Analytical Chem istry - DePauw University

256 Analytical Chemistry 2.0In calculating the ionic strengths of thesesolutions we are ignoring the presenceof H 3 O + and OH – , and, in the case ofNa 2 SO 4 , the presence of HSO 4– fromthe base dissociation reaction of SO 42– .In the case of 0.10 M NaCl, the concentrationsof H 3 O + and OH – are 1.0 × 10 –7 ,which is significantly smaller than theconcentrations of Na + and Cl – .Because SO2– 4 is a very weak base(K b = 1.0 × 10 –12 ), the solution is onlyslightly basic (pH = 7.5), and the concentrationsof H 3 O + , OH – , and HSO– 4 arenegligible.Although we can ignore the presence ofH 3 O + , OH – , and HSO 4– when calculatingthe ionic strength of these two solutions,be aware that an equilibrium reactionmay well generate ions that affect thesolution’s ionic strength.Example 6.13Calculate the ionic strength for a solution of 0.10 M NaCl. Repeat thecalculation for a solution of 0.10 M Na 2 SO 4 .So l u t i o nThe ionic strength for 0.10 M NaCl is1 + 2 −2µ= [ Na ] ×+ ( 1) + [ Cl ] × ( −1)21= ( × +2 010 . ) ( 1 ) + ( 010 . ) × ( −1)= 010 . M{ }2 2{ }For 0.10 M Na 2 SO 4 the ionic strength is1 + 2−µ= [ Na ] ×+ ( 1) + [ SO ] × ( −2)421= ( × +2 010 2 2. ) ( 1) + ( 0. 20) × ( −2)= 030 . M2 2{ }{ }Note that the unit for ionic strength is molarity, but that a salt’s ionicstrength need not match its molar concentration. For a 1:1 salt, such asNaCl, ionic strength and molar concentration are identical. The ionicstrength of a 2:1 electrolyte, such as Na 2 SO 4 , is three times larger than theelectrolyte’s molar concentration.Activity a n d Activity Co e f f i c i e n t sFigure 6.15 shows that adding KNO 3 to a mixture of Fe 3+ and SCN – decreasesthe formation constant for Fe(SCN) 2+ . This creates a contradiction.Earlier in this chapter we showed that there is a relationship between a reaction’sstandard-state free energy, DG o , and its equilibrium constant, K.∆G o =−RT ln KBecause a reaction has only one standard-state, its equilibrium constantmust be independent of solution conditions. Although ionic strength affectsthe apparent formation constant for Fe(SCN) 2+ , reaction 6.61 musthave an underlying thermodynamic formation constant that is independentof ionic strength.The apparent formation constant for Fe(SCN) 2+ , as shown in equation6.62, is a function of concentrations. In place of concentrations, we definethe true thermodynamic equilibrium constant using activities. The activityof species A, a A , is the product of its concentration, [A], and a solutiondependentactivity coefficient, γ A .