Analytical Chem istry - DePauw University

Chapter 6 Equilibrium Chemistry263A B C D1 pH = 3.00 2.00 1.00(a)2 [H3O+] = = 10^–b1 = 10^–c1 = 10^–d13 [OH-] = = 1e–14/b2 = 1e–14/c2 = 1e–14/d24 [F-] = = b2 – b3 = c2 – c3 = d2 – d35 [HF] = = (b2 * b4)/6.8e–4 = (c2 * c4)/6.8e–4 = (d2 * d4)/6.8e–46 error = b5 + b4 – 1 = c5 + c4 – 1 = d5 + d4 – 1A B C D1 pH = 3.00 2.00 1.002 [H3O+] = 1.00E-03 1.00E-02 1.00E-13 [OH-] = 1.00E–11 1.00E–12 1.00E–134 [F-] = 1.00E–03 1.00E–02 1.00E–015 [HF] = 0.001470588 0.147058824 14.705882356 error -9.98E-01 -8.43E-01 1.38E+01A B C D1 pH = 1.59 1.58 1.572 [H3O+] = 2.57E-02 2.63E-02 2.69E-023 [OH-] = 3.89E-13 3.80E-13 3.72E-134 [F-] = 2.57E-02 2.63E-02 2.69E-025 [HF] = 0.971608012 1.017398487 1.0653476 error -2.69E-03 4.37E-02 9.23E-02(b)(c)Figure 6.18 Spreadsheet demonstrating the use of Excel to solve a set of simultaneous equations. The spreadsheetin (a) shows the initial guess for [H 3 O + ] in the first row, and the formulas that you must enter in rows 2–6. Enterthe formulas in cells B2–B6 and then copy and paste them into the appropriate cells in the remaining columns.As shown in (b), Excel replaces the formulas with their equivalent values. The spreadsheet in (c) shows the resultsafter our final iteration. See the text for further details.6J.2 RR has a simple command—uniroot—for finding the chemically significantroot of a polynomial equation. In addition, it is easy to write a functionto solve a set of simultaneous equations by iterating in on a solution. Let’swork through two examples.Ex a m p l e 1: So l u b i l i t y o f Pb(IO 3 ) 2 in 0.10 M Pb(NO 3 ) 2In our earlier treatment of this problem we arrived at the following cubicequation4x+ 0. 40x= 25 . × 10−3 2 13