163 (1975):Chem. Abstr., 83,83863 (1975). (464)Zsako, J.; Arz, H. E., J. Therm, Anal., 8, 651 (1974);Chem. Abstr., 82,35355 (1975).
(465) Zsako, J.; Vahelyi, Cs., J. Therm. Anal., 7 , 33 (1975). (466)Zuda, A,. Thermochim. Acta, 8, 217
(1974). (467)Zynger, J., Anal. Chem., 47, 1380 (1975).
Titrations in Nonaqueous Solvents Byron Kratochvil Department of Chemistry, University of Alberta, Edmonton, Alberta, Canada T6G 2G2
This review covers approximately the literature reported in Chemical Abstracts over the period January 1974 to December 1975, plus some additions from other sources. As the editors have requested, emphasis is on developments in theory, methodology, and instrumentation, with applications included only insofar as they appear to advance the state-of-the-art or have particular current relevance. The selection of what to include necessarily is a matter of judgment, and so certain areas may not have received the attention considered appropriate by some. The comments and suggestions of readers are welcomed. The general area of titrations in nonaqueous solvents has seen a steady accumulation of information on solvent-solute interactions by a variety of techniques, and the background knowledge necessary for useful analytical applications is increasing. As a result, improved methods of determining compounds that are insoluble in or react with water should continue to appear, expecially in the area of analytical electron-transfer and complexation reactions. BOOKS AND REVIEWS Over the period covered by this review, several books and reviews of general interest have appeared. Reviews concentrating in specific areas are mentioned in the pertinent sections of this article. The properties and reactions of electrolyte solutions in dipolar aprotic solvents have been reviewed by Cox (51), as has the area of ionization phenomena in solutions (151). Aqueous and nonaqueous titrations of organic acid-base systems have been treated in two reviews (32, 227) and a book (69).The effect of neutral salts on acid-base reactions has been discussed ( 4 4 ) , as has the analytical aspects of voltammetry in nonaqueous solvents and melts ( 1 1 ) . The chemical and electrochemical properties of solutes in nitromethane have been surveyed (31). Two valuable reference books containing extensive data on solvent and solute properties have appeared (48, 9 9 ) , and a useful list of the physical properties of over 900 organic solvents has been compiled (194).An English translation of the 1971 French edition of “Chemistry in Nonaqueous Solvents” is now available (217). FUNDAMENTAL Acid-Base Equilibria. Quantitative measurements of proton-transfer energies in the gas phase are now being made by several experimental techniques (7). From these data, it is possible to divide classical acid-base thermodynamic quantities into two terms, one relating to solvation and the other to internal energy, that provide information on the nature of the primary solvation sheath around solutes and on the effects of substituents on the acid-base properties of solutes. For example, the solvation energy of aliphatic alkoxide ions can be measured experimentally and related to size and structure (8). The Hammett acidity function concept requires that the ratio of the activity coefficients of the acid and base forms of the indicator used be unity; that is, that there,be a linear relationship with a slope of one between PKHAfor any acid in a given solvent and PKHA’ in a reference solvent, usually water. This had always been recognized as a source of possible error in the method, but recent results indicate that
the approximation breaks down more often than is usually realized. Thus, for a variety of phenolic acids in 80% dimethyl sulfoxide-20% water, the slope is 1.4, and for carboxylic acids in pure dimethyl sulfoxide it is 2.7 (118). The use of nmr to extend the Hammett concept to compounds other than spectrophotometrically accessible ones has increased greatly the scope of this approach, but has in turn brought some of the limitations of the method into clearer focus. Among indicator systems used for nmr determinations of acidity functions are pyrimidines in fuming sulfuric acid (66),and aliphatic esters (137) and a range of amides and esters (138) in sulfuric acid. Different solvation requirements are found when the nature of the base is varied, and so different acidity functions are required for various ketones. It has been pointed out that deprotonation of nitroalkanes by ammonia cannot be described in terms of equilibrium constants when nmr data are used because, although temperature variations cause changes in the concentration of the nitroalkane anion, chemical shifts are not affected (234). But at constant temperature, chemical shifts are highly dependent on concentration. Thus, for some systems, nmr results must be interpreted carefully. An acidity scale for water and nonaqueous solvents based on the rate of hydrolysis of an acetal molecule under standard conditions has been proposed (110). The system assumes, in common with the Hammett concept, that the ratio of the activity coefficients of the acid and base forms of the acetal is constant in a given solvent medium. Data taken in dioxane-water mixtures support the method (111). In another approach, a function based on the Ostwald dilution law has been suggested as a way of describing quantitatively the ability of a Bronsted acid to transfer a proton to any solvent, or of a Bronsted base to remove a proton from an acidic solvent (139).Dimethyl sulfoxide has been suggested as a desirable solvent for measuring the acidities of carbon acids such