chelate formation by steric hindrance will not lose as much conformational entropy upon reaction as a flexible one. However, if the molecule is too rigid, the chelate rings may be strained, and the heat of reaction will suffer an endothermic effect. The release of hydrating water molecules from both the metal ion and the chelating agent accounts for a very important portion of the entropy of reaction and the number of donor groups in the chelating agent should be sufficient t o occupy all the coordination sites of the metal ion. While charged donor groups are more highly hydrated than noncharged groups, certain noncharged groups may form stronger bonds with a metal ion of interest resulting in a heat of reaction which overcomes any decrease in the entropy of reaction. Charged oxygen containing groups of the carboxylate type are ideal donor groups for alkaline earth metals. The scarcity of stable alkaline earth-amino complexes suggests that amine donor groups are less suitable. The data in Table I indicate that amino groups produce the most favoraable heats of reaction for transition metal complexes. However, charged groups are necessary if large entropies of reaction are desired. Thus, polyaminocarboxylates are ideal chelating agents for these metals. The magnitudes of the heavy metal heats of reaction in Table I suggest that both acetate and amino groups form strong metal donor-group bonds. However, the charged acetate groups release more water molecules upon reaction and ensure a large entropy of reaction. The effect of donor groups containing such atoms as phosphoivs and sulfur has not been considered. For some metals, these groups may be superior to the amino and carboxylate groups. Application of Data to Thermometric Titrations. The A H values in conjunction with other heat data can also be used to predict the shape of thermometric titration curves. Because the chelometric titrants generally used are protonated species, the heats of protonation of the chelating agents must be known. Work is in progress a t this laboratory to determine the heats of protonation of the ligands studied in this work. Also, a knowledge of the metal-buffer bond
892
ANALYTICAL CHEMISTRY
strengths and the heats of protonation of the buffers is necessary if the titrations are conducted in buffer solutions in order to control the pH. Two components in a mixture can be determined by a thermometric titration if their log K values differ by as much as 2 units provided the difference in the PH values is sufficiently large. Jordan and Alleman (18) have reported a procedure whereby both Ca+2 and Mg+2 can be determined in a mixture using EDTA. In this case, the log K values differ by less than 2 units, but approximately 9 kcal./mole separates the aH values. Presumably other multicomponent mixtures can be analyzed thermometrically.
(18) Jordan, J., Alleman, T. G., Ibid., 29, 9 (1957). (19) McDonald, J. E., King, J. P., Cobble. J. W.. J . Phus. Chem. 64. 1345 (1960). ’ (20) Nancollas, G. H., J . Chem. SOC. 1956, 744. (21) Paoletti, P., Vacca, A,, Ibid., 1964, 5051. (22) Randall, M., Rossini, F. D., J . Am. Chem. SOC.51. 323 11929). (23) Reilley, C. X.,’ Holloway, J. H., J . Am. Chem. SOC. 80, 2917 (1958). (24) Reilley, C. N.,, Schmid, R. W., J . Elisha Mitchell Scz. SOC.73, 279 (1957). (25) Reilley, C. N., Vavoulis, A., ANAL. CHEM.31, 243 (1959). (26) Rossini, F. D., Wagman, D. D., Evans, W. H., Levine, S., Jaffe, I., “Selected Values of Chemical Thermodynamic Properties,” Circular of the National Bureau of Standards 500, United States Printing Office, Washington, 1952. (27) Schmid. R. W.. Reillev. C. N.. ANAL.CHEM.29, 264 (1957):‘ (28) Schmid, R. W., Reilley, C. N., J. Am. Chem. SOC.78, 5513 (1956). (29) Schwarxenbach, G., Heller,. J.,. Helv. Chim. Acta 34, 576 (1951). 130) Schwarxenbach. G.. Senn. H..’ ‘ hderegg, G., Ibd., 40, 1886 (1957). (31) Spike, C. G., Parry, R. W., J . Am. Chem. SOC. 75,2726 (1953). (32) Vasil’ev, V. P., Zolotarev, E. K., Kapustinskii, A. F., Mischenko, K. P., Podnornava. E. A.. Yatsimirskii. K. B..‘ Zh& Fik khim. 34, 1763 (1960). (33) Wright, D. L., Ph,D. Thesis, University of North Caroha, 1964. RECEIVEDfor review August 14, 1964. Accepted March 31, 1965. Presented in part at the Sixth Eastern Analytical Symposium, New York, N. Y., November 11-13, 1964. Research supported in part by the United States Air Force through the Air Force Office of Scientific Research, Air Research and Development Command, Contract No. AF 49(638)-333 and by National Institutes of Health Grant RG-8349. I
LITERATURE CITED
I-
’
Correction Gasometric Determination of Nitrogen in Refractory Metal Nitrides of Groups IVB, VB, and VIB In this article by L. P. Morgenthaler 1964.
(16) Holloway, J. H., Ph.D. Thesis, University of North Carolina, 1959; C.A. 54, 9452b (1960); Dksertalim Abstr. 20, 2588 (1960). (17) Holloway, J. H., Reilley, C. N., AXAL.CHEM.32, 249 (1960).
CHEM.37, and R. P. Menichelli [ANAL. 570 (1965)l on page 571, Table I, the third column of figures (N, %, found) is incorrect. The figures should read from the top as follows: 23.0, 21.7, 21.5, 12.7, 13.1, 5.5., 5.5., 8.5, and 7.2.
