Complete Conductance Equation of 1-1 Electrolytes and the Programmable TI 59 Calculator P. Rechberger and W. Linert Technical University of Vienna Getreidemarkt 9 A-1060 Vienna. Austria
Conductivity measurements are highly suited to familiarize students with the law of mass action. the activitv coefficient. and the terms of conductivity theor;. In laboratory practice equivalent conductivity values A(R-' cm2 eq-') of 1-1 electrolytes are obtained as a function of concentration c (mol dm-3) bv experiment. An experimental setup for conductivity measur&nent has hem pubiiihed recently i38,3YJ. After the experiment has heen performed, the student has to evaluate theequivalent conductivity a t infinite dilution Ao and the association constant KA according to the complete conductance equation (40)-(43): If a and f are the degree of dissociation and the mean activity coefficient, respectively, the complete conductance equation is given by
+
A = [An - S ( ~ C ) ' / ~ E ( a e ) l n ( a c )
+ J ~ ( a c -) J 2 ( a c ) 3 / 2 -
K~Aacf~]
with S,E, JI,and J2being functions of the dielectric constant e, the absolute temperature T, the dynamic viscosity q, Ao, and the ion size parameter a. Data analvsis is nerformed according to the Newton-Gauss method (44;,(45):'Stnrting from estimates of K and of .I,,, AIAoXn) . ", ... IS expanded into a Taylor serlei. Neglecting higher terms yields
with A'' being manding that
&.I,
from estimates of KA and of Ao. DeN (A&
- AObCrYLd)Z
be a minimum gives two linear equations in AAo and AKA( N = number of data pairs). AAo and AKAare added to Ao and KA,respectively. Calculation is repeated until KAvalues of consecutive runs are within 0.01%. The program for calculating A. and KAon a Texas Instruments T I 59 calculator consists of two parts: Program I stores the Alc data pairs, c, q, T, the estimate of Ao, the estimate of KAand the ion size parameter a. Up to 12 data pairs can be handled. S,E, J1,and J 2 are computed and stored. Program I1 performs the Newton-Gauss procedure. After entering program I either manually or by magnetic card the student stores the Wc data pairs and the parameters needed for calculation. A reasonable value for the ion-size parameter a has to be chosen, the sum of the crystallographic radii being the lowest limit. Program I1 has to he entered and the iteration procedure is performed. Calculation can be repeated with a different ion-size parameter a, and program I1 includes the facility of choosing the hest-fitting ion-size parameter a. Program I and program I1 contain 476 and 474 steps, respectively. A Texas Instruments T I 59, the Standard Software Module, and Printer PC 100 A is needed. If PC 100 A is not available, output of results can be obtained manually after slight modification of the program. The background of electrolytic conductivity theory, program instructions, flow charts, program listing, and sample execution are available from the authors upon request. A fee of $15 (US.) for postage and handling should be sent to Wolfgang Linert, account number 2.036.184, Raiffeisenbank Seilerg. 8,1010 Vienna, Austria. The authors thank forsupport Prof. Dr. mult. V. Gutmann and the Fonds zur Forderung der wissenschaftlichen Forschung in Osterreich, Projekt 3004. Literature Cited 111 Butler. William M., and Griffm,Henry C.. J.CHEM.E ~ ~ ~ . . 5 6 . 5119791. 49 121 Muore, 3. W., Gerhold, C., Brenoman. G. L.. own. C. S.. Butler, W., Smith, S. %and Lyndrup, M. L., J.CHEM.EDUC.56,776(1979). I31 Ksrger, Barry L.. Snyder, Lloyd R., and Huwath. C.. "An lntrdvefiun toSopsrstion Science: John Wileyand Sons. Nevi York. 1973. (1) Oshorne. A,. Jsmhson.S., and Kane, J.,"An Intnduction to Micrucumputerr~Vul. 11.. Adam Oshorne and Associates, Berkeley, 1977. (51 Gorhold, G., Macero. D. 3.. Lyndrup, M.. and Moore, 3. W..J CHEM.EDUC.. 5 4 701
\.",=,.
,,"q",
(61 Some BASICS havefunetionswhbhallowtheusertawrita IOUTlorresd llNP1 sport directly from the BASIC. The TRS-80 disk BASIC level 11 BASIC have this capability. We feel this is sdesirahlefeature. (71 K , U P ~s., , coscio, M. R., and waod, F. A,, J ~ i ~ rr d i u t i o nControl Assor.. 26.221 (1976). 1s)Tho TRS-80BASlCeUowptheusertajumpf o a machine languagepmgram and return. Thin in a feature that is ueful in the development o f d t w a r e . (91 Grm. Gunner. Internotionol Conprerr on Ana1,~tirolChrmisrry. 77,661 (19521. (LO1 The MP 20 is available for 52W from Burr-Brown, International Airport Industrial Park, Tucan. AZ85734. (11) Didendorfer, A. James, "Principles of Electronic Inatrumentation." 2nd ed.. Chsp. 9. W. B.SaundersCo.. Philadelphia, 1979.p.221. (12) Gray, E T.,and Workman, H. L,"Chunislnand Computers Now h e o n One"(Editor Petar Lykosl ACS Symposium Series, in pr-. (la1 Perone,S. P.,and Eaglestan, J. F.,J. CHEM,EDUC.,48,438 (197ll. I141 Perone, S. P.. and Jones, D. O.."Digitsl Computers in Scientific Instrumentation," McGraw-Hill. New York. 1973. I151 So1t.heg.L. J . 3 . CHEME~uc..56.644 (19791. 1161 MP 10 is availshle fmm Burr-Brawn for $99. (171 Brand. M. J.D.,J.CHBM.ED~C.,53,771 l1976):Soltrberp,L.,Shah,A.A.,Saber,J.
Volume 58
Number 3
March 1981
245
C., and Canly, E. T., "BASIC and Chemistry", H I I Y L ~Mifflin ~ O CIL B ~ s t m 1975. . 0 . 178. 1181 Heiiley, C. N.. and Sawyer, D. T.. "Experintents for lnsfrum
