(118) Phoenix Precision Instrument CO., Philadelphia, Pa. Bull. R-1000, “Dif-
ferential Refractometers.”
(119) Picon, hI., A n n . pharm. franc. 6 84-92 (1948). (120) Pillsbury Mills, Inc., Minneapolis, Minn., Chem. Procesving 18, (July I95.Si.
(12i)Pope, XI. I., J . ~ c i znstr. . 34, 22932 11957). (122) ‘Pouradier, J., Dubois, A., Research London 2, 11’&21, 1949; Suppl.
(Surface Chemistryj.
(123) Rabatin, J. G., Gale, R. H., ASAL. CHEY.28. 1314-16 (1956). (124) Rogeis. 11. C., Earle, P. L., Znd. Eng. Chem. 33, 642-7 (1941). (125) Rulfa, C. L.. - 4 x . 4 ~ . CHEM. 20, ‘ 262-4 (1948,. (126) Sarakhov, A. I., Doklady A k a d . K a u k S.S.S.R. 86, 98’&92 (1952). (127) Sartorius-Werke A . G., Gottingen,
Germany, Bull., “De Keyser Differential Thermobalance.” (128) Zbid., Bull., “Electrona RecordingMicrobalance.” (129) Zbid., Bull., “Recording Attachment for Selecta Balances.” (130) Zbid., Bull., “Sedibal Recording Sediqentation Balance.” (130a) Satava, V., SzlikiLty 1, 188-90
(1957). 1131) Scholten. P. C.. Smit. W. 11.. Wijnen, 11.’D., Rec. trau.‘ chim. 771 305-15 (1958). (132) Sharples C o r m Bridgeport, Pa., Bull. 103, “Cniversal Recording Bal~
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(133) Simons, E. L., Sewkirk, .4. E.,
Aliferis, I., AXAL. CHEY. 29, 48-54 (1957). (134) Simons, J. H., Scheirer, C. L., Ritter, H. L.. Rev. Sci. Instr. 24, 3 W 2 (1953j. (135) Sinclair, D., J . A p p l . Phys. 21, 38C-6 (1950). (136) Sinclair, D., Reo. Sci. Instr. 27, 34-6 (1956). (137) Smith, B. O., Stevens, J . W.,J. Sci. Znstr. 36, 206-9 (1959). (138) Spinedi, P., Chime i n d . ( M i l a n ) 33, 777-82 (1951). (139) Spinedi, P., Ricerca sci. 23, 2009-14 (19,U’r. ( l & S p l i t e k , R., Hutnickd listy 8 697705 (1958). (141) Stanton Instrumefts, Ltd., Lon-
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13, 1096-9 (1947). (143) Stephenson, J. L., Smith, G. W., Trantham, H. V., Rev. Sci. Instr. 28, 380-1 (1957). (144) Stock, A . , 2. physik. Chem. 139, 47-52 11928). 1145) Suito, -E., hrakawa, M., Bull. Z w t . Chem. Research, Kyoto Univ. 22, 7-17 (1950). (146) Svedberg, T., Rinde, H., J. Am. C h a . SOC.45,943-54 (1923). 1147) Szabo. Zoltan. KirBlv. Dezso. Magyar K h . ‘ F o l y o i r a t 63, l“5S-65 (1957). (148) Teetzel, F. hI., Monroe, M. A., Williamson, J. .4., Abbot, ,4. E., Stoneking, D. J., C.S.A.E.C. Bull., NLCO-713, 1958. (149) Testing Equipment Sales Co. (Tesco), Murray Hill, N. J., Bull. ~
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145,663-70 (i946). (153) Torsion Balance Co., Clifton, S . J. (154) Trenner, S . R., Warren, C. W., Jones, S.L., ASAL. CHEhf. 25, 1685-91 (1953). (155) Tryhorn, F. G., Wyatt, W. F., Trans. Faraday SOC.23, 23S-42 (1927). (156) Urbain. >I. G., Cornpt. rend. 6. 347-9 (1912). (157) Van Nordstrand, R . .4.,U. S. Patent 2,692,497 (Oct. 26, 1954). (158) Vieweg, R., Gast, T., Kunslslofle 34, 117-19 (1944). Vladimir, Vytasilova, (159) Vytasil, Sona. Hejl. Vladimir, Silikdtu” 2.. 285-9 (1958). (160) Waters, P. L., Coke and Gas 20, 252-6 (1958). (161) Waters, P. L., J . Scz. Zns1r. 35, 41-6 (1958). (162) Waters, P. L., S u t u r e 178, 3 2 4 4 (1956). (163) Wendlandt, W. W., ANAL. CHEW 30, 56-8 (1958). (164) Killiamson, J. A., Summary Tech. Rept., National Lead Co. NLCO-650, 142-4 (1956). (165) Zagorski, Z., PrzemysE Chem 31 (S), 326-30 (1952). .
