and it functions exactly as intended. However, two other useful applications should be noted. First, it simulates the spectra of campounds containing two or more separate spin systems. For example, the spectrum of ethyl propionate, with two AzX3spin systems, is created by treating the compound as a 50150 mixture of two separate five-spin "molecules". Similarly, the spectrum of t-butyl acetate is obtained by simulating an equimolar four-component mixture, with one component containing the acetate methyl and the other three each having one of the t-butyl methyls. Second, the ability to integrate affords instructors the option of creating mixture spectra for use in problem sets or exams. For examole. ~.the 90 MHz simulated s~eetrumof a mixture of 11.9r~ m~thdnul.33 W r arrlonr, 11.2'; rduene, and 13 3% methyhe chloride, shown m F ~ ~ m 1, r e is nmrl?. ~ndisr~npmshahlr from the spectrum of a sampled huusehold pninr remover.
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Carbon NMR This nronam affords the simulation of nmton-decouoled carbon-13 spectra of mixtures containing as many a s eight components, each with up to 50 carbon atoms. A separate program is first used to create a file that contains the shift data for everv comnonent in the mixture. The main program reads this fileand then prompts the user for the percent com~ositionof the mixture to be simulated. A plot of the spec&um is provided, as in the proton case, with user specification of the delta range, plot size, and linewidth. As before, integration is provided i p o n request. The optional pen plot has one feature not found in the proton simulation: If a plot height of less than three inches is chosen, a "stick plot" of each component will be drawn directly above the mixture spectrum. An example is shown in Figure 5.
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tive to hardware and the number of coupled nuclei. For example, the ABXBcase requires about 22 s to compute, 2 s to plot, and 11 s to integrate if the IBM PC is equipped with a n 8087 math coprocessor. Otherwise, the times increase to 50, 5, and 30 s, respectively. An IBM PS2 Model 60 equipped with the math coprocessor gave times of 5,2, and 4 s for the same calculations. Carbon simulations require virtually no time to calculate the pattern, but considerable time to plot, owing to the rather large spectrum widths encountered in carbon-13 NMR. A six-component mixture with 36 different chemical shifts spanning 100 ppm required 65 s to calculate the Lorentzian line shapes and display the resulting spectrum on an IBM PC with 8087 math chio. Copies ofthese programs are available on either 3 112-in. or 5 114-in. disks for $5.00 (free if formatted disks and prepaid mailer are sent). Please specify disk size desired and indicate EGA and 8087 availability. Checks should be made payable to the Virginia Tech ~ h e k i s t r y Department and should be sent to H. M. Bell, Chemistry Department, Virginia Tech, Blacksburg, VA 24060.
A Tutorial on the Use of Curved Arrows in Organic Chemistry William N. Turek St. Bonaventure University St. Bonaventure, NY 14778
The use of cuwed arrows in organic chemistj is a n excellent wav to illustrate the flow of electrons a s reactants form intermediates or products. Properly used, curved arrows also act as a mide to the mechanism of a reaction. L~nfortunatrly,some students have dittictilty using curved arrowscorrectlv At the June 1988 ACS meetinc in 'll~mnto this fact was biought out as participants critiqued current textbooks. Curved arrows, to varying degrees, appear in most textbooks but only a few devote significant space to describing the fundamentals of curved arrows (7).Since some authors do not include the nonbonding electron pairs on nucleophiles, the mistaken notion that cuwed arrows are used to move atoms and not electrons can be given. In other cases the curved arrows are imprecisely printed leading to student confusion. To complement textbooks in their treatment of curved arrows a computer tutorial has been developed. +he tutogal displays a curved arrow equation for Hz0 and HBr. The direction of the cuwed arrows is discussed in terms ofeleciron donor nucleophilic, sites and electron accentor rel~~troohihc, sites. The factors that drtwminc the nucleophilicity of a site are explained. After the curved arrows are erased, the student can draw them to reinforce how curved arrows are correctly drawn. An example of curved arrows emanating from implied nonbonding electrons is included. I n addition, a n erroneous way of drawing cuwed arrows is ~ v e and n explained. ouro other examples of &wed arrow equations are given and explained: the ionization of tert-butyl chloride, the reaction of the methoxymethyl cation with water, the formation of a n acylium ion from acetyl chloride a n d aluminum chloride, a n d t h e reaction of ethene with hydrogen chloride. The last example illustrates that the chemical properties of the reactants must be known if curved arrows are to be drawn correctly. The second part of the tutorial contains 11equations in which the curved arrows are drawn correctly or incorrectly. The student is asked to indicate hisher choice; then the response is graded followed by a n explanation that is correlated with the response. The equations used are given in the following list:
h.
. i , . i t . i , . i , . I b . . * . n . CHEll SHIFT
Figure 5. Methyl-b-glucoside-3,6-dinitrate. OH on C2 and C4 30% deuterated. Thisis a nortion of the snedrum of methvl-b-ducoside-3.6a; C-2 and C-4 dinitrate'in acetone. he hydroxyl are nartlv deuterated, which causes the corresponding signals near 72.1 and 68.'5 to be "doubled". signal; a t 72.7 a i d 73.7 correspond to C-6 and C-5, respectively. The program is limited in that no allowance is made for different nuclear Overhauser enhancements or different degrees of saturation from carbon to carbon, or from component to component. However, even with thislimitation it still is useful in many situations involving analysis of mixtures by carbon-13 NMR. Both oroerams are written in FORTRAN and are available fo; t h i IBM-PC and compatibles, in four versions, with and without the 8087 math comocessor, and with CGA or EGAgraphics. As long a s a pen plotter is available, the choice of eranhics d i s ~ l a v is s not important. However, ~ give good-quality screen only t h e E G &aphics'w;ll dumps. Run times for proton simulations are very sensi-
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Volume 69 Number 1 January 1992
45
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.
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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