as ketones, nitriles, sulfones, and nitro compounds (148). An indicator method is used. Deviations of results by the described approach from the H - scale are thought to be caused by deviations of H functions from ideal behavior. A review on the determination of acidity constants contains much useful information on the problem of measurement and interpretation of data in nonaqueous and mixed aqueous solvents (47). Hydrogen-bonding effects on acid-base equilibria in several aprotic organic solvents have been reviewed by Kolthoff (112, 113). Homoconjugation studies of a series of organic acids (41) show that the monoanions of malonic and o-phthalic acids are strongly intramolecularly hydrogenbonded in methanol, but not in water, while the monoanion of glutaric acid contains an intramolecular hydrogen bond in acetonitrile and dimethyl sulfoxide. The monoanion of oxalic acid, on the other hand, shows no evidence of intramolecular hydrogen bonding in methanol, dimethyl sulfoxide, or water. In acetonitrile, intramolecular hydrogen bonding is greatest for the monoanion of malonic acid, and decreases in the homologous series to azelaic acid (115). The monoesters and diacids are not intramolecularly hydrogen bonded in acetonitrile. Factors affecting values of dissociation constants of mono- and polyprotic acids in mixed solvents have been reviewed (166), and the acidbase properties of ethylene glycol mixtures with a variety ANALYTICAL CHEMISTRY, VOL. 48,
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of solvents studied with a glass electrode (233). Hydration constants between water and carboxylic acids, picric acid, and methanesulfonic acid in sulfolane have been measured by vapor pressure and calorimetric methods (20). Values ranged from 0.4 for acetic acid to 5.7 for methanesulfonic acid. The basicity of water in sulfolane and acetonitrile appears to be lower than that of the bromide ion. Dissociation constants of acids and bases in various solvents can be determined by iterative linearization of the potentiometric titration curve if ion association is not significant (211. A standard deviation of 0.01 pK units was obtained. A rapid, simple procedure for the determination of acid dissociation constants with a glass electrode, also limited to solvents of high dielectric constant, has been suggested by Bos and Lengton (29). Several methods for the determination of excited singlet state acidity constants in 2:1 water-dioxane have been compared, and a fluorescence titration procedure found to give the best correlation (186). Increases in acidity of from 5 to 16 orders of magnitude over the ground state were observed for substituted anthraquinones, fluorenes, and fluorones. Triplet state acidity constants for the same compounds were within 1 or 2 pK units of the ground state values, however (187). Weakly basic solvents such as acetonitrile or sulfolane are more suitable for the determination of protonation constants of very weak bases than is water (114). Protonation constants in acetonitrile of a series of organic acids, esters, phenols, and other compounds were determined by the effect of these solutes on the conductivity of methanesulfonic or trifluoromethanesulfonic acids in acetonitrile (114),and titration curves near the first equivalence point in the titration in acetonitrile and dimethyl sulfoxide of diprotic acids with a strong base have been compared (116). The value of the acid dissociation constant of protonated tris(hydroxymethy1)aminomethane (Tris) in N-methylpropionamide, a solvent of high dielectric constant, is smaller than it is in water, but increases with increasing water content to a maximum at about 0.6 mol fraction water, then decreases (14).A similar pattern is seen in methanol-water mixtures, and in N-methylpropionamide-methanol mixtures, even though the dielectric constant of methanol is lower than that of water (23).Comparison of transfer energies for the individual species Tris, Tris-hydrochloride, and hydrochloric acid shows that proton stabilization is the primary cause for the increase in acidic strength of protonated Tris when N-methylpropionamide is added to a predominantly aqueous medium. With N-tris(hydroxymethy1)methylglycine (tricine), the situation is different because protonated tricine is a dibasic acid (15).Both acids become weaker as methanol is added to the aqueous solvent, apparently because the zwitterion form is strongly stabilized in water. The behavior of acids and bases in pyridine, sulfolane, and propylene carbonate have been reviewed by Mukherjee (160). Values of hydrogen ion activity were measured for mixtures of water with acetone (100, 200), propanol ( l o o ) ,and dioxane ( 1) by potentiometry, and with dimethyl sulfoxide by spectrophotometry (16). The general problem of measurement of hydrogen ion activity in mixed solvents has been discussed (134). A chapter on acid-base equilibria in an advanced analytical textbook discusses systematically this area in the solvents glacial acetic acid, acetonitrile, and ethylenediamine (135). Solvation. In most reactions of analytical interest, ionic species are involved as reactants or products or as transient intermediates. Thus, new theoretical and experimental data on ion-solvent interactions provide valuable bases for future analytical methodology. The ion-pair concept and methods of estimating free energies of solvation in mixed solvents have been discussed in a review by Strelow, Knoche, and Schneider (211). The role of the continuum approximation in the theory of electrolytes has been reexamined and modified from a mathematical point of view (76, 77), and by assumption of a polar solvent structure (62). Solvent effects on donor-acceptor and ion-molecule bonding have been discussed (220), as has ionic equilibria in donor solvents (150). The effect of ligand solvation on the stability of metal 356R