I
Review of Fundamental Developments in Analysis
Thermometric Titration S. T. Zenchelsky Rutgers, The Stote University, New Brunswick,
A
Utilizes the enthalpy change of the reaction involved to locate the end point (23, 56, 101). It has been defined (43) as “a titration in a n adiabatic system yielding a plot of temperature us. volume of titrant.” The procedure consists of delivering the titrant from a thermostated buret into a solution contained within a thermally insulated vessel. and observing the temperature change of the solution either upon continuous addition, or after each successive incremental addition, of titrant. These temperature-volume plots resemble the corresponding graphs obtained from conductometric, photometric, and amperometric titrations. Yet while each of the latter three methods is severely limited to specific kinds of systems--e.g., conductometric titration requires electrolytic solutes in solvents of high dielectric constantTHERhlOMETRIC TITRATION
N. 1.
almost all reactions exhibit detectable enthalpy changes (positive or negative). This wide applicability, coupled with simplicity, suggests a potential increase in the use of thermometric titrations in analytical chemistry, particularly in those media in which electrometric and photometric methods are inapplicable Indeed, the importance of this subject has been sufficient in recent times to warrant its inclusion in two symposia (2, 102). Because of the increasing interest in thermometric titrations on the part of analytical chemists, there exists the need for a review paper which contains a comprehensive bibliography, including references to recent literature. Although several earlier papers (22, 45, 57, 62, 95) and texts (23, 65, 101) contain good general discussions of the subject, some with many references, none of them
fulfills that need. This paper is intended t o do so and covers the existing literature from the origin of thermometric titrations, in 1913, to September 1959. HISTORICAL
The first published paper on therniometric titrations was by Bell and Cowell (6) in 1913. Although Howard (@), in 1910, had suggested using the heat of chemical reactions as the basis for a new analytical method, he was referring to conventional calorimetry rather than t o a titrimetric procedure. Richmond and hlerreywether (80) used Hon ard’s method in 1917, but it was not until 1922, nhen Dutoit and Grobet (22) employed thermometric titrations for a variety of systems including acidimetry, precipitation, and complexation, that the scope and power of the method nere demonstrated. This work was followed in succeeding years b y a large number VOL 32, NO. 5, APRIL 1960
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of applications involving a wide variety of systems, as reported in the chemical literature of six countries. No important modification of the method of Dutoit and Grobet was adopted by workers in the field until 1953 when Linde, Rogers, and Hume (57) replaced the Beckmann thermometer with a thermistor and used a constant flow-rate buret to permit automatic recording of titration curves.
used a resistance-capacitance network t o record first and second derivative curves, automatically, from the outp u t of the thermistor bridge, to increase the precision and accuracy of end point location. Various instrumental aspects have been discussed by hluller (65) and Muller (66).
