The authors are pleased to provide copies of the computer stack. Send a check for S5.00 made out to the University of Nebraska to Biotechnolow. Science Center. 118-HenalikUNL, Lincoln, NE 68588.y;~may send SASE's and unformatted 3.5-in. flonoies. (These comouter materials are copv.. righted but intenhd tobe supplied at no cost.) Thanks to Wavne Moore of Southeast Community Col. lege, Beatrice, Nebraska, and to Grand Rapids ~ u n i i Colr lege for access to their glossary of terms.
Simulation of the Infrared Spectrum of HCI Qlan Pu
University of Suzhou 215006 P.R. China SUZ~OU. Figure 2. Screen from which informallonregardingthe Western Blot procedure is acce5sBd.
up specificbut brief information about the technique. Clickine on an unfamiliar term in this description will bring the user to a glossary definition of the term if one has been included. (Clicking on terms within the glossary has a similar result.) Clicking on the letter label of a technique from within that information bringsone directly t o a description of the specific information. (That is, clicking on an (A44)anywhere in the text of the tutor will bring the user directly to information about the Western Blot.) The stack can be linked directly to an interactive videodisc olaver. The confieuration of small buttons in the umer right h k d corner of Kgure 2 constitute a videodisc conGoller. These give the user complete control of the videodisc. Simply clicking on the title will bring the videodisc to the first frame of the experiment beginning with that title. Whenever five-digit numbers appear in the text of stored material, clicking on the line containing the number will bring that frame intoview. Cues tell the user when to flip the videodisc, and when to turn their attention from the computer screen to the videoscreen. So as to make videodisc materials more readily available (sav. , ".to show the soecifics of restriction analvsis to students as part of undergraduate pre-lab instructibn), a tool has been devised for creating VHS tapes. The user can click on the title of an experiment from alist, choose a time from 5 to 20 to view the "stopped" or single frames, connect a VHS recorder to the videotape player, and record the computer controlled output. Thus portions of the rich visual database can be used with low cost VHS playback equipment in the laboratory.
Figure 3. Vibralonai-relational Infrared spectrum of gaseous hydrogen chloride.
Journal of Chemical Education
The IR spectrum analysis of HC1 is a very important experiment in the elementary physical chemistry course ( I , 2).The experiment allows students to determine the equilibrium bond distance and force constant of HC1 from its infrared Data analvsis also oermits the evaluation of - soectrum. ~ ~ the &h&monicity constant, the vibration-rotation interaction constant, and the centrifugal distortion constant, etc. To do this experiment, a higb-resolution infrared spectrophotometer with scale expansion capability is needed. However, such an instrument is not available in many colleges, so students cannot acquire their own IR spectrum of HCl. Often college teachers, owing to the lack of this instrument, are unahle to provide their students with extensive practice. The puipose of this project was to develop computer program that helps students master the method and tech&iq;e of infrared measurements on hydrogen chloride, even if they have no spectrophotometer.It also presents the results more accuritelv. The program is written in Applesoft BASIC and can be adapted to other computers without difficulty. It consists of three parts. Part one is an introduction to the traditional double-beam infrared spectrometer and to the preparation of gaseous HCl. This teaches students the essential features of a typical instrument and the procedure for preparing HC1 gas, as well as giving students an atmosphere in which they seem to be doing the experiment with a real IR spectrometer in the laboratory. When the program disk is booted, students are shown two pictures. One is of an apparatus for preparing HC1 gas. The name of each part of this apparatus is shown on the screen. Then waits for the user to tvne - - ~ the ~ -oroeram ~ ". T to turn on the vacuum pump. The pressure in the gas cell is decreased accomnanied bv motor sounds. The oressure of the svstem is change of mercury ievels in the manometer indicated by ~
Vlbratlonal-Rotational Spectrum of HCI
Figure 4. Potenlial energy internuclear distance.