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complexes was found to be significant when the stability constants of cyclic and open-chained amine complexes of nickel were compared (93, 94). The enhanced stability of the macrocyclic ligand-metal complex is due to a more favorable enthalpy term. This is attributed to decreased solvation of the macrocycle compared to the open-chain ligand. Solvation effects of this kind are especially important for systems where strong solvation of the ligand is possible, Experimental investigations of solvent interactions with specific species by optical and magnetic resonance spectrometry and by conductance have been especially fruitful. An expression relating the nmr chemical shifts of solutes in binary solvent mixtures to changes in solvation number was derived (49);subsequently ion solvation was treated in terms of step-wise equilibria in which the free energy of solvent exchange changed as the amount of one component in the solvation shell increased (50). Solvation of lithium (17, 36), sodium (78),and chloride (36) ions was studied in several aprotic solvents by nmr, Raman, and infrared spectrometry. The formation of both solvent-separated and contact ion-pairs was shown to occur. A discussion of this area has been provided by Popov (178).Calculations of solvation energies and ion-pair formation of alkali metal halides in dimethyl sulfoxide at the molecular level gave good agreement with experimental enthalpies of solvation (75). An energy profile for an anion moving from a solvent-separated ion-pair position to a contact ion-pair position was also presented. Solvation numbers and association constants of the perchlorate salts of sodium, lithium, and magnesium were measured in acetone by infrared spectrometry (175);the same technique was used to show that the tetrabutylammonium cation is not solvated to any measurable extent in acetonitrile or dimethylformamide (133).The solvation of cadmium, zinc, and barium ions in a series of aprotic organic solvents was studied by determination of the energy of transfer from water to the other solvents (91) and the hydration of several ions in dimethyl sulfoxide, propylene carbonate, acetonitrile, and sulfolane was estimated by several techniques (19). Hydration constants were not highly sensitive to the nature of the ion, but were sensitive to the nature of the solvent. The solvation of silver(1) in water-dimethyl sulfoxide mixtures has been studied in detail by nmr (45). Conductance measurements also provide useful information on ion mobilities and ion association in non-ionic solvents. Tetraalkylammonium nitrates show some association in 3-tert-butyl-2-oxazolidone; association values decrease for other salts in the order bromides, perchlorates, and tetraphenylborates (13). Measurements of 1:l salts in hexamethylphosphotriamide were consistent with strong cation solvation but weak anion solvation (88, 172). Perchloric and trifluoromethanesulfonic acids are completely dissociated in dimethyl sulfoxide, while association constants for nitric, sulfuric, methanesulfonic, and hydrochloric acids increase in the order given (46, 142). Hydrochloric acid is a very weak electrolyte in sulfolane (37);formation of HC12- occurs. The nature of ion-pairing in dioxanewater mixtures was studied using alkali metal halide systems (149).At lower dielectric constants, the ion pairs were mostly contact pairs; as the dielectric constant was increased, the number of solvent-separated pairs increased. The effect of variation in bulk dielectric constant on ion pairing and ion mobilities has also been studied by Fuoss and coworkers using tetraalkylammonium salts and mixtures of iso-butyronitrile with chloro-substituted benzenes, 1,2-dichloromethane,carbon tetrachloride, n -pentanol, and tetrahydrofuran (54, 98). Hydrogen bonding of water with acetonitrile, dimethyl sulfoxide, and tetrahydrofuran appears weaker in solutions containing little water or in pure water than in solutions of intermediate composition (24, 25). In alcohol-water mixtures containing little alcohol, the fraction of “symmetrically” bonded water generally is smaller than in wateraprotic solvent mixtures (26).In mixtures of dimethyl sulfoxide and water, formation of a 2:l water-dimethyl sulfoxide complex is indicated (106). Ion solvation in a series of 3-substituted 2-oxazolidones was investigated by infrared and magnetic resonance techniques (35).The 3-methyl derivative had the highest dielectric constant of the alkyl series studied, 77.5, and has promising solvent properties.
Byron Kratochvll, Professor of Chemistry and chairman of the analytical division at the University of Alberta, received his B.S., M.S., and Ph.D degrees all from Iowa State University. He was a faculty member at the University of WisconsinMadison from 1961 to 1967, when he joined the chemistry department at Aiberta. His research interests are in the areas of solvent effects on solute properties and reactions, applications of nonaqueous systems to chemical analysis, and methods for determining substances of clinical interest.,He also has a strong interest in the teaching of analytical chemistry.
0
II
o-’ I
C
‘-N-CH, I
H,C -CH,
A study in nitromethane of solvation of alkali and alkaline earth halides by solubility determinations, and of silver, mercury, and copper reduction potentials, has been made (10).
