CHsCH=CHz+HCI RzNCH=CHz + HCI CHz=COCHs + Brz CH3CHO + OHCH3CHO + CN CHFCHZ + Brz
HCCk +OH (CH3CHz)zO+ BF3 NHs + H z 0 CHsOCHzt + H z 0 CH3COCH3 + Ht
These examples were chosen to show that curved arrows always emanate from an e-pair; even though in the case of an n-pair, it may not be written in, the tail of an arrow follows the head of a previous arrow, and while the curved m w s mav be formallv correct. thev are drawn erronmusly lithe; do nor refl4r the chemical propcrtm of the reactants At the beginning of the tutorial the student has the option of reviewing the explanation of the use of curved arrows or of branching to the exercises. At the end of the description of curved arrows, the student can review the material again or continue to the exercises. At the end of each exercise the option to exit the program exists, while at the end of the tutorial one can branch to the beginning of the tutorial or to the start of the exercises. Since the tutorial is protected from wrong key response, it is user friend15 The tutorial entitled CURVARR and written in GWBASIC used as programmer tools from SERAPHIM a machine language routine, BSGRAPH, written by Felino Pascual; a BASIC program, CHR$GEN, authored by Mart i n Rose; and a well-written documentation, CHR$GEN.DOC, by James R. Hutchison. The program, which requires 64K memory, a 640 x 200 graphics adapter, MS DOS 2.0 or greater, and GWBASIC 2.02 or greater, runs on IBM compatible clones including the ATT 6300. The program also executes with an EGA or VGA system. A disc copy of the tutorial and documentation is available through SERAPHIM.
Spreadsheet Titration of Diprotic Acids and Bases G. L. Breneman and 0. J. Parker Department of Chemistry and Biochemistry Eastern Washington University Cheney, WA 99004
Spreadsheets have been shown to be powerful tools for handling a variety of chemical problems. Use of the iteration feature found in many spreadsheet programs is especially useful when coupled with standard equation-solving techniques such a s the Newton-Raphson procedure. Described below is a spreadsheet and chart, set up using Excel, for showing titration curves of any diprotic acid or base. Ifthe chart and worksheet are shown simultaneously on the screen, changes in the curve will be seen immediately as data on the worksheet are changed, making this an especially useful tool for theoretical studies of the curves, student exercises, or classroom demonstrations. The worksheet described here can he set up on other spreadsheet programs such as Lotus 1-23. Consider the dissociation of the species HzA. The two equilibria expressions, the dissociation of water, the charge balance, and the mass balance can he manipulated into the following fourth degree polynomial in terms of [H11(8).
I
S u l f u r ~ u Acid ~ Titration Curve
rnL b.
I
I
I
I
I
i
I
4
Figure 6. Spreadsheet for calculating pH versus volume of titrant for diprotic acid-base species. (In this specificcase. 10 mL of 0.1 M sulfurousacid is being titrated with 0.1 M sodium hydroxide).The plot of these results is also shown. The root that corresponds to the correct solution for a titration can be obtained using the Newton-Raphson iteration (9).An initial value for [H+l is selected and the following equation is iterated until convergence is reached.
where fl[H+l,ld)is the polynomial and f ([Ht1,d is the derivative of this function. Acheck is included in the actual spreadsheet to make sure the solution does not converge on the wrong root (see below). Similar equations can be derived in terms of [OH-] ion for the titration of a base. Figure 6 shows part of the spreadsheet for calculating the pH as a function of titrant added. Cell B2 contains which species is being titrated, a n acid or base. Cell B3 contains the sample volume in milliliters. Cell B4 contains the sample concentration in molarity. Cells B5 and B6 contain the two dissociation constants, K1 and Kz. Cell F4 contains the titrant concentration in molarity Cell F5 contains the titrant aliquot size in milliliters. Cell I3 contains the dissociation constant for water. Cell B8 contains the initial titrant volume (zero). Cell C8 contains the formula =B8+$F$5which adds the aliquot size to the previous cell to get the next titrant volume. This cell is then copied into cells D8 through AF8 to calculate all of the titration point volumes (a total of 31) in the curve. The formula for calculating pH is entered into cell B9: = IF($B$Z="hase",l4+ LOG(B514).-LOG(B$14))
The IF checks to see if a base or an acid is being titrated and then the appropriate formula is used where B$14 will contain either the final [Hi] or [OH-] concentration. The following cells had names defined as indicated and these names are used in the remaining formulas: initial sample volume [ H + I+~ ([NatI + K~)[H+I~ + ( K ~ [ N ~ + I - K ~ C . + ' ~ ~ K ~ K W ) [5B53 ~ I ~ va initial sample concentration 5B$4 ca + (KlK2[Na'I-2KlKzCa-KIKK)[H I - K1K& = 0 5B$5 ka Kl (kl is not a legal name in Excel) The total acid concentration, C,, and the sodium ion con5B56 kb Kz titrant concentration 5F54 cb centration added, ma+], must be corrected for dilution as $153 kw K, the titration proceeds. 46