(0of me diatomic molecule plolted against the
and by digits shown at bottom of the screen. When the pressure reaches 3 mm HE, 0 is typed to turn off the pump motor. Then 0 is typed again to open valve 1and valve 2. As sulfuric acid reacts with NaC1, the pressure of HC1 in the gas cell will increase. According to experience, the most appropriate presswe of HCI in the cell should be between 300 mmHe and 600 mmHc. So when the oressure exceeds 300 m&~g,z+nalarm is sothded, which t e h students to type C to close the valves. If the pressure surpasses 600 mmHg, the above procedure must be restarted. The next picture shows the layout of a typical douhle-beam spectrophotometer. The parts are named one by one. Typing T turns on the instrument and the light source sends light to the detector along the optical pathyIt will flash until the user types S to scanPart two of the program is used to produce a spectrum of HCI. To do this, we must prepare a data file in advance, i.e., digitize a real spectrum of HCI (3). This is done by the instructor. After the 5 key is pressed according to the reminder, the screen is cleared, and the spectrum is drawn in 3. It has I cm-' resolution, which is suffitwo napes (Fig. . cient to allow the required calculation. In order to find the eauilihrium distance (Fie. 4) and force constant, we must have a series of absorption lines breaking naturallv into two stem: P branch, occurrina at higher energies, and R branch, oEcurring at lower energies. 1; the past, we used calipers or a millimeter scale to measure the wavenumbers of the absorption lines. This is not only very tedious, but also inaccurate. In our program, we designed a movable cursor that can he moved anywhere on the screen.
Experimental Data: Vr(0) = 2905 Vp(1) = 2864 Vp(2) = 2842 Vr(1) = 2925 Vp(3) = 2821 Vr(2) = 2944 Vp(4) = 2799 Vr(3) = 2962 Vp(5) = 2775 Vr(4) = 2979 Vp(6) = 2751 Vr(5) = 2995 Vp(7) = 2727 Vr(6) = 3013 Vr(7) = 3029 Vp(6) = 2703 Vr(8) = 3044 Vp(9) = 2677 Vp(l0) = 2651 Vr(9) = 3058 Vp(l1) = 2625 Vr(l0) = 3072 Vp(12) = 2599 Vr(l1) = 3085 Vp(13) = 2572 Vr(12) = 3096 Bi = 10.11179321/cm sigrnabi = .02503986181/cm D = -5.00200567E-04 rigmaD = 1.58370214E-04 Caeff. of Correlation: r = -.706676538 B 0 = 10.4098781/cm sigmab = .01805688091/cm D = -4.86934836E-041/cm sigma0 = 1.14204787E-04 Cmfi. of Correlation: r = -.803196277 V1 = 2884.765051/cm Bi-BO = -.299689477 Coeff. of Correlation: r = -.803196277 Equilibrium internuclear Distance: Re = 1.27582595E-08 Xe = ,0169912548 Ve = 2986.24516 XeVe = 50.7400522 Force Constant: K = 515614.632dyne/cm Dissociation Energy: De = 8.73399022E-l2eng/mol~c~Iar Constant of Morse Potential Energy: beta = 171807163
When the W kev durine the movement. the - is oressed . wavenumber at the cursor position is printed just below the cursor. Thus, it is not difficult for students to aet all the required data by moving the cursor to the absorpgon peaks. Part three is calculation. A sufficiently complete account of all effects that need to be considered in this simulation is given by Crockford (4). When the program begins, students are asked to input their names, date, and the wavenumbers of the P and R branches. Then the computer will output the desired properties. Statistical information such as standard deviations and correlation coefficients are also produced by the proVolume 67 Number 12 December 1990
Derivation of a General Formula
gram. Table 1presents a typical set of student experimental results. The program is available from Project SERAPHIM.
