D. Harvey - Modern Analytical Chemistry (794078), страница 51
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When the solubility product for AgIO3is calculated using the equilibrium concentrations of Ag+ and IO3–Ksp = [Ag+][IO3–]ionic strengthA quantitative method for reporting theionic composition of a solution thattakes into account the greater effect ofmore highly charged ions (µ).its apparent value increases when an inert electrolyte such as KNO3 is added.Why should adding an inert electrolyte affect the equilibrium position of achemical reaction? We can explain the effect of KNO3 on the solubility of AgIO3 byconsidering the reaction on a microscopic scale. The solution in which equilibriumis established contains a variety of cations and anions—K+, Ag+, H3O+, NO3–, IO3–and OH–.
Although the solution is homogeneous, on the average, there are moreanions in regions near Ag+ ions, and more cations in regions near IO3– ions. Thus,Ag+ and IO3– are surrounded by charged ionic atmospheres that partially screen theions from each other. The formation of AgIO3 requires the disruption of the ionicatmospheres surrounding the Ag+ and IO3– ions. Increasing the concentrations ofions in solution, by adding KNO3, increases the size of these ionic atmospheres.Since more energy is now required to disrupt the ionic atmospheres, there is adecrease in the formation of AgIO3, and an apparent increase in the equilibriumconstant.The ionic composition of a solution frequently is expressed by its ionicstrength, µ1µ = ∑ c i zi22 iwhere ci and zi are the concentration and charge of the ith ion.EXAMPLE 6.14Calculate the ionic strength of 0.10 M NaCl.
Repeat the calculation for asolution of 0.10 M Na2SO4.SOLUTIONThe ionic strength for 0.10 M NaCl isµ =11([Na + ](+1)2 + [Cl – ](–1)2 ) = [(0.10)(+1)2 + (0.10)(–1)2 ] = 0.10 M22For 0.10 M Na2SO4, the ionic strength isµ =activityTrue thermodynamic constants use aspecies activity in place of its molarconcentration (a).activity coefficientThe number that when multiplied by aspecies’ concentration gives that species’activity (γ).112–([Na + ](+1)2 + [SO4 ](–2)2 ) = [(0.20)(+1)2 + (0.10)(–2)2 ] = 0.30 M22Note that the unit for ionic strength is molarity, but that the molar ionic strengthneed not match the molar concentration of the electrolyte.
For a 1:1 electrolyte,such as NaCl, ionic strength and molar concentration are identical. The ionicstrength of a 2:1 electrolyte, such as Na2SO4, is three times larger than the electrolyte’s molar concentration.The true thermodynamic equilibrium constant is a function of activityrather than concentration.
The activity of a species, aA, is defined as the product of its molar concentration, [A], and a solution-dependent activity coefficient, γA.aA = [A]γA1400-CH06 9/9/99 7:41 AM Page 173Chapter 6 Equilibrium ChemistryThe true thermodynamic equilibrium constant, Ksp, for the solubility of AgIO3,therefore, isKsp = (aAg+)(aIO3–) = [Ag+][IO3–](γAg+)(γ IO3–)To accurately calculate the solubility of AgIO3, we must know the activity coefficients for Ag+ and IO3–.For gases, pure solids, pure liquids, and nonionic solutes, activity coefficientsare approximately unity under most reasonable experimental conditions.
For reactions involving only these species, differences between activity and concentrationare negligible. Activity coefficients for ionic solutes, however, depend on the ioniccomposition of the solution. It is possible, using the extended Debye–Hückel theory,* to calculate activity coefficients using equation 6.50– log γ A =0.51 × z 2A × µ6.501 + 3.3 × α A × µwhere ZA is the charge of the ion, αA is the effective diameter of the hydrated ion innanometers (Table 6.1), µ is the solution’s ionic strength, and 0.51 and 3.3 are constants appropriate for aqueous solutions at 25 °C.Several features of equation 6.50 deserve mention.
First, as the ionic strengthapproaches zero, the activity coefficient approaches a value of one. Thus, in a solution where the ionic strength is zero, an ion’s activity and concentration are identical. We can take advantage of this fact to determine a reaction’s thermodynamicequilibrium constant. The equilibrium constant based on concentrations is measured for several increasingly smaller ionic strengths and the results extrapolatedTable 6.1Effective Diameters (α) for Selected InorganicCations and AnionsIonH3O+Li+Na+, IO3–, HSO3–, HCO3–, H2PO4–OH–, F–, SCN–, HS–, ClO3–, ClO4–, MnO4–K+, Cl–, Br –, I–, CN–, NO2–, NO3–Cs+, Tl+, Ag+, NH4+Mg2+, Be2+Ca2+, Cu2+, Zn2+, Sn2+, Mn2+, Fe2+, Ni2+, Co2+Sr2+, Ba2+, Cd2+, Hg2+, S2–Pb2+, CO32–, SO32–Hg22+, SO42–, S2O32–, CrO42–, HPO42–Al3+, Fe3+, Cr3+PO43–, Fe(CN)63–Zr4+, Ce4+, Sn4+Fe(CN)64–Effective Diameter(nm)0.90.60.450.350.30.250.80.60.50.450.400.90.41.10.5Source: Values from Kielland, J.
