Chapter 9Electrolyte Effects: Activity or Concentration?Class NotesActivity Coefficients:Limit Aion (as gamma gets closer to 1) = [ion]Ionic Strength = I or μDeby – Huckel LawThermodynamic Equilibrium Constant ExpressionKw′ = (AH3O) (AOH) = γ[H3O+] γ[OH-]K′eq = concentration equilibrium constant expressionKeq = thermodynamic equilibrium constant expressionHenderson Hasselbach EquationMean Activity CoefficientText NotesChapter 9Electrolyte Effects: Activity or Concentration?Class NotesActivity Coefficients:Concentration = Molarity = mol/LConcentrations can be calculated from formulaM1V1 = M2V2 Example:H2O + HCl  H3O+ + Cl-100% dissociation because HCl is a strong acid If HCl is 0.100 M then H3O+ and Cl- will be 0.100 MolarpH = [H3O+] = -log 0.100 = 1.0  very acidic[H3O+] = 0.100 = apparent concentrationActivity = A[H3O+] = Effective Concentration  real or actual concentrationA = γ[H3O+] x [H3O+]0 < γ(ion) ≤ 1 called ACTIVITY COEFFICIENTLimit Aion (as gamma gets closer to 1) = [ion]As a given ionic solution becomes more dilute, the ionic concentration drops as its respective γ approaches 1.Example:HCl0.1 M = γ10.1 M = γ2γ1 < γ2 < γ3 < γ40.001 M = γ3 0.0  1.0 0.0001 M = γ4Ionic Strength = I or μμ = ½ Σ c1z12 c = molar concentrationsz = ionic chargesDeby – Huckel Law1) –log γ = 0.5 zion2 √μ2) -log γ = 0.5 z 2 √μ 1 + √μ3) -log γ = (0.51) (z2) √μ alpha = ionic diameter1 + 0.33 (α) √μ 4) A = γ [ion]5) μ = ½ [c1z12 + c2z22 + c3z32 + …]Example:H20 + HCl  H3O+ + Cl-HCl = 0.05 M, so H3O+ and Cl- are both 0.05 MCa(NO3)2  Ca2+ + 2NO3-Ca(NO3)2 = 0.06 M, so Ca2+ is 0.06 M and 2NO3- is 0.12 MpH = -log[H3O+] = -log[0.05] = 1.3μ = ½ {[H3O+] (1)2 + [Cl-] (-1)2 + [Ca2+] (2)2 + [NO3-] (-1)2}μ = {(0.5) (1) + (0.5) (1) + (0.06) (4) + (0.12) (1)} = 0.230.23 = activity coefficient -log γ = (0.51) (z2) √μ = 1 + 0.33 (α) √μ (0.51) (1)2 (√0.23) = 0.244587 1 + (0.33) (0.9) (√0.23) 1.1424γ = 0.3749 ≈ 0.4A[H3O+] = [H30+] (γH30+) = (0.5) (0.4) = 0.02 MpAH = -log A[H3O+] = -log 0.02 = 1.69 % relative error = 1.69 – 1.30 X 1001.69% rel error = 23%Thermodynamic Equilibrium Constant ExpressionH2O + H2O ↔ H3O+ + OH-Kw = [H3O+] [OH-] = 1.00x10-14Kw′ = (AH3O) (AOH) = γ[H3O+] γ[OH-]aA +bB ↔ cC + dDK′eq = [AC] c [AD] d [AA]a [AB]b Keq = [γC] c [γD] d [γA]a [γB]bK′eq = concentration equilibrium constant expressionKeq = thermodynamic equilibrium constant expressionHenderson Hasselbach EquationpH = pKa + log [A-/HA]Example:γHg2+ = ? -log γ = (0.51) (2)2 √0.085 = 0.4016μ = 0.085 1 + (0.33) (5) √0.085α = 5 γ = 0.4016[Hg] = 1.0 M 1/log Hg = 2.52A Hg2+ = ? A Hg = (1.0 M) (0.4016) = 0.40A = 0.40PHg = -log 0.40 = 0.3979Mean Activity Coefficientγ+/- = (γAm • γBn)AB ↔ A(AQ)+m + B(aq)-nKsp = [A]m [B]n γAm γBn = [A]m [B]n γ+/-m+nText NotesI. Effects of Electrolytes on Chemical EquilibriaA. The position of most solution’s equilibria depend on the electrolyte concentration of the medium, even if the added electrolyte contains no ion thatis in common with the species involved in the equilibrium.H3AsO4 + 3I- + 2H+ ↔ H3AsO3 + I3- + H2OIf an