coefficient decreases.
 → 
  0   1
As the charge of the ion increases, the departure of its activity coefficient from unity increases. Activity corrections are much more important for an ion with a charge of 3 than one with the charge 1.
Z→ g 
Activity coefficients for differently charged ions with a constant hydrated radius of 500pm.
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25. Activity and Equilibrium
The correct form of the equilibrium expression is…
aA + bB  cC + dD
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26. Solubility of a salt x = 2.14×10-4M
calculate [Ca2+] in saturated CaF2 solid.
Ksp = 3.9×10-11
CaF2(s)  Ca F-
Ksp = 3.9×10-11 = [Ca][F]2
3.9×10-11 = X·(2X)2=4X3
x = 2.14×10-4M
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27. Solubility in presence of common ion
calculate [Ca2+] in M NaF saturated with CaF2 solid.
Ksp = 3.9×10-11
CaF2(s)  Ca F-
Initial conc. (M)
0.050
Eq conc. (M) x
2x+0.050
Change 2x
Without activity coefficient considerations:
Ksp = 3.9×10-11 = [Ca][F]2
3.9×10-11 = x·(0.050)2
x = 1.6×10-8M
<< 2.14×10-4M
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28. Solubility and Activity
With activity coefficient considerations:
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29. Calculating Activity Coefficients
Calculate the activity coefficients of
Ca2+ and F- in M NaClO4
(Ca2+= nm, F- = nm)
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30. Solubility and Activity
With activity coefficient considerations:
Assume that 2x << and  due to Ca2+ is negligible.
3.9×10-11 = x(0.49)(0.050)2(0.81)2
x = 4.9×10-8 M
[Ca2+] or solubility of CaF2 solid in M NaF
With activity coefficient considerations:
3 times
x = 1.6×10-8M
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31. Solubility and Activity
Solubility of PbI2 in 0.1M KNO3
m = [0.1(1+) (1-)2]/2 = 0.1 (ignore Pb2+,I-)
ƒPb = ƒI = 0.76
Ksp = (aPb)1(aI)2 = ([Pb2+]Pb )1([I-]I )2
Ksp = ([Pb2+] [I-]2) (Pb I2 ) = Ḱ sp (Pb I2 )
Ḱ sp = Ksp / (Pb I )
Ḱ sp = 7.1 x 10-9 /((0.35)(0.76)2) = 3.5 x 10-8
(s)(2s)2 = Ḱ sp s = (Ḱ sp /4)1/ s =2.1 x 10-3 M
s = (Ksp/4)1/3 then s =1.2 x 10-3M
Without activity coefficient considerations:
With activity coefficient considerations:Solubility approx.43%
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33. Acids, Bases, and Activity
Calculate the pH of water containing 0.10 M KCl at 25°C.
(H+ = nm and OH- = nm)
1.0×10-14 = x(0.83) x(0.76)
x = 1.26×10-7 M with activity
x = 1.00×10-7 M without activity
pH=-log aH+
aH+= g.[H+]
pH = -log (0.83×1.26×10-7) = 6.98
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34. Calculating Activity Coefficients
Calculate the activity coefficients of
Ca2+ in M NaClO4.
TEXT  g
0.1
0.4
0.08
0.05
0.48
reverse
???
0.432
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35. H+ in NaClO4 solution of varying ionic strengths
At high ionic strengths:
Activity coefficients of most ions increase
Concentrated salt solutions are not the same as dilute aqueous solutions
In diluted salt solutions g is independent to type of ion
In concentrated salt solutions g is dependent to type of ion and interpretation is difficult.
H+ in NaClO4 solution of varying ionic strengths
We try not to work with solutions >0.01 M
If µ→0 g =1activity ≈ concentration
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