shows up rlearlv in eight o i his ten examples. The moit mpurrant contribution to the rntn,py change in a readion - - - ~ ~(for . ~ eround state molecules with no unpaired electrons) is the change in translational entropy which accompanies the change An in the number of molecules. Next in importance is the entropy change accompanying changes in the total number of degrees of freedom of rotational motion, and finally that associated with vibrational degrees of freedom. Effects due to symmetry are usually included in the rotational part. For mado or's reactions (3,5,9) in which An = 0. there is ameement within 1%between AGOacmtand AGo,~,. Here one expects near zero entropy change. Fdr reactions (2, 4, 6, 8, lo), in which An = -1, AG",,I, is less negative than AGO by 10,7,42,3, and 9 percent, respectively, or in absolute values, by amounts of the order of TAS" expected for An = -1. In all the above examples AGo,,~, is less negative than AG".,,,t, and in all of them, -TASo is expected to he near zero or positive. Thus the selected hond free energies behave rather like bond enthalpies, and the difference between AGo,,~, and AGo.,,pt is qualitatively just the TASo term. These reactions are all of a kind in which AGO is much more strongly dependent on AHo than on TASo, so that the direction of spontaneous reaction is determined by the AH' tern). 'I'he final two examples (7 and 11) provide a n interesting contrast. In these react ioni An = +2 and -2, respectivelv. T h r omduct molecules are ouite different in chemical and struch a 1 character than theieadant molecules, and large changes in the total number of vibrational modes occur. The AG0,.,, values differ by only 2 and 3 percent from AG0,,,t, and the differences are in omosite directions than one would expect .from the reasoning above applied to the other 8 examples. Thus I believe the "serious discrepancies" mentioned by Amador are due to the inability of tabulated "hond free energies" to cope adequately with the TASDterm, in various kinds of reactions. I doubt that second and higher order approximations to hond free energies would reduce the discrepmcies, as he pruposps. Instend it would be I~etrert o e ~ t i mate ACo IIVcalculating W"frum tahlesof hond enthalpies and estimnting the TASo term from simple entropy considerations. University of Iowa E. David C a t e r Iowa City, IA 52242 ~
.,,,
To the Editor: In response to Cater's welcome critique on bond freeenergies, may I fust of all be allowed to specify, although belatedly, that the free energy terms were calculated using the same straight-forward methods used in calculating hond enthalpies. Values of 673 kJ/mole and 203 kJ/mole were used for AGp (C;g) and AGP (H;g), respectively. To derive the free energy terms for the C-H and C-C bonds one can select any two of the normal alkanes and their accepted AGfo values. For example: (at 25°C) AGP (CzHs;g) = ZAG? (C;g) + 6AGP (H,g) + AGP (C-C bond) + 6ACf (C-H bond) AGro (CaH8;g)= 3 AGr" (C;g)+ XAGP (H;g) + 2AGt0 (C-C bond) +BAG? (C-H bond) Using AGfO(CzH6;g) = -32.9 kJ/mole and AGro (C3Hs;g) = -23.5 kJ/mole, the above two simultaneous equations can be resolved to obtain the C-H and C-C free energies. In this case the calculated values are: AGP (C-H hond) = -382 kJ/mole and AGro (C-C bond) = -306 kJ/mole. If one uses instead the next two hnmologs (n-butane and n-pentane) the 326 1 Journal of Chemical Education
values are: -381 and -310 kJ/mole for the C-H and C-C bonds, respectively. As stated in my article, one also encounters this situation when calculating hund enthalpy terms and a "best fit" value has to he decided on in each case. That is, unless one wishes to make minor adjustments by calculating the effects of secondary and tertiary carbon atoms, nearest neighbors, etc. But to get to the main point, I agree with Cater that bond free enerev -" calculations fail to exwlicitlv "handle the TASo terms" in AGO = VI" - TA.,'". since ail the calculations are dune. o b inilio. with AGO'S. it wuuld seem that thr f:nlrous .terms are implicitly included. But Cater is correct in questioning how hond free enernv terms could account for the entropy contribution to when there is a change in the number of moles. In cases where An > 121 it appears that the changes in the number of rotational and vibrational modes fortuitously offset the effects of a change in the number of moles. For example: ~ F ~ O + ~ N H S - ~ N ~ + ~ H ~ O + (1) ~ H F AG".,,,t = -2246 kJ and AGo,,r = -2236 kJ AGr" ( C ~ H I G ; = ~ 8) kJ1mole ~.~~~ (2) AGP (C7H16;g)ca~. = 3 kJ/male This is within the limit allowed bv the uncertaintv in the free energy of formation of gaseous carbon. Although the "hond free energy'' method may seem to be conceptu& incorrect, it should be pointed out that estimating AGD by first calculating AHo from bond enthalpy tables and then making the appropriate TASo corrections from "simple entropy considerations" also has its drawbacks. First of all. the oercent error usine bond e n t h a l ~ tables v is of the same eider of magnitude as theerror in usinithe hond free energy table. If, on top of that, one must make some further estimates to include the TASo term, then I doubt if the final result will he a substantial imurovement. In conclusion I would like to mention that a table of "bond entrooies" can likewise be derived from the same set of compounds using, of course, the standard entropy data in place of AH? or AGr". Such a table can be used to calculate the standard entropy of other compounds or ASo of chemical reactions in the gas phase. But more importantly, one can derive anew the bond free energy table using the relationship: AGro (A-B bond) = AHt" (A-B band) - T A P (A-B bond) (3) The numerical values thus derived are the same as when calculated directly from AGP data. This certainly lends more credence to the validity of bond free energies. Colegio Universitario d e Cayey A. Amador Cayey, P R 00633 To the Editor: In the May 1979 issue of the JOURNAL OF CHEMICAL EDUCATION I read the article "Interference with the Molybdate Test for Phosphate in Qualitative Analysis" (p. 342). The author's explanations are very interesting. But there is n'method which is nracticed a t the Universitv of Karlsruhe, ----- W.-Germany whici avoids the difficulties of'the molyhdate test. You prepare the hot and strong HCI-acidified solution rH,S has to be ahsenr!~.then add zirconvl chloride (ZrOC12). and there will be a white precipitate of &onium phosphate. If you want to avoid interference by iodide in practicing the molybdate test, then oxidize the iodide by heating the solution with conc. HN03, cool to room temperature, and add ammonium molyhdate solution. Ilridelbergrr Str. 20 731 t Leopoldshafen \\'esl tirrmnny
M. Brender