Journal of Chemical Education
Oxslic
Add
Tltrstlon
Curve
Figure 8. Titration curve for a base, in this case 0.1 M ethylenediamine,with 0.1 M strong acid. Figure 7. Titration curve foroxalic acid showing the indistinct first end point. Cell B10 contains = cb*B$8/(va+B$8). This corrects the [Nail concentration for dilution when NaOH is added to the sample volume. Cell B11 corrects for dilution of the sample on adding t i t r a n t using the formula = ca*va/(va+B$8).Cell B12 contains the fourth degree polynomial in terms of [Hi] or [OH-] depending on the sample type. B$14-ka*kb*kw Cell B13 contains the first derivative of the knction. =4*B$14"3+3*(B$lO+ka)*B$14"2+2*(ka*B$lO-ka*B$ll +ka*kb-kw)*B$l4+(ka*kb*B$10-2*ka*kb*B$ll-ka*kw)
Cell B14 contains the Newton-Raphson iteration formula: =IF(B$14+0,ca,B$14B$12/B$13) The IF checks to see if the iteration is giving a negative solution that is the incorrect one for this system. If so, the value is reset to a positive value (equal to the concentration of the sample that is the highest value it could have assuming all of the sample dissociated). Iteration from this point will then give the correct solution. The cells B9 through B 14 are then copied into cells C9 throughAF14 to finish the sheet. Options, Calculation, Iteration is selected (100 maximum iterations and 0.001 maximum change) &om the menu bar to start the iteration. It is necessary to select Options, Calculate Now each time after changing variables to ensure that all columns will iterate using the new values. To make a titration curve similar to the chart in Figure 6, select cells A8 through AF9, Files, New, Chart, and OK. Change the column chart first displayed to a line chart or scatter chart. Add labels and select Arrange AU under Win-
dow to view both the worksheet and the chart. You can view simultaneously both the changes in your worksheet and the corresponding changes in your chart. Some of the principles that can be demonstrated are described next. As a reminder be sure to select Options, Calculate Now each time after changing variables a s described below to ensure that all columns will iterate using the new values. Figure 6 shows the titration curve for sulfurous acid. What if the two K values are not so widely different? Figure 7 shows the curve for oxalic acid obtained by just changing the two Kvalues (Kl= 1.7 x lo-' and Kz = 6.4 x lod). This shows that the first end point is not nearly as distinct when the twoK's are closer together. The effect of changing concentration or volume on the position of the end points can be shown by changing, for example, the concentration of the acid to 0.05 M. For strong acid dissociations just enter the K value as some large number such as 1x lo5. So for example use Kl = 1x lo5 and Kz = 1.2 x 1@for sulfuric acid. To titrate a base with a strong acid, such as HC1, just change cell B2 to "base" and enter the two base dissociation constants. Figure 8 shows t h e titration of ethylenediamine (Kbl = 8.5 x and &2 = 7.0 x lo4). Then try another base such as the carbonate ion (Kbl= 2.1 x 10-4 and Kb2= 2.2 x lo4). Literature Cited 1. Ths Irkrcl Art of Schco; American Assmiaticm for the Advancement of &once: Washingtrm,DC, 1990;pxiv 2. Thmbore, C.N.J. C h m . E d u e 1W4,51,117-118. 3. (a)Walfera, J. P. l(ale-PlayLlgLabratotiea" Presentationgiven at the the Biennial Conference onChemical Education, 1988. (blvoress,L., Ed.Anol$kl Chemisfn
1991.63.347A353A.
4. Whisnant, D. M. J C h m Edue. 1384,61,621429. 5 . Abraham, R J.AnolysisofHigh ReaolutionNMR Spoetm:Elaevier: New York,1911; "%s"+u..-r
&
6. Clark, M.; Threeher, J. S. J Chom. Educ. 1980.67.7.35-236. 7. Ege, S. OrgonicChemisrry, 2nd ed.; D.C.Heath and Co: Lexington, MA, 1989;p 131 Solomons, TWO.Organic Chembtry, 4th ad., Wiley & Sons: New Yo& NY,1988: "" -m-r -d.. 8. Breneman.0. L. J. CksmEduc 1674.51.812813. 9. Dam, W S.;Maracken, D. D. N u m r r h l Methods with F0rtrn" lv Cam Sfdie, rr
Wiley: New York,1972:pp 2S27.
1992 EOUCOM Software Awards Program Entries are being solicited for the 1992 EDUCOM Higher Education SoftwareAwards Competition. The 1992 Competition will consider entries from the natural sciences, the social sciences, and accounting. The deadline for submission is February 24, 1992. To receive an entry form, write to: Higher Education SoftwareAwrads Program, Attn: Gail Miller, Computer Science Center, Building 224, the University of Maryland, College Park, MD 20742-2411; e-mail: awards~cristal.umd.edu.
Volume 69 Number 1 January 1992
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