Analytical Chem istry - DePauw University

Chapter 6 Equilibrium Chemistry257a A= [ A]γThe true thermodynamic formation constant for Fe(SCN) 2+ , therefore, isAK12+a2+[ Fe(SCN) ]γ2Fe(SCN)Fe(SCN)= =3+ −a a [ Fe ] γ [ SCN ] γ3+ −Fe SCN3+ −FeSCNThe activity coefficient for a species corrects for any deviation betweenits physical concentration and its ideal value. For a gas, a pure solid,a pure liquid, or a non-ionic solute, the activity coefficient is approximatelyone under most reasonable experimental conditions. For reactions involvingonly these species, the difference between activity and concentration isnegligible. The activity coefficient for an ion, however, depends on the solution’sionic strength, the ion’s charge, and the ion’s size. It is possible to calculateactivity coefficients using the extended Debye-Hückel equation+Unless otherwise specified, the equilibriumconstants in the appendices are thermodynamicequilibrium constants.For a gas the proper terms are fugacity andfugacity coefficient, instead of activity andactivity coefficient.log γA. µA= − 051 × z 2×1+ 3.3× α × µA6.63where z A is the ion’s charge, α A is the effective diameter of the hydrated ionin nanometers (Table 6.2), m is the solution’s ionic strength, and 0.51 and3.3 are constants appropriate for an aqueous solution at 25 o C. An ion’s effectivehydrated radius is the radius of the ion plus those water moleculesclosely bound to the ion. The effective radius is greater for smaller, morehighly charged ions than it is for larger, less highly charged ions.Table 6.2 Effective Diameters (a) for Selected IonsIonEffective Diameter (nm)H 3 O + 0.9Li + 0.6Na + , IO – 3 , HSO – 3 , HCO – –3 , H 2 PO 4 0.45OH – , F – , SCN – , HS – , ClO – 3 , ClO – –4 , MnO 4 0.35K + , Cl – , Br – , I – , CN – , NO – –2 , NO 3 0.3Cs + , Tl + , Ag + +, NH 4 0.25Mg 2+ , Be 2+ 0.8Ca 2+ , Cu 2+ , Zn 2+ , Sn 2+ , Mn 2+ , Fe 2+ , Ni 2+ , Co 2+ 0.6Sr 2+ , Ba 2+ , Cd 2+ , Hg 2+ , S 2– 0.5Pb 2+ , CO 2– 2–3 , SO 3 0.45Hg 2+ 2 , SO 2– 4 , S 2 O 2– 3 , CrO 2– 2–4 , HPO 4 0.40Al 3+ , Fe 3+ , Cr 3+ 0.9PO 3– 3–4 , Fe(CN) 6 0.4Zr 4+ , Ce 4+ , Sn 4+ 1.14–Fe(CN) 6 0.5Source: Kielland, J. J. Am. Chem. Soc. 1937, 59, 1675–1678.