Analytical Chem istry - DePauw University

266 Analytical Chemistry 2.0(a) pH error(b) pH error (c)1 7 -1.00000002 6 -0.99999903 5 -0.99998994 4 -0.99988535 3 -0.99752946 2 -0.84294127 1 13.80588248 0 1470.5882353Figure 6.20 The output of three iterations to find the pH for a solution of 1.0 M HF. The results are for pHvalues between (a) 7 and 0, (b) 2.0 and 1.0, and (c) 1.60 M and 1.50. The columns labeled “error” show anevaluation of the mass balance equation for HF, with positive values indicating that the pH is too low andnegative values indicating that the pH is too high.which varies the pH within these limits. The result, which is shown inFigure 6.20a, indicates that the pH must be less than 2 and greater than 1because it is in this interval that the error changes sign.For our second pass, we explore pH values between 2.0 and 1.0 tofurther narrow down the problem’s solution.> pH = c(2.0, 1.9, 1.8, 1.7, 1.6, 1.5, 1.4, 1.3, 1.2, 1.1, 1.0)> func(pH)The result in Figure 6.20b show that the pH must be less than 1.6 andgreater than 1.5. A third pass between these limits gives the result shown inFigure 6.20c, which is consistent with our earlier result of a pH 1.59.Practice Exercise 6.15Using R, calculate the solubility of AgI in 0.10 M NH 3 without makingany assumptions. See our earlier treatment of this problem for therelevant equilibrium reactions and constantsClick here to review your answer to this exercise.6K1 2.0 -0.842941182 1.9 -0.754338223 1.8 -0.614756004 1.7 -0.394595665 1.6 -0.047002696 1.5 0.502211017 1.4 1.370536008 1.3 2.744069369 1.2 4.9176129510 1.1 8.3582173011 1.0 13.80588235pH error1 1.60 -0.0470026882 1.59 -0.0026880303 1.58 0.0437011674 1.57 0.0922623485 1.56 0.1430975446 1.55 0.1963135867 1.54 0.2520223318 1.53 0.3103409019 1.52 0.37139192810 1.51 0.43530381611 1.50 0.502211012Some Final Thoughts on Equilibrium CalculationsIn this chapter we have developed several tools for evaluating the compositionof a system at equilibrium. These tools differ in how accurately theyallow us to answer questions involving equilibrium chemistry. They alsodiffer in their ease of use. An important part of having several tools availableto you is knowing when to use them. If you need to know whethera reaction if favorable, or to estimate the pH of a solution, then a ladderdiagram will meet your needs. On the other hand, if you require a more