electrolyte like barium nitrate or potassium sulfate were added to thisreaction the color of the triiodide will become less intense because itsconcentration has decreased as the equilibrium has been shifted to the left by theadded electrolyte.B. As electrolyte concentrations become smaller, concentration-based equilibrium constants approach their thermodynamic values: Ksp, Kw and Ka.C. The magnitude of the electrolyte effect is very dependent on the charges of thespecies in an equilibrium reaction- If only neutral species are involved equilibrium position is basically independent of electrolyte concentration.- With charged species, the magnitude of the electrolyte effect increases with charge.D. The electrolyte effect results from the electrostatic attractive and repulsive forces that exist between the ions of an electrolyte and the ions involved in an equilibrium.II. Determination of Ionic StrengthA. The effect of added electrolyte on equilibria is independent of the chemical nature of the electrolyte but depends on a property of the solution called ionic strength (μ). Ionic Strength = μ = ½ [c1z12 + c2z22 + c3z32 + …]When c = molar species concentration of ions and z = ionic charges.Problem 9-7a) 0.040M on FeSO4μ = ½ [0.04(2)2 + 0.04(2)2] = 0.16b) 0.20M in (NH4)2CrO4μ = ½[2(0.2)(1)2 + 0.2(2)2] = 0.60c) 0.10M in FeCl3 and 0.20M in FeCl2μ = ½ [0.10(3)2 + 0.3(1)2 + 0.2(2)2 + 0.4(1)2 = 1.2d) 0.060M in La(NO3)3 and 0.030M in Fe(NO3)2μ = ½ [0.06(3)2 + 3(0.06)(1)2 + 0.03(2)2 + 0.06(1)2] = 0.45- The ionic strength of a solution of a strong electrolyte consisting solelyof singly charged ions is identical with its total molar salt concentration.- Ionic strength is greater than the molar concentration if the solution contains ions with multiple charges.Problem 9-3Would the ionic strength increase, decrease or go unchanged with the addition of NaOH to a dilute solution of:a) magnesium chloride – MgCl2 + 2NaOH  Mg(OH)2 +2NaCl- A divalent Mg is replaced by and equivalent amount of univalent Na, decreasing ionic strengthb) HClHCl + NaOH  NaCl + water- Equivalent amounts of HCl and NaCl are produced and all are singly charged, ionic strength will go unchangedc) acetic acidNaOH + HOAc  NaOAc + water- NaOH replaces HOAc with equivalents of water, Na and OAc-, increasing ionic strengthIII. Activity CoefficientsA. Activity, A, is a term used to account for the effects of electrolytes on chemical equilibria.- activity or effective concentration, of a species, X, depends on the ionic strength of the medium and is defined as:AX = γX[X]A = the activity of X[X] = molar concentration of Xγ = the activity coefficient of XProblem 9-6Aqueous ammonia, at an ionic strength of 0.1 is an uncharged molecule, so the activity coefficient is unity and has no numerical value.B. General Properties of Activity Coefficients1. dependent on ionic strength, μ2. approach 1.0 as ionic strength approaches 0.03. is a smaller value for species with multiple chargesProblem 9-5The slope of the curve for Ca2+ in Figure 9-3 on page 208