Estimation of Transfer Activity Coefficients. The problem of estimating transfer activity coefficients, or of correlating potentials between solvents, has received continuing attention. Of the variety of extrathermodynamic assumptions that have been used to estimate single ion transfer activity coefficients, the one in which the transfer activity coefficients of the tetraphenylarsonium cation and the tetraphenylborate anion are considered equal is supported by several lines of evidence (179) and has been used to correlate solvent properties toward ionic solutes (52,53). The assumption of negligible solvent effects on the potential of the ferricinium-ferrocene couple as a means of correlating potentials also has been investigated in several solvents and has been found not to agree with the above system in many cases (58). Alfenaar ( 5 ) suggests that the ferrocene couple should be rejected because of ferricinium ion-solvent dipole interactions and because of quadrupolesolvent dipole interactions by ferrocene. However, this couple has been used in potentiometric studies of ion solvation in nitromethane (10) and in methanol-dimethyl sulfoxide mixtures (144),while the cobalticinium-cobaltocene couple has been employed in mixtures of dimethyl sulfoxide and propylene carbonate (147). Parsons (171) points out that another approach, the division of the chemical potential of a single ion into a measurable “real potential” and a surface term, may give valuable information. The surface term involves the work required to transfer the ion across the surface layer, and can be measured by a cell in which the junction between the two half cells consists of an air gap between one soluution flowing over the inner wall of a cylinder and the other solution directed in a jet down the axis of the cylinder. Thus measurement of the potential of the cell Ad AgC4 NaCl(aq)(air)NaCl(so1vent S)l AgC4 Ag allows direct determinatoon of the free energy of transfer of the chloride ion from water to solvent S. Though the experimental difficulties are formidable, and the results not highly precise, this method may ultimately prove to be the most satisfactory. Discussions of this area are included in reviews on the more general topics of ion solvation (211) and of electrolyte solutions in dipolar aprotic solvents (511. The relation between polarographic half-wave potentials and standard electrode potentials for R+/R and R/R- couples, where R is a large ion, has been considered (197). Liquid junction potentials have also received some attention. A mathematical method for calculation of junction potentials between miscible solvents involves an improved approach to solving the differential equation describing diffusion potentials (71). Conditions necessary for proper functioning of a salt bridge between different solvents also are discussed. In another study, potentials at a number of junc-
tions between solvents were determined using the tetraphenylarsonium-tetraphenylborate extrathermodynamic assumption (59). Kinetics. Although acid-base reactions generally are rapid in nonaqueous solvents, other types often are not. Kinetic studies of rates and mechanisms, therefore, can provide background for possible new analytical methods by allowing selection of conditions for direct titrations or by slowing interfering reactions. Among several useful surveys of this area are ones on the use of kinetics to study carbon acid reactivity ( 5 9 , on the effects of pure and mixed solvents on reaction rates and mechanisms (34), and on the relation between solvent donicities and the kinetics of formation and dissociation of metal-ligand complexes (95). The utility of kinetic methods in the study of ion solvation comprises a part of a general discussion of the topic (211). An example of methods and systems used in kinetic investigations is the measurement of rate constants and activation energies of electron transfer between organic anion radicals and neutral organic molecules in aliphatic alcohols by pulse radiolysis (153). The solvent effect is greater for slow than fast reactions, and there is no regularity in solvent effects on reaction rates between species with the same functional groups. Also, kinetic parameters of the reaction change in a complicated way with variations in composition of binary mixtures. In a voltammetric study of the kinetics of alkali metal reduction, it was found that, although water solvates lithium ions more strongly than propylene carbonate does, electron transfer between lithium metal and lithium(1) is more rapid in water (60). The effect of ion-solvent interactions on rate constants for the reduction of a series of metal ions in dimethyl sulfoxide and propylene carbonate was investigated at a mercury cathode by Hills and Peter (92). The rate of formation of the monochloro complex of iron(II1) in aqueous solution is increased if methanol is added (226). Factors affecting the kinetics of ligand substitution reactions of a number of metal ions are being evaluated in a range of organic solvents by stopped-flow or temperature-jump spectrophotometry. For example, a study of the reactions of nickel(I1) and cobalt(I1) with pyridine, bipyridine, phenanthroline, and related ligands in acetonitrile, indicated that a modified dissociative mechanism with outer-sphere stabilization of the transition state is involved (43). EXPERIMENTAL TECHNIQUES Because nonaqueous titrations generally are affected by exposure to atmospheric water, carbon dioxide, or oxygen, and by solvent volatility, improvements in titration systems are always of interest. Automatic digital titrators, often controlled by a minicomputer, are finding use both in routine and developmental work (96, 102, 174, 193) and, in the future, microprocessors will make these instruments even more flexible and less expensive (18). Improvements in the design of motor-driven microburets (79) and of reference electrode junctions (159), and a procedure for gravimetric calibration of microsyringe volumes (132) were