Consider an aqueous solution of L acids (H,A, HmB,. . .). The apparent dissociation constants are:
A Short Program for the Automatic Calculation of pH in Solutions Having Many Acids or Bases
and the total concentration of each acid is
Juan Mlguel Campanarlo and Reyes Ballesteros Universldad de Aicala 28871 Alcala de Henares Madrid. Spain Much time in analvtical and eeneral chemistry courses is devoted to introduring students to methods to calculate the oH of solutions. Althoueh the whole theoretical framework is frequently presented; calculations very rarely deal with solutions in which more than one monoprotic acid is involved. When several hydrogen ions are dissociated from the acid, different approximations are usually carried out in order to facilitate calculations. When there are several acids in solution, a set of formulas is presented to students comprising different possible cases (e.g., strong acidlweak acid, weak acidlweak acid). This does nothing but increase arhitrariness and decrease the logical meaning of the subject to be learned. As a consequence, many students, and even graduates, have difficulties in selecting the formula that will he most convenient in a special case. Thus, it is not rare that students use rote learning strategies instead of meaningful ones. A new approach using computational methods is presented in this paper. In the same way that modern calculators have removed logarithm tables (essential in the past for pH calculations) from classrooms, it is useful to introduce computers into laboratory and classroom as a calculation tool. Students' understanding of general principles and scientific theories is preferable t o devoting their efforts to carrying out overwhelming calculations that contrihute little to their scientific training, which can even increase students' tendency toward using formulas without a full understanding of general principles. For example, i t is not surprising that a student could obtain pH = 9 from a 10-9 M HC1 solution. This student has followed the rule: "When dealing with a strong acid, the hydrogen ion concentration is the same as acid concentration." H e or she has forgotten, or never understood, that when an acid concentration is very low, the concentration of the hydrogen ion from water is greater than that from the acid itself, however strong it is. All these problems can he overcome by using computational methods. In this paper we describe a short GW-BASIC program for pH calculation. Mass adion law and the electroneutrality condition are the basis of classical methods for the derivation of equations that may be used for pH calculations. However, the problem has never been treated as a whole. and. as we have already pointed out, different approxima;ionshave been used. The short GW-BASIC proeram nresented here tries to facilitate thestudents pH calcurations in problems dealing with an arbitrary number of acids without the common specifications that we have already seen. This new approach takesaccount ofall the dissociations that contribute to hydrogen ion concentration. Furthermore, the strong acids are treated in the same way as the weak ones by assuming an arbitrarily high constant without additional simplifications. The program can also quickly compute the concentration of any chemical species in solution.
Hydrogen ion concentration is solution is [Ht] = [OH-].,
+ [H,_,A-] + 2[H,_,A2-1 + 3[H,_,A3-]
+ . . . + n[A"-] + [H,_,B-] + 2[H,_,B2-] + 3[H,_,B3q + . . .+ m[Bm-1 + (other acids)
The first term of eq 5 is the hydrogen ion concentration from the dissociation of water. The remaining terms represent the contribution of successive dissociations of each of the acids in the solution. The hydroxyl ion concentration from Hz0 can be obtained from the K , constant:
A similar equation for a solution containing a given numYm-, . .) can he written in the following ber of bases (Zn-, form:
+ [HZ'"-"-] + ~[H,z'"-~'-]+ 3[H3Z'"-3'-] + . ..+ n[H,Z] + [HY'"-"-] + 2[HZY'm-2)-]+ 3[H3Y'm-3)-]
[OH-] = [OH-],,
+ . ..+ m[H,Y] + (other bases)
In eq 5, the H,-,A- ion concentration can be calculated from eq 3 and from the group in eq 1.
Reducing eq 7 to a common denominator we obtain
Journal of Chemical Education
If we r e p e a t t h i s c a l c u l a t i o n f o r H,-zAZ-, . .. , Bm-, . . . , we can H,_3A3-, . . .An-, H,-,B-, Hm_~B2-, see that the denominator for each species always has the same mathematical expression as in eq 8. The numerator for the H.-,A,- ion is formed by the j 1addend of the denomi-