The solution containing no added KNO3 for Figure 7-1 contains 5.0 mM Fe(NO3)3, 5.0 M NaSCN, and 15 mM HNO3. We will use Davies activity coefficients to find the concentrations of all species in the following reactions:


This problem is harder than you might think, so we will guide you through the steps.
(a) Write the four equilibrium expressions (including Kw). Express the effective equilibrium constants in terms of equilibrium constants and activity coefficients. For example, . Write expressions for [Fe(SCN)2+], [Fe(SCN)+2], [FeOH2+], and [OH-] in terms of [Fe3+], [SCN-], and [H+].
(b) Write the charge balance.
(c) Write mass balances for iron, thiocyanate, Na+, and NO-3.
(d) Substitute expressions from part (a) into the mass balance for thiocyanate to find an expression for [Fe3+] in terms of [SCN-].
(e) Substitute expressions from part (a) into the mass balance for iron to find an expression for [H+] in terms of [Fe3+] and [SCN-].
(f) In a spreadsheet, guess a value for [SCN-]. From this value, compute [Fe3+] from part (d). From [SCN-] and [Fe3+], compute [H+] from part (e).
(h) Compute the net charge. We want to vary [SCN-] to reduce the net charge to 0. When the net charge is 0, you have the correct concentrations. Solver did not work well for these equations. You have several recourses. One is to use Goal Seek, which is similar to Solver but only handles one unknown. Start with μ = 0 and guess [SCN-]= 1e-6. In Excel 2007, click on the Microsoft Office button at the upper left of the spreadsheet. Click on Excel Options and select Formulas. In Calculation Options, set Maximum Change to 1e-16 and click OK. On the Data ribbon, click on What-If Analysis and then Goal Seek. In the Goal Seek dialog box, set Maximum Change to 1e-16. Set cell {net charge} To value 0 By changing cell . Click OK and Goal Seek finds a solution. Calculate the new ionic strength and activity coefficients from the Davies equation. Calculate effective equilibrium constants. Repeat the process until is constant to three significant digits. If Goal Seek fails to work at some stage, vary [SCN-] by hand to reduce the net charge to near 0. When you are close to a correct answer, Goal Seek can take you the rest of the way. When you have a solution, verify that mass balances are satisfied and compute PH = - log([H+]).γH+)
In earlier versions of Excel, go to the Tools menu, select Options and Calculation. Set Maximum Change to 1e 16. Then select Goal Seek from the Tools menu and continue as described above.
(i) Find the quotient [Fe(SCN)2+]/({[Fe3+] + [FeOH2+]}[SCN-]). This is the point for [KNO3] = 0 in Figure 7-1. Compare your answer with Figure 7-1. The ordinate of Figure 7-1 is labeled [Fe(SCN)2+]/([Fe3+][SCN-]), but [Fe3+] really refers to the total concentration of iron not bound to thiocyanate.
(j) Find the quotient in part (i) when the solution also contains 0.20 M KNO3. Compare your answer with Figure 7-1.