reported. The development of more sensitive and precise titration calorimeters (89), together with past advances in enthalpimetric titration devices, should prove useful in many nonaqueous systems where the heat capacity of the solvent is low, and the corresponding temperature changes upon chemical reaction are relatively large. A variety of new electrode materials have been studied. These include fluorographite (216), graphite-Teflon (108), pyrolytic graphite, carbon and graphite fibers, and natural graphite (214) for electrochemical studies, and palladiumhydrogen (103), oxidized vitreous carbon ( 6 1 ) ,aluminum, gallium, silicon, germanium, and antimony (80) as indicating electrodes in nonaqueous acid-base titrations. Biamperometric indicating systems consisting of a pair of tin (70) or bismuth (225) electrodes also have been used for end-point detection in acid-base reactions, as have polarized quinhydrone electrodes (219). Ion-selective electrodes are beginning to be used in nonaqueous media, and will undoubtedly become more important. For example, in the potentiometric titration of thiols by precipitation with silver(1) using a silver sulfide single crystal electrode (I 76), precipitation of silver hydroxide ANALYTICAL CHEMISTRY, VOL. 48, NO. 5, APRIL 1976
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can be avoided by titration in an ethanol-benzene solvent mixture. Sulfate was titrated potentiometrically in 60% dioxane with lead perchlorate a t a lead ion-selective indicating electrode (195). A sodium-selective glass electrode also functions as an indicating electrode for the potentiometric titration of sulfate in 70:30 acetone-water with barium chloride (3). The potential break at the end point arises from response of the electrode to barium, and increases with increasing acetone concentration because of the decreased solubility of barium sulfate. A chloride homogeneous membrane ion-selective electrode was employed as indicating electrode for the potentiometric titration of chloride salts in water-isopropanol mixtures 10 to 100% in isopropanol (105), and for direct potentiometric measurements in pure aliphatic alcohols (120). Single-crystal chloride-selective electrodes were also studied in the lower aliphatic alcohols, acetone, dimethylformamide, and their mixtures with water (104). Potentiometric titration curves showed larger potential changes at the equivalence point as the concentration of organic solvent increased. A thiocyanate-selective membrane electrode showed a similar response in mixtures of water and dioxane, ethanol, acetone, dimethylformamide, and dimethyl sulfoxide (213). Variations in potential of the lanthanum fluoride membrane electrode when used as a reference electrode in water-acetonitrile mixtures can be predicted from differences in solubility of the membrane materials as a function of the solvent composition (208). Complex formation between lithium ion and various solvents as ligands was studied in acetonitrile by use of a cation-sensitive glass electrode (163). The analysis of titration data also has received attention. General studies include computer analysis of titration data (97, 143) and computation of end-point errors when using Gran or second-derivative plots (6, 33, 154). Relationships that define conductometric and high-frequency acid-base titrations in nonaqueous solvents (87), and that allow calculation of homoconjugation constants from titration curves (210) have been derived. Equivalence-point detection for new applications is turning more and more to potentiometry, although visual indicators and polarized electrode systems are still widely used. A review on indicators for nonaqueous acid-base titrations has been written (68). Acidity constants for a series of indicators in acetonitrile (190) and in benzene (199) have been measured, and the suitability of several indicators in acetic acid, acetic anhydride, and acetic anhydride-chloroform mixtures has been surveyed (180). The color changes of the indicators were strongly influenced by impurities in chloroform. Nitrophenoxazines are recommended as indicators for the titration of weak acids with tetrabutylammonium hydroxide in acetonitrile because they show no homoconjugation in this solvent (209). Hessian Bordeaux, 4,4’-bis(4amino-l-naphthylazo)-2,2’-stibenedisulfonic acid, is proposed as a new indicator replacing the carcenogenic dimethyl yellow in the determination of organic acid anhydrides by the morpholine method (189). An interesting method of end-point location has been developed in which the heat of ionic polymerization of acrylonitrile or ethylvinylether, initiated by excess titrant, is detected thermometrically (81-83). The method has been applied to the determination of weak acids (81, 84), bases and water (83), thiols (82), and alkyl dithiocarbonates and metal iodides (851. Bis(l-butyl-2,6-dimethyl-4-pyridone)perchlorate has been suggested as a primary standard for nonaqueous acidbase titrimetry ( 4 ) . It can be used for the standardization of both acids and bases because it consists of 2 mol of base associated with 1 mol of perchloric acid; also, it is highly soluble in many organic solvents. This compound and the similar antipyrene perchlorate, proposed as a standard by Busev in 1968,both exist as the monohydrate at room temperature. The water of hydration is removed on drying under vacuum at 60 “C for 24 h, but the dried material is hygroscopic. The thermal stability of both compounds and their suitability as acid-base standards in a variety of solvents, have been studied (161). METHODS A N D APPLICATIONS Acids. Dimethylformamide, methanol, and acetone continue to be popular solvents for the titration of weak acids, 358R