NOMENCLATURE
For convenience, the various papers referred to are listed under headings which may be somewhat arbitrary. The first four headings refer only to reactions in aqueous solution. Where several classifications are possible, the one used is dictated by the apparent principal objective of the author involved. Neutralization. Weak acids and bases have been studied b y several workers. Bell and Cowell (5) recommended the use of thermometric titration for the preparation of neutral solutions of ammonium citrate. Linde, Rogers, and Hume (57) titrated both weak and strong acids and bases, showing that clear end points were obtainable even in emulsions and thick slurries, and that a mixture of sodium hydroxide and sodium carbonate could be determined with good accuracy. Jordan and covorkers (48, 49) show that, unlike potentiometric titration which is dependent upon free-energy changes, thermometric titration works very well even for extremely weak acids. End points are precise and accurate for acids as weak as boric acid, because the enthalpy change of neutralization is not very different from that of a strong acid. Thus, Miller and Thomason (61) were able to titrate boric acid n i t h high precision even in the absence of mannitol. These same authors (60) were able to titrate acids in the presence of hydrolyzable cations because of the large difference between the enthalpy changes for the respective reactions. Chatterji and Ghosh (18) estimated some biologically important amino acids, both individually and in mixtures, with a n accuracy within 25% of theoretical. Paris and Vial (74) determined phenol and its homologs by thermometric titration, aftisr brominating to increase the acidity. The polyprotic acids. sulfuric and orthophosphoric, were titrated by Dutoit and Grobet ( Z ) ,who obtained two and three equivalence points, respectively. They found three equivalence points and a fourth barely discernible, for periodic acid, which led them to suggest a dimer as the species in solution. Mondain-RIonval and Paris (64) found only one equivalence point for the titration of boric acid or arsenous acid with sodium hydroxide, and at a molar ratio of unity
Different authors have used a variety of terms to designate the subject: thermometric titrations (3, 7 , 35, 65, 57, 61, 67, 70, 77, 83, 87, 95, 103), enthalpy titrations ( 4 6 , 4 7 ) ,calorimetric titrations (32, 55, 7 6 ) , thermochemical titrations (1, 46), thermal titrations (23), thermoanalytical titrimetry (2), and thermovolumetry (18). The first of these is used by the greatest number of authors and this was one of the chief reasons for recommending its adoption (43)’ APPARATUS
The original method of Dutoit and Grobet (22) employed a water-jacketed buret for titrant delivery, a Dewar flask as the reaction vessel, and a Beckmann thermometer to measure temperature increments. PIluller (67) replaced the Beckmann thermometer with a thermopile which actuated a photoelectric relay through a light-beam galvanometer, thus controlling the duration of addition of electrical heat, a t constant rate, to a Dewar flask containing the reference junctions of the thermopile. An electric timer, controlled by the same relay, indicated the duration of heat input. The time increments were thus proportional t o the temperature increments within the titration vessel. Muller also used a thermistor for temperature indication in 1950, but the results \yere not reported in the literature. The first published use of thermistors for thermometric titration was by Linde, Rogers, and Hunie ( U ) ,who employed a direct current Kheatstone bridge, the output of which was fed to a recorder. They also provided a bucking voltage for the purpose of shifting the trace with respect to the voltage origin. I n addition, they used the flow of titrant through a capillary under constant hydrostatic head to make the volume delivered porportional to time, and hence, to recorder-chart distance. These changes made the method autoinatic and rapid, thus greatly increasing its utility. The same authors suggested using a motor-driven syringe-buret like that of Lingane (58)) for delivery of titrant. This suggestion was adopted by subsequent workers (44, 48, 75, 103). Zenchelsky and Segatto (104)
