Nov., 1961
A COMPLETE IONIZATION SCHEME FOR CITRICACID
dences indicates rotational isomerism in triethylphosphate, and it is very likely also present in the phosphite IV.9 Presuming that rotational isomerism exists in both triethyl phosphate and triethyl phosphite, the difference in moments between these two does not afford a good measure of the P = 0 group moment, because the conformations of the isomers, and the distributions between them, may be different in the two compounds. This objection is absent from the comparison of I with 11, or of I with I11 in the case of the P = S group. The difference in moments between triphenyl phosphine and triphenyl phosphine oxide (Table 11),is close to the difference between I and 11. It is interesting in the light of this that the difference between triphenyl phosphine and triphenyl phosphine sulfide is significantly larger than that between I and 111. A similar situation is encountered in the series triphenyl phosphite, phosphate and thiophosphate, but here the variation in moment may include contributions from rotational (8) F. S. Mortimer, Spectrochim. Acta, 9, 270 (1957). (9) Measurement of the dipole moments of both I and I V a t 35.0' in dioxane gave values of 4.17 and 1.60 D,respectively. The moment of I is therefore essentially constant, whereas the moment of I V decreases by about 0.2 D. The existence of a temperature-dependent distribution of rotational forms in I V is indicated.
2053
isomerism. The present results, therefore, appear to be the first which show unambiguously that the P =S group moment in thiophosphates is lower than the P = O group moment in the analogous phosphates, as distinct from the phosphine analogs in which the opposite is true. It is widely recognized that the relatively low values for the P = 0 and P = S group moments are the result of a-bonding between oxygen or sulfur and phosphorus.lOpll Undoubtedly a-bonding also occurs in phosphites, and the difference in the moments of I and I1 or I and I11 includes changes in the bonding between phosphorus and the alkoxy oxygens in going from the phosphite to the phosphate or thiophosphate. It is clear that the group moments obtained by the comparisons made above are only apparent values, and include a number of contributions which cannot, on the basis of the dipole moment data alone, be separately evaluated. Acknowledgments.-We thank the National Science Foundation for a grant and a fellowship
(J.G.V.). (10) J. W. Smith, "Electric Dipole Moments." Butterworths, London, 1955,p. 230. (11) G. M. Phillips, J. 6. Hunter and L. E. Sutton, J . Chem. Soc., 146 (1945).
A COMPLETE IONIZATION SCHEME FOR CITRIC ACID BY R. BRUCEMARTIN Cobb Chemical Laboratory, University of Virginia, Charlottesville, Vu. Received May 39, 1961
Titration analysis of citric acid and selected methyl esters indicates that about 60% of the monoionized and 45% of the diionized species are symmetrical.
Recently two independent determinations were made of the relative ionizing tendency of the two kinds of carboxylic acid groups in citric acid. A nuclear magnetic resonance (n.m.r.) study indicated that ionization from the terminal carboxylic acid groups is predominant.' By measuring the relative chemical shifts of the methylene doublet as citric acid underwent progressive ionization and comparing these values with a scale for the chemical shift established by similar measurements on selected methyl esters, the mole fractions of the several ionic species could be estimated. In a second study, analysis of X-ray diffraction data demonstrates that the central carboxylic acid group is ionized in solid sodium dihydrogen citrate.2 These two studies are not necessarily contradictory because the ionization favored in the solid state may not be favored in solution. For many purposes it is the equilibria in solution that are of interest. A more direct method than n.m.r. exists for estimating the favored ionizations in citric acid with the aid of selected methyl esters.
Titration of the esters and comparison with the accurately known acid ionization constants of citric acids permits quantitative determination of the favored ionizations. This paper presents a titration analysis of the same esters used in the n.m.r. study and arrives a t the opposite conclusion ; the ionization from the central carboxylic acid group is predominant.
(1) A. Loewenatein and J. D. Roberts, J . Am. Chem. Soc., 82, 2705 (1960). (2) J. P. Glusker, D. van der Helm, W. E. Love, M. L. Dornberg and A. L. Petterwn, ibid., 83, 2964 (1960).
(3) R. G. Bates and G. D. Pinching, ibid., 71. 1274 (1949). (4) W. E. Donaldson, R. F. McCleary and E. F. Degering, ibid., 66, 459 (1934). (5) G. Bahroeter, Bm., 88, 3190 (1906).
Experimental Citric acid trimethyl ester4had m.p. 75-76', lit. 76"* and 73-73.5" .1 Citric acid symmetrical dimethyl ester6 had m.p. 116-118', lit 125-126'6 and 115-117'.' Anal. Calcd. for monohydrate: C, 40.3; H, 5.9; eq: wt., 238. Found: C, 40.9; H, 6.0; eq. wt., 257. Titrations were performed at 25" on a Beckman Model G pH meter by addition of standard base from an ultramicroburet. KOsalt was added to keep the ionic strength low so the thermodynamic ionization constants of citric acids could be used. Because of the problem of ester purity and the selectivity of the hydrolyses described later, the results are rounded to 0.05 log units, but should be considered reliable to only &0.1 log units.