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with quaternary ammonium hydroxides the most widely used titrants. Potassium tert- butoxide in 1:l tert- butanolbenzene is recommended as a titrant because it is readily prepared, stable, and convenient (64); to show its versatility, a variety of acids were titrated in dimethylformamide. N,N’-Diacylhydrazines were titrated in dimethylformamide with tetrabutylammonium hydroxide in a tert- butanolisopropanol-benzene mixture (65). o -Nitroaniline or 2-nitrodiphenylamine are suitable indicators for the method which is useful in monitoring peptide synthesis. Imido-oximes in dimethylformamide can be titrated potentiometrically with the same titrant (181), as can mixtures of acetylsalicylic acid, acetaminophen, and salicylamide (185).Lithium hydroxide in dimethylformamide was used for the potentiometric differentiating titration of mixtures of salicylamide and paracetamol ( 2 ) . The halides of aluminum, gallium, indium, thallium, zinc, bismuth, antimony, and arsenic all behave as acids of varying strength in alcohols, ketones, and dimethylformamide, and can be determined in mixtures by differential potentiometric titration with potassium hydroxide in isopropanol (124-126, 155). The halide, nitrate, and perchlorate salts of the alkaline earth metals in the same range of solvents could be titrated (156).Rare earth iodides were titrated similarly in acetone (127). Acidities increase with increasing atomic number, but the differences are not great enough to allow differential titration. A glass indicating electrode was used. Long-chain alkyl phosphates were studied in several solvent systems. Monoalkylphosphates act as dibasic acids in pyridine but the second acid group is not easily titrated (117). In ethanol, they also are dibasic, but are monobasic in methanol. Mixtures of monoalkyl phosphates in methanol titrate together to give a single break, but it is not quantitative unless about 10%water is present. Analysis of dialkyl phthalates for sulfuric acid, monoalkyl sulfate, phthalic anhydride, and monoalkyl phthalate was done by differential potentiometric titration in acetone with morpholine in methanol to determine sulfuric acid and monoalkyl sulfate (218). Titration of a second sample in methanol with potassium hydroxide in a mixture of ethanol and methanol gave two potential jumps, the first corresponding to the sum of sulfuric acid and monoalkyl sulfate, and the second to the sum of phthalic anhydride and monoalkyl phthalate. Methyl ethyl ketone, methyl butyl ketone, and methyl isobutyl ketone were evaluated as solvents for the differential titration of mixtures of mono- and dicarboxylic acids (131). All are sufficiently aprotic to be useful for the titration of extremely weak acids, while still permitting differential titration of acid mixtures. The autoprotolysis constants of methyl ethyl and methyl butyl ketone were determined to be 10-25.5 and 10-25.0. Tetrafluoroboric acid was titrated with piperidine dissolved in acetone (224). Either potentiometric or visual indicator end-point detection could be used. N-Methylpyrrolidone and acetone are both suitable solvents for the high-frequency titration of mono- and dicarboxylic acids (9). The use of N-methylpyrrolidone as a solvent for the potentiometric titration of sterically hindered phenols and bisphenols with tetraethylammonium hydroxide allowed differential titration of several binary mixtures (119). 3-Methyl-2-oxazolidone was investigated as a solvent for the titration of carboxylic acids and phenols (215). It has a wide liquid range, a high dielectric constant (77.5 vs. 78.3 for water) and a potential range of a t least 0.8 V for acid-base work. Among the compounds titrated with tetrabutylammonium hydroxide were barbiturates and sulfa drugs (56). rn-Cresol is recommended as a medium for the coulometric titration of acids having pK, values as small as 13 (28). The hydrochlorides of tetracycline and chlorotetracycline can be titrated either as acids in dimethylformamide with sodium methoxide in benzene-methanol, or as bases in 3:l acetic acid-benzene with perchloric acid in dioxane (182, 183). An indicator titration method for the simultaneous determination of an anhydride and its parent carboxylic acid in binary mixtures has been described (140). Mixtures of isomeric aminobenzenesulfonic acids can be determined by differential potentiometric titration in ace-
tonitrile with potassium hydroxide (130). Bases. Nitrogen-containing heterocyclic compounds and thioesters, normally too weakly basic to be titrated with perchloric acid in glacial acetic acid, can be determined through formation of a mercury(I1) acetate complex prior to titration (146).The mechanism is postulated to be 2B + Hg(0Ac)n HgBg(0Ac)n
+ 2HC104
+
-
HgBn(0Ac)n
2HOAc
+ HgB2'+(C104-)~
Kadin (101) observed that traces of acetic anhydride or acetaldehyde in the acetic acid titration solvent affected the ability to titrate primary aromatic amines with perchloric acid. The recommended solution to the problem is a change to a nitrite titration using ferrocyphen indicator. Use of m-cresol as solvent for the coulometric titration of weak bases has been investigated and found satisfactory (28).Amounts on the order of 5 pequiv can be determined with a relative error of fl%.About 1 wt % of water in acetonitrile is sufficient to stabilize solutions of perchloric acid, which can then be used as a medium for the titration of weak bases (221). Mixtures of long-chain tertiary amines and quaternary ammonium thiocyanates were analyzed by extraction of the amine and the quaternary ammonium ion as the iodide into toluene, adding acetic acid, and titrating the free amine with perchloric acid to a crystal violet end point (22).Then mercury(I1) acetate is added to form undissociated mercury(I1) iodide and the acetate released, which corresponds to the salt present, is titrated to the same end point. Removal of thiocyanate is necessary because, being the conjugate base of a weak acid, it is protonated along with the amine in the first titration. Molybdenum can be determined in the presence of tungsten by potentiometric titration of the molybdenum complex of 8-hydroxyquinoline as a diacidic base in 4:l acetic acid-acetic anhydride with perchloric acid (121). The corresponding tungsten