290 R
ANALYTICAL CHEMISTRY
APPLICATIONS
in each case; however, for arsenic acid (62), three breaks in the curve were observed. Mixtures of meta-, pyro-, and orthophosphoric acids were titrated by Paris and Robert j72; with results generally 1% 10%. Paris and Tardy analyzed mixtures of hypophosphorous, metaphosphoric, and orthophosphoric acids ( 7 3 ) . I n the case of thermometric titration, unlike that of conductometric or poteutiometric titration, it was unnecessary to add barium ion to obtain the final end point break of orthophosphoric acid Precipitation. Zinc, plumbous, and magnesium cations n ere found to give three, four, a n d three end point breaks, respectively, when titrated n i t h sodium hydroxide by Dutoit and Grobet ( 2 2 ) . Zinc and cadmium were titrated with sodium hydroxide, and alkalies 1% ere determined by titration with standard solutions of zinc and cadmium nitrate by Ben-Yair (6). Grobet’s investigation of the coprecipitation of aluminate during the ammoniacal precipitation of aluminum hydroxide (34) shoir ed that aluminum hydroxide is never obtained pure, regardless of whether the precipitation is accomplished by use of aluminum nitrate, aluminum chloride, aluminum sulfate, or potassium alum. The titration of calcium, strontium, barium, and mercurous ions rrith oxalate was reported by Mayr and Fisch (59). They achieved an accuracj nithin 0.170, even for the determination of mercurous ion in the presence of mercuric. Nercuric ion was titrated with cyanide ion by XIondain-Monval and Paris (62) and with ammonia by Ben-Yair (6). Calcium and magnesium in dolomite Kere determined by Chatterji (IC), after first precipitating the iron, titanium, and aluminum with ammonia, by titrating with oxalate ion for calcium and then with microcosmic salt for magnesium. H e also determined zinc in brass (f6) using the mercury(I1) thiocyanate complex ion as titrant. Copper had to be removed first by precipitation as cuprous thiocj anate. Suluble sulfate was titrated n i t h barium chloride by Dean and Watts (20) in the determination of sulfur in a copper ore, with results accurate within 0.1%. Dean and Nen-comer (19) deterniined chloride, bromide, iodide, and cyanide by titration n ith sil1,er ions, achieving a n accuracy within 2%. Mixtures of thesp anions failed to give multiple end point break., so that only total anion could be determined. Linde Rogers, and Hume reported a n accuracy within 1% for the titration of silver Fyith chloride (57). Paris ( 7 f )studied the precipitation of the insoluble ferrocyanides of plumbous, silver, zinc, ferric. cuprous, cobaltous, nickelous, and cadmium ions, and ?\‘Iondain-Monval and Paris (62) titrated
lead acetate with ferrocyanide ion. Gel formation, on addition of aluminum sulfate to primary, secondary, and tertiary arsenate ion, was investigated by Shroff and Kabadi (84). Hydroxides of nickel in its higher oxidation states have been studied by Glemser and Einerhand (32). Leibmann et al. determined 2-naphthalenesulfonic acid by precipitation as the sulfanilamide salt (56). Complexation. T h e greatest number of papers on thermometric titration deal mith investigations of complex formation, all of which are of analytical importance either directly or indirectly. Halide and pseudohalide studies include: fluoride n i t h beryllium (77), chloride n ith beryllium ( Y O ) , iodide with mercury(I1) (53) and with cadmium (38), and cyanide with zinc, cobaltous, and nickelous ions (63). Ammonia complexes of cupric ions (22, 88),of cobaltous and nickelous ions (as), and of zinc and cadmium ions (6), have been investigated. The basic sulfates of cadmium (M), cupric (%), zinc (37), and beryllium (40) ions were studied by Haldar, who also investigated the complex carbonates of uranium (39). Complex formation between