Results The complete ionization scheme for citric acid is
R. BRUCEMARTIN
2054
coo-
Vol. 65
coo kl2
--+
COOH
7
4
COOH
HO-
COOH
!(I -COOH
/k*1
/
k\z
IcooCOOH
where 1 he 10s are microscopic acid ionization constants, and the last subscript refers to the number of the carboxylic acid group ionizing in the indicated equilibrium. This scheme is simpler than that of the general case of a tribasic acid6 because the equivalence of the terminal carboxylic acid groups introduces an element of degeneracy. From the definitions of the micro and macroconstants, it may be shown that the macroconstants determined by titration are related to the microconstants by
+
K I = 2ki kz KiKz = k i k ~ 2kzk21 = 2kikiz kik13 K I K z K ~= k i k i ~ k m kiki3kiaz = kikzikiz3 K3-1 = 2k123-1 k132-1
+
+
(1) (2) (3) (4)
The accurately known macroconstants at zero ionic strength and 25' are3: pK1 = 3.13, pK:, = 4.76 and pK3 = 6.40. Two of the seven microconstants must be independently determined if the complete ionization scheme is t o be delineated. Preparation of appropriate esters to block selected ionizations permits the microscopic ionization constants of unblocked groups to be estimated. The equivalence of an ester and an un-ionized carboxylic acid group finds support, in the identical chemical shifts in the n.m.r. spectra of citric acid and its methyl esters.' Hydrogen bonding effects are probably minimal in the case of citric acid.7 The complete ionization scheme may be worked out from titration with standard acid after selective hydrolysis of one or two terminal ester groups of the trimethyl ester. Addition of one equivalent of base to trimethyl citrate and titration with acid after 10 minutes yield pkl = 3.85 over a range of acid to base ratios from 0.4 to 2.5. From equation l, pkz = 3.35. Addition of two equivalents of base and titration with acid after 10 minutes yield two overlapping ionizations which may be analyzed by a pM LIS. a plot.8 The results are pkl = 3.85, which checks well with the above value, and pk13 = 4.40. From equation 2, pklz = 4.60, pkzl = 5.10 and from equation 3, pk1z3 = 5.85, @132 = 6.05. The last two results are in agreement with equation 4. ( 6 ) R. B. Martin, J. T. Edsall, D. B. Wetlaufer and B. R. Hollingworth, J . Bzol. Chem., 233, 1429 (1958). (7) F. 11. Westheimer and 0. T. Benfy, J . Am. Chem. Soc., 7 8 , 5309 (1956). (8) J. .?I'
\k121
\coo-
\\/
/\
CHzCOOH
+
7
\k13
CHzCOOH
COO-
Edsall, R. B. Martin and B, R. Hollingworth, Proc. Natl. Acarl. Sei., 44, 50.5 (1958).
coo -
\ cooCOOH
Y O 0 -
/k131
cooThough the complete scheme has been worked out as described in the previous paragraph, some checks in addition to the one for pkl are desirable. Titration of citric acid symmetrical dimethyl ester over a range of acid to base ratios from 0.4 to 2.5 yields pkz = 3.40, in satisfactory agreement with the above value of 3.35. Addition of two moles of base to the same ester, titration with acid, and analysis by a pM vs. a plots yield a macroconstant KE a t the high pH end of the curve which is given by ~ K = E 5.25. From the ionization scheme, this constant is related to the macroconstants by KE-' = k12-l kz1-l. From the microconstant values E 5.20, in already estimated, the calculated ~ K = satisfactory agreement with the experimental value. Thus two more checks lend confidence to the estimated microconstant values.
+
Discussion Relationships between the microconstants could be estimated by electrostatic theory, but the results would probably not be too reliable. Comparison with model compounds is perhaps more profitable. The kIk13 ionization sequence occurs in glutaric acid where the difference in the logarithms of the micro ionization constants is 0.47.9 In this work pkl3 p k l 0.55, ~ in fair agreement with the model compound result. The ratio of monoionized citric acid molecules with the terminal carboxylic acid groups ionized to those with the central group ionized is given by 2kJk2. From this work this ratio is about 0.6 so that the inverse ratio of central group ionized to terminal groups ionized is 1.6. At any pH in a solution of citric acid, 40% of the monoionized species have terminal carboxylic acid groups ionized. Thus the symmetrical monoionized citric acid species is predominant. The only groups of citric acid not insulated from each other by a t least two tetrahedral carbon atoms are the hydroxy group and the central carboxylic acid group. It might be expected that the central carboxylic acid group would be the most influenced by other groups on the molecule, Comparison of p k a values of glycolic (hydroxylacetic) acid, p K a = 3.8 with acetic acid, pK, = 4.7, demonstrates the acid strengthening effect of a hydroxy group on a neighboring carboxylic acid group. On these grounds the central carboxylic acid group of citric acid should be more acidic than the two terminal (9) R. H. Jones and D. I. Stock, J . Chem. Soc., 102 (1960).
