Analytical Chem istry - DePauw University

Chapter 6 Equilibrium Chemistry261cell B1. We expect x to be small—because Pb(IO 3 ) 2 is not very soluble—so setting our initial guess to 0 seems reasonable. Finally, we access theSolver function by selecting Solver... from the Tools menu, which opensthe Solver Parameters window.To define the problem, place the cursor in the box for Set Target Celland then click on cell B2. Select the Value of: radio button and enter 0 inthe box. Place the cursor in the box for By Changing Cells: and click on cellB1. Together, these actions instruct the Solver function to change the valueof x, which is in cell B1, until the cubic equation in cell B2 equals zero.Before we actually solve the function, we need to consider whetherthere are any limitations for an acceptable result. For example, we knowthat x cannot be smaller than 0 because a negative concentration is notpossible. We also want to ensure that the solution’s precision is acceptable.Click on the button labeled Options... to open the Solver Options window.Checking the option for Assume Non-Negative forces the Solver to maintaina positive value for the contents of cell B1, meeting one of our criteria. Settingthe precision takes a bit more thought. The Solver function uses theprecision to decide when to stop its search, doing so whenexpected value − calculated value × 100 ≤ precision (%)where expected value is the target cell’s desired value (0 in this case), calculatedvalue is the function’s current value (cell B1 in this case), and precisionis the value we enter in the box for Precision. Because our initial guess ofx = 0 gives a calculated result of 2.5×10 –13 , accepting the Solver’s defaultprecision of 1×10 –6 stops the search after one cycle. To be safe, set the precisionto 1×10 –18 . Click OK and then Solve. When the Solver functionfinds a solution, the results appear in your spreadsheet (see Figure 6.17b).Click OK to keep the result, or Cancel to return to the original values.Note that the answer here agrees with our earlier result of 7.91×10 –7 Mfor the solubility of Pb(IO 3 ) 2 .Be sure to evaluate the reasonableness ofSolver’s answer. If necessary, repeat theprocess using a smaller value for the precision.Ex a m p l e 2: pH o f 1.0 M HFIn developing our solution to this problem we began by identifying fourunknowns and writing out the following four equations.+ −[ HO ][ F ]−= = 68 . × 10 4[ HF]K a3K w 3= [ HO+ ][ OH− ] = 100 . × 10 −14C HF= [ HF] + [ F− ]+ − −[ HO ] = [ OH ] + [ F ]3