lead nitrate and rubidium nitrate (68, 69) and between lead nitrate and potassium nitrite (100) has been studied. Ferrocyanide complexes of cupric ( 9 ) , cadmium (IO), ferric (81), ferrous (sa),and thallous (31) ions have been investigated. Similarly, the ferricyanide complexes of cadmium (25), cobaltous (29), cupric (26), ferric (II), ferrous (12), nickelous (28), and zinc (27) ions have been studied. Phosphorus complexation investigations include ferric ion with orthophosphoric acid (5)and n-ith hypophosphorous acid (4). and beryllium with pyrophosphate ion (41). The thiosulfates of silver (SO), cadmium (8), and cupric (17) ions have also been investigated. Organic ligands also have been used. The interactions of lead ion with acetate ion (78), of zinc, cadmium, and cupric ions with citrate and tartrate ions (7, 47), of thorium ion \d,h oxalate ion ( I S ) , of thiourea with cadmium ion (87), of ethylenediamine and trimethylenediamine with nickelous and cupric ions (76), and of lead, cadmium, cupric, nickelous, calcium, zinc, cobaltous, and magnesium ions with (ethylenedinitri1o)tetraacetic acid (EDTA) (2, 46) have been investigated. For the EDTA titrations, a n accuracy within 3y0 is possible with cation concentrations as low as 5 X 10-4M. Redox. T h e least a m o u n t of work has been done with redox reactions, although this method seems very promising. Mayr and Fisch (59) showed that ferrous, oxalate, and
ferrocyanide ions, as well as hydrogen peroxide, could be determined with good accuracy b y titration with permanganate ion, and that bromate and hypochlorite ions could be determined accurately with arsenous trioxide solution. hluller (67) has also reported the titration of iron(I1) with permanganate. Schafer and Wilde (85) determined various aromatic sulfonamides b y titration with hypochlorite solution. Ewing (23) has titrated iron with dichromate ion. Nonaqueous. Thermometric titrations have been performed in organic as well as in other nonaqueous soivents. T o improve accuracy, Somiya (90, 96) used thermometric titration in place of the calorimetric method of Richmond and hlerreywether (80) to determine the water content of concentrated sulfuric acid. He was also able to analyze mixtures containing concentrated nitric and sulfuric acids (89) b y titration with oleum. Richmond and Eggleston (79) determined acetic anhydride b y t h e heat of its reaction with aniline in toluene, but their procedure was not titrimetric; however, Somiya determined acetic anhydride in the presence of strong acids (97) using a titration based on Richmond and Eggleston’s method (79). Acetic anhydride in acetic acid was determined by titration with water (SS), and water in acetic acid was determined with acetic anhydride. Somiya analyzed mixtures of sulfuric acid, acetic acid, and acetic anhydride (91,92). He also determined acetyl values (98) and iodine numbers (94) of fats and oils. Parsons (76) suggested the direct titration of phenol and t a r acids with alcoholic potassium hydroxide using pyridine as solvent, for routine industrial control. Trambouze (98) titrated a suspension of the solid Lewis acid, aluminum chloride, in benzene, with the bases dioxane and ethyl acetate and obtained a n accuracy within 3%. This method was also used t o determine the Lewis acidity of mixed silica-alumina gels (99) to establish the coordination number of aluminum in these compounds. Zenchelsky, Periale, and Cobb titrated stannic chloride with dioxane in the solvents benzene, nitrobenzene, chloroform, and carbon tetrachloride (105). Zenchelsky and Segatto titrated stannic chloride with dioxane, morpholine, pyridine, and tetrahydrofuran, in benzene (105). Hume and Keily (4) determined various weak organic bases in glacial acetic acid b y titration with perchloric acid. Forman and Hume (24) titrated amines in acetonitrile with hydrobromic acid. Jordan et al. employed thermometric titrations in molten salt solvent for a variety of reactions including precipitation, complexation, and redox (51-63).