complex is not sufficiently basic to be titrated. By careful variation of solvent composition, it is possible to perform differentiating potentiometric titrations with perchloric acid in dioxane or 4:l dioxane-acetic acid of a number of drug mixtures containing codeine phosphate (196). When sodium salts of benzoate, phenobarbital, or barbital are the second component, 1:l acetic acid-dioxane is best; with aminophenazone, propionic anhydride is recommended; with caffeine, 4:l dioxane-acetic acid; and with phenacetin, 3:lO:lO propionic acid-propionic anhydridebenzene. The inclusion of formic acid in the solvent mixture used for the titration of the hydrochlorides of tetracycline and its derivatives with perchloric acid was found to inhibit oxidation of the tetracyclines by mercury(II), which is added to eliminate interference by chloride (90). A 1:2:2mixture of formic acid, acetic acid, and dioxane is suggested. Use of 1:l chloroform-acetic acid as solvent for the titration of methaqualone in its dosage forms with perchloric acid eliminates interference from additives (42).Either visual or potentiometric end-point detection is satisfactory. Some mixtures of sulfanilamides can be determined by differential potentiometric titration in acetonitrile with perchloric acid in isopropanol (129).Other mixtures were titratable as acids by the same workers in a similar way with potassium hydroxide in isopropanol. An unusual method for the determination of alkali metal nitrates is based on conversion of the nitrate salt to the formate by heating with formic acid, then titrating the formate with perchloric acid in a medium of 1:l acetic anhydride-acetic acid (212). Oxidation Reduction. Several reductants have been investigated as analytical reagents. Tin(I1)-chloride reactions with iron(III), manganese(VII), copper(II), and iodine in acetonitrile, pyridine, acetic acid, acetylacetone, and acetone were studied potentiometrically (152). Complex formation has a significant effect on the shape of the titration curves. Solvents with a low dielectric constant show a leveling effect toward ligands, but those with a higher dielectric constant tend to differentiate between ligands. Sulfur and organic disulfides in hydrocarbon solvents are reduced quantitatively to hydrogen sulfide and thiols by sodium aluminum bis(2-methoxyethoxy)dihydride, and
then can be titrated with sodium o-hydroxymercuribenzoate (229).This reductant is commercially available, and is reported to be active, stable, and convenient to use. By masking the thiols through reaction with acrylonitrile, hydrogen sulfide can be determined alone. Vanadium(I1) and molybdenum(111) have been employed as reducing agents in ethanol and acetone for 1-nitroso-2-naphthol,dimethylglyoxime, dipicrylamine, and the corresponding cobalt, nickel, and potassium complexes, as well as the cupferron complexes of titanium, vanadium, and zirconium (73).The excess reductant is titrated with iron(II1). Either the metals or the organic reagents can be determined by this method with a relative error of less than 0.4%. Azo dyes can be determined by potentiometric titration in a glycerol-dimethylformamide mixture with a formate complex of titanium(II1) (191). In aqueous-organic solvent mixtures, ferrocene quantitatively reduces several metals. Molybdenum in steel and alloys has been determined by amperometric titration with ferrocene in water-acetone (205), and by potentiometric titration in water-ethanol (231) and water-acetic acid-ethano1 mixtures (232). Vanadium(1V) in steels and alloys also was titrated with ferrocene in a 1:l water-ethanol medium (203). Phosphorus in steel can be estimated indirectly by extraction as the molybdophosphate complex and amperometric titration of the molybdenum(V1) with ferrocene in a solvent mixture of water, acetone, and isobutyl alcohol (204). Chromium, iron, and nickel do not interfere, and amounts of phosphorus as low as 1 pg can be estimated within f5%. Procedures for the determination of iron(II1) (202), antimony(V) (206), and rhenium(VI1) (201) also have been worked out. A number of applications of iodine and bromine compounds in nonaqueous solvents have been made. Among the more interesting reactions is the determination of oxalate by oxidation with iodine in carbon tetrachloride (207). The iodide produced then is determined by reaction with excess iodate in sulfuric acid or, if chloride is present, in benzyl alcohol. The scope of iodosobenzene diacetate ( 1 77) and iodobenzene dichloride (162) in glacial acetic acid as new oxidizing agents has been surveyed. Among the substances determined were ascorbic acid, phenol, aniline, and 8-hydroxyquinoline. Bromine cyanide, BrCN, was used for the potentiometric determination of a variety of inorganic and organic substances, including sulfide, sulfite, iodide, thiocyanate, and hydrazines in acetic acid and acetic acidacetic anhydride mixtures ( 173). Thioureas could be titrated in methanol, and dithiocarbamates in ethanol and acetonitrile. Phenols can be determined with 2~0.25%relative error in acetic acid or acetic acid-acetic anhydride mixtures by substitution upon potentiometric titration with BrCN or ICN (170).Xanthates and dithiocarbamates can be oxidized quantitatively with iodine monobromide in acetonitrile (222). Thioureas do not interfere and, if present, can be determined also by addition of aqueous acid a t the end point, followed by titration of the thiourea to a second end point. Dimethylformamide can also be used as solvent (223).Tetraphenylboride can be titrated in 9.55 methanolacetic acid with 4,7-dichloroquinoline bromide perbromide (192).Two bromine atoms are taken up rapidly per molecule of tetraphenylboride. Solutions of potassium triiodide in hexamethylphosphotriamide are stable and convenient for the determination of ethylmagnesium bromide or diethylmagnesium (72).An excess of KI3 is added and the excess titrated with thiosulfate. Water in the triiodide titrant must be taken into account. Arsenic(II1) in organic compounds can be titrated potentiometrically or conductometrically in anhydrous methanol with iodine (168), as can triphenylantimony in methanol, ethanol, or methanol-acetic acid mixtures (167). Chlorine, bromine, iodine, iodine monochloride, and nitrosyl chloride have been investigated as oxidizing agents in acetic anhydride for the preparation of compounds formed on the oxidation of arsenic(III), antimony(III), and phosphorus(II1) (145). The sodium-anthracene complex in tetrahydrofuran reacts quantitatively with monohydric alcohols, monobasic acids, ketones, and anhydrides in a 1:l ratio (165).All the above compounds can be determined by conductometric titration. As mentioned elsewhere, this reagent is also applicable to the determination of water, and water is recomANALYTICAL CHEMISTRY, VOL. 48, NO. 5, APRIL 1976
