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**Activity Coefficients**

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**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 slides 35 slides

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**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 slides 35 slides

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**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” slides

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**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. slides 35 slides

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**“inert electrolyte effect”or “diverse ion effect”**

(B) No common ion: “inert electrolyte effect”or “diverse ion effect” slides

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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 slides 35 slides

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**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) slides

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**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 slides 35 slides

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**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. slides 35 slides

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**Activity Coefficients**

The activity coefficient accounts for available ‘acid’ species in solution at high concentrations Activity Activity Coefficient Concentration slides 35 slides

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**Activity Coefficient Effective concentration of decreases**

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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. slides 35 slides

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**Ionic Strength Find the ionic strength of a KCl solution:**

At 0.10 M KCl… At M KCl… slides 35 slides

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**Ionic Strength Find the ionic strength of a CaCl2 solution:**

At 0.10 M CaCl2 … At M CaCl2 … slides 35 slides

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**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) slides 35 slides

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**Calculating Activity Coefficients**

Calculate the activity coefficients of Ca2+ and F- in M NaClO4 (Ca2+= nm, F- = nm) slides 35 slides

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**Activity of the ion in a solution depends on its hydrated radius not the size of the bare ion.**

α → g slides 35 slides

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**Z → g α → g 920116......34 slides http:\\asadipour.kmu.ac.ir**

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**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 slides 35 slides

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**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. slides 35 slides

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**Activity and Equilibrium**

The correct form of the equilibrium expression is… aA + bB cC + dD slides 35 slides

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**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 slides 35 slides

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**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 slides 35 slides

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**Solubility and Activity**

With activity coefficient considerations: slides 35 slides

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**Calculating Activity Coefficients**

Calculate the activity coefficients of Ca2+ and F- in M NaClO4 (Ca2+= nm, F- = nm) slides 35 slides

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**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 slides 35 slides

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**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% slides

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**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 slides 35 slides

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**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 slides 35 slides

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**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 =1activity ≈ concentration slides 35 slides

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