Miscellaneous. This category deals with t h e determination of various thermodynamic parameters and stoichiometry. Several papers deal 55ith t h e use of thermometric titrations for determining heats of reaction, heats of solution, heats of dilution, equilibrium constants, and the stoichiometry of reactions. Siddhanta (85, 86) has discussed the use of thermometric titrations in Job’s method of continuous variations t o determine the stoichiometry, equilibrium constant, and enthalpy change of complex formation, and suggested modifications to simplify the procedure. Poulsen and Bjerrum (76) have employed thermometric titrations to estimate the heats of successive steps in the formation of metal-ammine complexes. Zenchelsky et al. (105) showed how the sensitivity of thermometric titration is affected by the choice of solvent. Keily and Hume (64) derived equations for the relationship between temperature change and volume of titrant, considering such effects as heat capacity of the apparatus, the change in volume during titration, and departure from adiabatic conditions. They sholv how t o estimate heats of reaction, solution, and dilution from the titration curves. Jordan and Alleman (46) describe the titrimetric determination of heats of chelation. Heats of reaction and equilibrium constants were obtained by Zenchelsky and Segatto (IO,$), using thermometric titrations in a variation of the procedure of Dilke and Eley (21). Fornian and Hume (24) measured heats of neutralization and strengths of amines in acetonitrile. Jordan and Dumbaugh (1, 48, 49) studied some proton-transfer processes and determined enthalpies and entropies of ionization of various acids (50) in aqueoussolution Chatterji (16) has pointed out the importance of correcting for the volume change during titration. LITERATURE CITED
(1) Alleman, T. G., Abstracts of Papers,
132nd Meeting, .4CS, p. IlB, Xew York, S . Y., September 195i. (2) Am. Chem. SOC.,.4bs+racts of Papers, 132nd Meeting, ACS, pp. 5B13B, Xex York, N. Y., September 1957. ( 3 ) Banerjee, S., J . Indian Chem. SOC. 27,417 (1950). (4) Banerjee, S., S i . and Culture (Calcutta) 16, 115 (1950). (5) Bell, J. M., Cowell, C. F., J. A m . Chem. SOC.35, 49 (1913). (6) Ben-Yair, M. P., Abstracts of Papers, 132nd Meeting, ACS, p. 6B, New York, N. Y., September 1957. (7) Ben-Yair, M. P., Jordan, J., Abstracts
of Papers, XIIth International Cdngress of Pure and Applied Chemistry, pp. 42-43, New York, N. Y., September 1951.
(8) Bhadraver, M. S., Gaur, J. N., J . Indzan C h m . SOC.36, 103 (1959). (9) Bhattacharya, A. K., Gaur, H. C.,
Ibid., 24, 487 (1947).
(IO) Zbid., 25, 185 (1948). VOL. 32, NO. 5, APRIL 1960
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(11) Bhattacharya, A. K., h e n s , R. S., Ibid., 29, 263 (1952). (12) Ibid. (13) Base: %$?howdhury, D. M., Ibid., 32, 673 (1955). (14) Chatterji, K. K., Ibid.,32,366 (1955). (15) Ibid., 35, 57 (1958). (16) ]bid., p. 709. (17) Ibid., p...883. (18) Chatterji, K. K., Ghoah, A. K., M., 34, 407 (1957). (19) De~m, P. M., Newcomer. E.. .I. Am. Chem. Sm. 47, 64 (19%i). (20) Dean, P. M., Watt&, 0. O., Ibid., 46, 855 (1924). (211 Dike. M. H.. Elev. D. D.. J. Chem. . Soc. 194.9, 2601. f22) Dutoit. P.. Grobet. E.. J- . d i m . . Phys. 19,324 i19m). (23) Ewing, G. W., "Instrumental Methods of Chemical Analysis," pp. 31113, McGraw-HiU, New York, 1951. (24) Forman, E. J., Hume, D. N., J . Phys. C h . 63, 1949 (1959). (25) Gaur, H. C., Bhattacharya, A. K., J . Indion Chem. Soc. 26, 46 (1949). (26) Ibid., 27, 131 (1950). (27) Ibid., 29,29 (1952). (28) Ibid.. D. 117. (29) Ga&,-H. C., Bhattscharya, A. K., Proc. Nail. A d . Sci. India 19A, 45I