Kov., 19G1
PHASE RELATIOXS IZJ THE FERRITE REGIOSOF
carboxylic acid groups. A more quantitative, but still approximate, comparison may be made by considering the pK, = 4.5 for p-hydroxypropionic acid. The difference of 0.7 log unit for the effect of a hydroxy group in the a- and P-positions is slightly larger than the difference p k l - plc, 'v 0.5 of this work. The results from the n.m.r. aiialysisindicated 80% of the monoionized species are in the unsymmetrical form. Assuming results of this paper correct, why are the n.m.r. results in error? The n.m.r. analysis for determining the relative importance of the kl and k2 ionizations depends upon a comparison of chemical shifts of 9.7 and 7.3 c./sec. relative to un-ionized citric acid, for the unsymmetrical and symmetrical monoionized species, respectively. The observed shift, on the same scale, for free monoionized citric acid of 9.2 c./sec. indicates only 20%.of the symmetrical monoionized species. Uncertainties of about 0.5 c./sec. allow for a coiisiderable margin of error when the difference of the numbers being compared is only 2.4 c./sec. Assuming, however, the correctness of the standard chemical shifts obtained on the esters, the n.m.r. analysis may be brought into agreement with the results of this paper if the 9.2 c. 'sec. value mere 8.2 c./sec. Apart from the n.m.r. measurements, the only assumption in deriving the 9.2 c./sec. value is a value for p K I 0 = 3.13. *in analysis shows, however, that if a value of pK1 = 3.08 had been used, a value of 8.2 c./sec. would have been obtained. This value of pK1, lower by only 0.05 log units, is a more reasonable value for the first ionization constant of citric acid when the minimum ionic strength is 0.2 X 3 as in the n.m.r. study. According to the view presented here. the n.m.r. study gave an incorrect result not because of' the n.m.r. data itself, but due to an inappropriate choice of pK1 to which the interpretation is sensitive. By selecting a value of pK1
THE
SYSTEM Xi-Fe-0
2055
more applicable to the conditions of the experiment, the n.m.r. results are consistent with the results of this study. Considering the diionized species, it may be shown that the ratio of the unsymmetrical to symmetrical microforms is given by 2lc132/k123. This ratio is 1.3 from the constants given above. Thus about 55% of the diionized species are unsymmetric. The statistically expected ratio and percentage are 2.0 and 67%) respectively. To the extent that the symmetrical diionized species permits greater separation of charges it would be favored. That this effect is not more pronounced is explained by examination of molecular models which indicate that the three carboxylic acid groups may distribute themselves nearly equidistant from one another. Several factors are operative in this situation, however. The results just quoted for the diionized species are in sharp disagreement with the n.m.r. results which were interpreted to indicate that 100% of the diionized species are symmetrica1.l Once again the discrepancy may be eliminated by lowering the impossibly high (in comparison with the ester standards) 20.2 c./sec. chemical shift to 16.9 c./sec. This change is in the direction expected for the effect of ionic strength on the assumed ionization constants. A decrease in pK2 of only 0.08 log unit can bring agreement between all results. To a first approximation, ionic strength does not change the ratio of the microforms of species of the same charge, but ionic strength does change the ratio of forms with differing charges. Acknowledgment.-This research was supported by grants from the National Science Foundation and the National Institutes of Health. The author thanks Charles W. Hill and Alice Parcel1 for performing the measurements.
HIGH TEMPERATURE PHA4SE RELATIONS IN THE FERRITE REGION OF THE Ni-Fe-0 SYSTEM BY M. W. SHAFER International Business Machines Corporation, Y o r k t m n Heights, New York Received M a y 29, 2962
Thermogravimetric analysis and quenching experiments have been used to determine phase equilibria in the ferrite region of the Ni-Fe-0 system. The area where single phase nickel ferrite spinels exists has been determined for oxygen pressures of 100, 10-0.' and lod2atmosphere a t 1400, 1500 and 1600'. Liquidus temperatures and compositions also have been determined and are presented in terms of the ternary system Xi-Fe-0.
Introduction This paper describes the results of a research program designed to improve the compositional control of ferromagnetic oxides with the spinel structure. Since the majority of these oxides can be thought of as solid solutions of transition metals in magnetite (Fe304),the problem of composition control is essentially one of determining the extent of the solid solution, Le., the spinel field boundary. Once this is done as a function of temperature, the task of preparing single phase polycrytalline
ceramics or even single crystals of any composition within the spinel field is relatively easy. The region of our primary interest in this work is the nickel ferrite spinel region, which will be discussed in terms of the phase equilibrium relations in the NiFe-oxygen system. Various people such as Blum and Zneimer,l Van Uitert2 and Okazaki3 have studied some (1) 9.Blum and J. Zneimer, J . Am. Cevom. Soc., 40 (61,208(1967). (2) L. Van Uitert, J . Chsm. Phys., 28 [IO], 1883 (1955). 13) C.Okazaki, J . Phye. Xoc. Jopcm, l S , 2013 (1960).