J. Am. Chem. Soc. 1937, 59, 1675.*See any standard textbook on physical chemistry for more information on the Debye–Hückel theory and itsapplication to solution equilibrium1731400-CH06 9/9/99 7:41 AM Page 174174Modern Analytical Chemistryback to zero ionic strength to give the thermodynamic equilibrium constant. Second, activity coefficients are smaller, and thus activity effects are more important,for ions with higher charges and smaller effective diameters. Finally, the extendedDebye–Hückel equation provides reasonable activity coefficients for ionicstrengths of less than 0.1.
Modifications to the extended Debye–Hückel equation,which extend the calculation of activity coefficients to higher ionic strength, havebeen proposed.6EXAMPLE6.15Calculate the solubility of Pb(IO3)2 in a matrix of 0.020 M Mg(NO3)2.SOLUTIONWe begin by calculating the ionic strength of the solution. Since Pb(IO3)2 isonly sparingly soluble, we will assume that its contribution to the ionic strengthcan be ignored; thusµ =1[(0.20 M)(+2)2 + (0.040 M)(–1)2 ] = 0.060 M2Activity coefficients for Pb2+ and I– are calculated using equation 6.50– log γ Pb 2 + =0.51 × (+2)2 × 0.0601 + 3.3 × 0.45 × 0.060= 0.366giving an activity coefficient for Pb2+ of 0.43.
A similar calculation for IO3–gives its activity coefficient as 0.81. The equilibrium constant expression for thesolubility of PbI2 isK sp = [Pb 2 + ][IO3– ]2 γ Pb 2 + γ IO3− = 2.5 × 10 –13Letting[Pb2+] = xand[IO3–] = 2xwe have(x)(2x)2(0.45)(0.81)2 = 2.5 × 10–13Solving for x gives a value of 6.0 × 10–5 or a solubility of 6.0 × 10–5 mol/L. Thiscompares to a value of 4.0 × 10–5 mol/L when activity is ignored.
Failing tocorrect for activity effects underestimates the solubility of PbI2 in this case by33%.Colorplate 3 provides a visualdemonstration of the effect of ionicstrength on the equilibrium reactionFe3+(aq) + SCN–(aq)Fe(SCN)2+(aq)tAs this example shows, failing to correct for the effect of ionic strength can leadto significant differences between calculated and actual concentrations.
Nevertheless, it is not unusual to ignore activities and assume that the equilibrium constantis expressed in terms of concentrations. There is a practical reason for this—in ananalysis one rarely knows the composition, much less the ionic strength of a samplesolution. Equilibrium calculations are often used as a guide when developing an analytical method.
Only by conducting the analysis and evaluating the results can wejudge whether our theory matches reality.1400-CH06 9/9/99 7:41 AM Page 175Chapter 6 Equilibrium Chemistry1756J Two Final Thoughts About Equilibrium ChemistryIn this chapter we have reviewed and extended our understanding of equilibriumchemistry. We also have developed several tools for evaluating the composition of asystem at equilibrium.
These tools differ in how accurately they allow us to answerquestions involving equilibrium chemistry. They also differ in their ease of use. Animportant part of having several tools available to you is knowing when to usethem. If you need to know whether a reaction is favorable, or the approximate pHof a solution, a ladder diagram may be sufficient to meet your needs.
On the otherhand, if you require an accurate estimate of a compound’s solubility, a rigorous calculation using the systematic approach and activity coefficients is necessary.Finally, a consideration of equilibrium chemistry can only help us decide whatreactions are favorable. Knowing that a reaction is favorable does not guarantee thatthe reaction will occur. How fast a reaction approaches its equilibrium positiondoes not depend on the magnitude of the equilibrium constant.
The rate of a chemical reaction is a kinetic, not a thermodynamic, phenomenon. Kinetic effects andtheir application in analytical chemistry are discussed in Chapter 13.6K KEY TERMSacid (p. 140)acid dissociation constant (p. 140)activity (p. 172)activity coefficient (p. 172)amphiprotic (p. 142)base (p. 140)base dissociation constant (p.
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