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(30)Gaur, J. N., Bhadraver, M. S., J . Indian Chem. Soc. 36, 10s (1959). (31) Gaur, J. N., Gaur, H. C., Bhattacharya, A. K., Z W . , 35, 144 (1958). (32) Glemser, O., Einerhand, J., 2. a w g . C h . 261, 26 (1950). (33) Greathouse, L. H., Janssen, H. J., Haydel, C. H., ANAL. C&M. 28, 357 (1956). (34) Grobet, E., J . Aim. phys. 19, 331 (1922). (35) Haldar, B. C., J . Indian C h . Soc. 23,147 (1946). (36) Ibid., p. 153. (37) Ibid., p. 183. (38)Ibid., p. 205. (39) Ibid., 24, 503 (1947). (40)Ibid..25.439 11948). (41j zbid.; 27; iSa (i95oj. (42) Howard, H., J . Soc. C h . Ind. (London)29,3 (1910). (43) Hume, D. N., Jordan, J., ANAL. &I!"E 30, 2064 (1958). (44)Hume, D. N.,Keily, H. J., .4bstracts of Papers, 132nd -Meeting, ACS, p. 6B, New York, N. Y., September 1957. (45) Jordan, J., Becord Chem. Progr. (Kresge-Hooker Sci. Lib.) 19, No. 4, 193 (1958). (46) Jdrdan,' J., Alleman, T. G., ANAL. CWM. 29, 9 (1957). (47) Jordan, J., Ben-Yair, M. P., Arkiv Kemz 11, 239 (1957).
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(48) Jordan, J., Dumbaugh, W. H., Jr., ANAL.CEEM.31,210 (1959). (49) Jordan, J., Dumbaugh, W. H., Jr., BuU. Chem. Thermo. (I.U.P.A.C.) 2, Sect. A.. 9 (1958). (50) zbid.,'g (iG6j. (51) Jordan, J., Meier, J., Billingham, E. J., Jr., Pendergrast, J., Abstracts of Papers, 135th M e e e g , ACS, p. 3OB, Boaton. h. ADrd . 1959: h A L . CEEM..' in (52) 1&.,-3ci439 (1959). (53) Jordan, J., Meier, J., Billingham, E. J., Jr., Pendergraat, J., Bull. Chem. Thermo. (I.U.P.A.C.) 2, Sect. A., 11 (1959). (54) Keily, H. J., Hume, D. N., ANAL. b Y . 28, 1% (1956). (55) Kolthoff. I. M.. Stenaer. V. A., "Volumetric Analy&," 2n-d .ed., Vol. I, p. 272, Interscience, New York, 1942. (56) Leibmann, W., Parson, J. S., Woods, J. T., Abstracts of Papers, 132nd Meeting, ACS, p. 12B, New York, N. Y., September 1957. (57) Linde, H. W., Rogers, L. B., Hume, D. N., ANAL.CHEM. 25, 404 (1953). (58) Lingane, J. J., Ibid., 20,285(1948). (59) Mayr, C., Fisch, I., 2.anal. Chem. 76, 418 (1929). (60)Miller, F. J., Thomaeon, P. F., ANAL.CHJCM. 31, 1498 (1959). (61) Miller, F. J., Thomason, P. F., Talanta 2, 109 (1959). (62) Mondain-Monval, P., Paris, R., Bull. soc. d i m . France [5] 5, 1641 (1938). (63) Mondain-Monval, P., Paris, R., C m p t . r e d . 198, 1154 (1934). (64)Ibid., 207, 338 (1938). (65) Muller, D. C., Abstracts of Papers, 132nd Meeting, ACS, p. 6B, New York, X. Y., September 1957. (66) Muller, R. H., Abstracts of Papers, 132nd Meeting, ACS, p. 5B, New York; N. Y., September 1957. (67) Muller, R. H., IND.ENG.CHE~., ANAL-ED.13, 671 (1941). (68)Nayar, M. R., Pande, C. S., 1. Indian Chem. Soc. 28, 107 (1951). (69) Ibid., p. 112. (70) Novoselova, A. V., Pashinkin, A. S., Semenenko, K. N., Vastnik Moskin~. Univ. 10, No. 3, Ser. Fiz.-Mat. i Estestua.Nauk No. 2,49 (1955). (51) Paris, R., C m p t . rend. 199, 863 (1934). (72) Paris, R., Robert, J., Zbid., 223, 1135 (1946). (i3) Paris, R., Tardy, P., Ibid., 223, 1001 (1946). (74) Paris, R., Vial, J., Chim. a d . 34, 3 (1952).
