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slides 1 Activity & Activity Coefficients

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EFFECT OF ELECTROLYTES ON CHEMICAL EQUILIBRIA H 3 AsO 4 + 3I - + 2H + H 3 AsO 3 + I H 2 O 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 H 3 AsO 4 + 3I - + 2H + H 3 AsO 3 + I H 2 O KCl H 3 AsO 4 + 3I - + 2H + H 3 AsO 3 + I H 2 O slides 2

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slides 3 Effect of Ions concentration on Solubility of Potassium tartarate ↑ concentration with addition of an “inert” ion ↓ concentration with addition of common ion “neutral” species K2C4H4O6K2C4H4O6

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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 BaSO 4 with BaCl 2 Ba 2+ is the “common ion” slides 4

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Predicted effect of excess barium ion on solubility of BaSO 4. ©Gary Christian, Analytical Chemistry, 6th Ed. (Wiley) slides 5

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(B) No common ion: “inert electrolyte effect”or “diverse ion effect” slides 6

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slides 7 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 The Salt Effect

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©Gary Christian, Analytical Chemistry, 6th Ed. (Wiley) Increases solubility of BaSO 4 Why??? shielding of dissociated ion species Predicted effect of presense of Na 2 SO 4 on solubility of BaSO slides 8

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slides 9 Consider: BaSO 4 Ba 2+ + SO 4 2- BaSO 4 (K sp = 1.1x ) as the sparingly soluble salt and NaNO 3 → Na + + NO 3 - as the “inert” salt. The cation (Ba 2+ ) is surrounded by anions (SO 4 2-, NO 3 - ) net positive charge is reduced attraction between oppositely charged ions (Ba 2+, SO 4 2- ) is decreased. Solubility is increased How? NO 3 - Na + The anion (SO 4 2- ) is surrounded by cations (Ba 2+, Na + ) net negative charge is reduced

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slides 10 Concentration v.s. Activity For many substances the active mass per unit volume is directly proportional to the concentration. a i ≈C i...but the approximation of activity being equal to concentration will not accurately reflect the actual behavior of matter under all conditions. a i =C i :is a reasonably valid approximation for an u< M Only an approximation of the equilibrium condition.

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slides 11 Activity Coefficients The activity coefficient accounts for available ‘acid’ species in solution at high concentrations Activity Concentration Activity Coefficient

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slides 12 Activity Coefficient Effective concentration of decreases

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slides 13 Ionic Strength Ionic strength, , is a measure of the total ionic charges in solutions where c i is the concentration of the iones species and z i is the associated charge.

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slides 14 Ionic Strength Find the ionic strength of a KCl solution: –At 0.10 M KCl… –At M KCl…

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slides 15 Ionic Strength Find the ionic strength of a CaCl 2 solution: –At 0.10 M CaCl 2 … –At M CaCl 2 …

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slides 17 Calculation of Activity Coefficients Requires the Debye-Hückel equation: z is the charge of the ion is the effective hydrated radius of the ion (in nm) is the ionic strength of the solution (Valid at 25°C for 0.1M)

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slides 18 Calculating Activity Coefficients Calculate the activity coefficients of Ca 2+ and F - in M NaClO 4 ( Ca2+ = nm, F- = nm)

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slides 19 Activity of the ion in a solution depends on its hydrated radius not the size of the bare ion. α →

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slides 20 Z → α →

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slides 21 Activity Coefficients approaches 1 in very dilute solution at which approaches 0. The effect of on is greater for larger z and small . Note that if >0.1 M it is necessary to experimentally determine , otherwise use referenceTable as an approximation Z,α→Z,α→

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slides 22 Activity coefficients for differently charged ions with a constant hydrated radius of 500pm. 1.As ionic strength increases, the activity coefficient decreases. 2.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→Z→ → → → → 0 1

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slides 25 Activity and Equilibrium The correct form of the equilibrium expression is… aA + bB cC + dD

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slides 26 Solubility of a salt calculate [Ca 2+ ] in saturated CaF 2 solid. K sp = 3.9× K sp = 3.9× = [Ca][F] 2 3.9× = X·(2X) 2 =4X 3 x = 2.14×10 -4 M CaF 2 (s) Ca F -

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slides 27 Solubility in presence of common ion calculate [Ca 2+ ] in M NaF saturated with CaF 2 solid. Initial conc. (M) Eq conc. (M) x2x Change x2x K sp = 3.9× Without activity coefficient considerations: K sp = 3.9× = [Ca][F] 2 3.9× = x·(0.050) 2 x = 1.6×10 -8 M CaF 2 (s) Ca F - << 2.14×10 -4 M

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slides 28 Solubility and Activity With activity coefficient considerations:

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slides 29 Calculating Activity Coefficients Calculate the activity coefficients of Ca 2+ and F - in M NaClO 4 ( Ca2+ = nm, F- = nm)

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slides 30 Solubility and Activity Assume that 2x << and due to Ca 2+ is negligible. 3.9× = x(0.49)(0.050) 2 (0.81) 2 x = 4.9×10 -8 M With activity coefficient considerations: 3 times x = 1.6×10 -8 M [Ca 2+ ] or solubility of CaF 2 solid in M NaF With activity coefficient considerations:

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Solubility and Activity Solubility of PbI 2 in 0.1M KNO 3 2 (ignore Pb 2+,I - ) ƒ Pb = 0.35 ƒ I = 0.76 K sp = (a Pb ) 1 (a I ) 2 = ([Pb 2+ ] Pb ) 1 ([I - ] I ) 2 K sp = ([Pb 2+ ] [I - ] 2 ) ( Pb I 2 ) = Ḱ sp ( Pb I 2 ) Ḱ sp = K sp / ( Pb I ) Ḱ sp = 7.1 x /((0.35)(0.76) 2 ) = 3.5 x (s)(2s) 2 = Ḱ sp s = (Ḱ sp /4) 1/3 s =2.1 x M s = (K sp /4) 1/3 thens =1.2 x M slides 31 Without activity coefficient considerations: With activity coefficient considerations: Solubility approx.43%

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slides 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× = x(0.83) x(0.76) pH=-log aH + aH + = pH = -log (0.83×1.26×10 -7 ) = 6.98 x = 1.26×10 -7 M with activity x = 1.00×10 -7 M without activity

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slides 34 Calculating Activity Coefficients Calculate the activity coefficients of Ca 2+ in M NaClO 4. ??? TEXT reverse 0.432

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slides 35 At high ionic strengths: Activity coefficients of most ions increase Concentrated salt solutions are not the same as dilute aqueous solutions H + in NaClO 4 solution of varying ionic strengths In concentrated salt solutions is dependent to type of ion and interpretation is difficult. In concentrated salt solutions is dependent to type of ion and interpretation is difficult. In diluted salt solutions is independent to type of ion In diluted salt solutions is independent to type of ion We try not to work with solutions >0.01 M If µ →0 =1 activity ≈ concentration

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