GEM (20 plus our revisions to procedure): Computes concentration of standardized base and determines gram equivalent mass of unknown acid. Checks if student knows correct gram equivalent mass of standard, oxalie acid. IODINE (15):Iodination of acetone kinetics. Computes concentrations of reagents, rate of reaction,order of reaction, rate constant, and prediction of time of reaction for additional reaction mixture. Cheeks to see if mixtures made by student are such that ratios of rates can he solved for reaction order; checks which ratios can be solved for which order. LIMITING (handout (2)): Demonstrates principle of limiting reagent by recovering product of reaction between NasP04 and BaCI2.Results indicate amounts of reactant in two initial solutions. Checks student's assumption of correct limiting reagent against actualone; checks his or her understanding of correct reagent to add to recover second crop of product. SOLPROD (22):Determines solubility product of PhI2 from speck a l data. Avallablllty 01 Programs All programs are written in interactive ANSI-standard FORTRAN and are run from HP-2645 or HP-2621 terminals (nongraphics, minimum of 80 characters per line) on an HP-3000 Series 111 system. Execution of longest program requires 22K W h i t words. Hard copies of selected sample executions available for 55. Source listinas and some sample executions provided on your 9-track, ASCII, magnetic tape at 1600 or 6400 BPI for 510. Format of returned tape will he 80 character record, unblocked, fixed record size, ASCII. User instructions also provided. Send requests and/or blank tape to J. Charles Templeton a t ahove address; make checks payable to Whitman College Computer Services. Specify desired tape density and system on which programs will he run.
Table 1. EHed ot lncreaslng Cube Size on the Calculated Madelung Constant for the NaCl LaHlce Ions per cube side
~adelunjlConstant
Percent Enor
2
1.45603 1.56654 1.62672 1.65493 1.67361 1.68501 1.69391
16.7 10.4
1.74756
on
3 4
5 6 7 6
...
-
.. .
6.6
5.3 4.2
3.6 3.1
...
Figwe 5. Onedimensional anangemem of f w r NaCl units
Calculation of Madelung Constants In the First Year Chemistry Course Mark Elert and Edward Koubek US. Naval Academy Annapolis. MD 21402 Figure 6. Cublc arrangement of four NaCl units
One of the most important topics in anv. beginning chemistry course is bonding. ~ n f o r t k a t e many l~ students are left bewildered by the quantum mechanics required to explain the formation of eovalent bonds and simply accept their professor's word that the sharing of electron pairs results in bond formation. This need not he the case ?or ionic bonding, as most students can visualize the simole conceots involvine electron transfer followed by ~ o u l o ~ hattrktion ic of theresulting ions. We first have the students consider four NaClunits in a linear array, as shown in Figure 5. The total potential energy associated with this arrangement of ions can be summed as follows:
magnitude of the coefficient in this potential energy expression, so we would say that the Madelung constant for an infinite one-dimensional NaCl crystal is 1.39. Of course, real crystals are not one-dimensional. This must mean that the potential energy can he lowered further by arranging the ions in a three-dimensional rather than a one-dimensional array. T o investigate this we again consider a system of four NaCl molecules, but now in a three-dimensional array as shown in Figure 6. The change in potential energy due to ionic bonding in this arrangement can he calculated as follows:
Dividing by four yields a change in potential energy per NaCl unit of -1.27e2/ro. Such an arrangement is 27% more favorahle than the simple molecular form for which the potential energy is simpiy -e2/ro. Clearly the same calculation applied to an infinite chain of NaCl units would lower the ene& still further. The ootential enerev can actuallv he evaluated quite easily in this case by summing the appropriate infinite series analvticallv" (3). . .. and the result is -1.39e2/m per NaCl unit. The ~ a d e l u nconstant ~ is defined as the
Dividing by four now gives a change in potential energy per NaCl unit of -1.46 e2/ro. At this point most students are willing toaccept the fact that, if one were to ronsidera much larger number of NaCl units in a three-dimensional array, one could arrive at a final value of -1,747558 e2/r... In fact. convergence of the method descrihed here is quite rapid: With a simole comouter oroeram. students can easilv calculate the ~adelungcons