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(36) Parsons, J. S., Abstracts of Pa 132nd Meeting, ACS, p. 12B, York, N. Y., September 1957. (76) Poulaen, I., Bjemun, J., A d a Chem. Scand. 9, 1407 (1955). (77) Purkayastha, B. C., J . Indian Chem. Soe. 24, 257 (1947). (78) Purkayastha, B. C., Sen-Sarma, R. M., Ibid., 23, 31 (1946). (79)Richmond, H. D., w e a t o n , J. A., Analyst 51, 281 (1926). (80) Richmond, H. D., Merreywether, J. E., Ibid.,42,273 (1917). (81) Ssxena, R. S., Bhattseharya, A. K., J . Indian Chem.Soc. 28, 703 (1951). (82) Ibid., 29, 632 (1952). (83)Shiifer. H.. Wdde. E.. Z. a d . Chem. . ljo, 396 (1949). 184) -, Shroff. S. N.. Kabadi. M. B.. J. Univ. Bombay 22, pt. ' 3 (Sciknce Number 34A), 47 (1953). (85) Siddhanta, 5. K., J . Indian C h . Soc. 25, 579 (1948). (86)Ibid., p. 584. (87) Siddhanta. S. I(.. Sci. and Culture '-(C&u&i) 12,'409(1&7). (88)Siddhanta, S. K., Guha, M. P., J . Indian Chem.Sm. 32,355 (1955). (89) Somiva. , T., . Chem. News 137, 14 ' (i928). (90)Somiya, T., J . Soc. Chem. Ind. (Japan) 30, 106 (1927). (91) Ibid., 31, 306 (1928). (92) Ibid., 32,490 (1929). (93) Ibid.,33, Suppl. binding 140 (1930). (94) Ibid., p. 174. (95) Somiya, T., J . Soc. C h . Ind. (Londa)51, 135T (1932). (96) Soiniya, T., Proc. Imp. A d . (Tokyo) 3 , 76 (1927). (97) Ibid., 5, 34 (1929). (98) Trambouze, Y., C m p t . rend. 233, 648 (1951). (99) Trambouze, Y., de Mourgues, L., Perrin, M., Ibid.,234, 1770 (1952). (100) Vartak, D. G., Kabadi, M. B., J . Indian Chem. Soc. 32, 351 (1955). (101) Willard, H. H., Memtt, L. L., Dean, J. A., "Instrumental Methoda of Analysis," pp. 594-98, Van Nostrand, Princeton, 1958. (102) Zenchelsky, S. T., Abstracts of Papers, Eastern Analytical Symposium, p. 21, New York, N. Y., November 1959. (103) Zenchelsky, S. T., Periale, J., G b b , J. C., ANAL. CHEM. 28, 67 (1956). (104) Zenchelsky, S. T., Segatto, P. R., Ibid., 29, 1856 (1957). (105) Zenchelsky, S. T.. Segatto, P. R., J . Am. Chem. Soc. 80, 4796 (1958). I
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part a t the Eastern Analytical Symposium, New York, N. Y., November 1959. ~ E N T E D in