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mended for standardization of the reagent. The titration error is f5%. Modifications of this system should be worth study. For example, polarographic investigations of the reduction of 9-nitro- and 9,lO-dinitroanthracene in dimethylformamide indicate that the first forms a radical anion and the second a dianion, both of which pair with alkali metal cations (107). Coulometric generation of polyaromatic anions may provide useful analytical applications. A procedure for the preparation of anhydrous solutions of chromium(I1) chloride through treatment of chromium metal with gaseous hydrogen chloride in tetrahydrofuran yields isolatable white CrClYTHF (136). This convenient method may lead to increased use of chromium(I1) as an analytical reductant in aprotic solvent systems. Determination of Water i n Solvents a n d Solutes. Karl Fischer reagent for water determination has changed little over the years despite many studies. A chapter in a book on moisture determination provides a relatively complete and critical discussion of Karl Fischer titrations (169), and a detailed study of the effects of storage and the nature of the storage container on moisture content of transformer oils by Karl Fischer reagent has been made ( 7 4 ) . Replacement of pyridine with sodium acetate is reported to give a more stable reagent (198). End-point detection remains a problem; a comparison of amperometric and potentiometric methods (39) showed greater precision for the potentiometric method, along with faster titration times. Coulometric generation of iodine is convenient, but the reagent composition must be optimized (38, 157, 230). The mechanism and kinetics of the coulometric approach have been investigated (12), and an automatic coulometric titrator constructed (158). Use of Karl Fischer reagent to determine substances other than water has also been reported; a number of low-valent metals and their phosphine derivatives are oxidized quantitatively (30). Organic nitro compounds can be reduced to the corresponding amines by electrochemically generated Tic13 in dimethylformamide and the water formed titrated (109). Also, a method for Tic14 has been developed based on the need for free pyridine to be present before iodine will react with water. In the presence of TiC14, pyridine forms a stable 2:l complex. When an excess of pyridine is present, the iodine reacts with water and the free iodine color disappears (63). A gas chromatographic method for determining water in ketones (141), and a method for water based on conversion of lead(1V) acetate to lead(1V) oxide in dimethylformamide, acetonitrile, or isopropyl alcohol (40) have been recommended. Alkali metal complexes with polycyclic hydrocarbons, such as the sodium-anthracene complex in tetrahydrofuran, can be used to titrate the water present in such materials as aliphatic amines, pyridine, and dimethylformamide (164). The high conductivity of the titrant solution makes end-point detection by conductance change the method of choice. The sensitivity of the method is 0.01 to 0.02% absolute moisture, and the relative error is about 3%. Miscellaneous Applications. Ketones and aldehyde-
LITERATURE CITED (1) Agrawal, Y. K., Talanta, 20, 1354(1973). (2) Agarwai, S. P., Walash, M. I., lndian J. Pbarm., 36, 47 (1974): Chem. Abstr., 81, 158724 (1974). (3) Akimoto, N., Hozumi, K.. Anal. Cbem., 46, 766 (1974). (4) Alessi, J. T., Bush, D. G., Van Allan, J. A,, Anal. Cbem., 46, 443 (1974). (5) Alfenaar, M., J. Pbys. Cbem., 79, 2200 (1975). (6) Anfalt. T.. Jaaner. D.. Anal. Chem., 45, 2412 (1973). (7) Arnett, E M I Acc. Cbem Res, 6, 404 11973) - -, (8) Arnett. E. M., Small, L. E., Mclver, R. T., Jr.. Miller, J. S..J. Am. Cbem. SOC.,96, 5638 (1974). (9) Azarova. L. N. Vasyutinskii, A. I., Zb. Anal. Khim., 29, 1831 (1974); Cbem. Abstr., 82, 38268 (1975). (10) Badoz-Lambling, J., Bardin. J. C., Electrocbim. Acta, 19, 725 (1974); Cbem. Abstr., 82, 65151 (1975). I
360R
ketone mixtures have been analyzed by direct oximation in isopropanol with hydroxylamine hydrochloride in pyridineisopropanol as titrant (27).An amperometric end-point detection system using two copper electrodes was employed. From 5 to 20 mg of ketone could be determined with a relative error on the order of 1%.Binary mixtures of aldehydes and ketones give two end points, the first corresponding to the aldehyde and the second to the ketone. Carbonyl compounds were determined in isopropanol by addition of excess hydroxylamine hydrochloride and a known excess of morpholine (86). The liberated hydrochloric acid reacted with morpholine, and the excess base with titrated potentiometrically with perchloric acid in dioxane. Calcium and magnesium were determined in mixtures by potentiometric titration with EGTA of calcium only at pH 8.5 to 9 in water, then making the solution 70 to 80 vol. % in ethanol and titrating the magnesium at pH 10 with EGTA (228). An amalgamated silver wire was used as the indicating electrode. Manganese was titrated in 1:l methanolwater at pH'9.8 with EDTA (67) and excellent precision and accuracy were obtained. 8-Hydroxyquinoline and its 5,7-dihalo derivatives in mixtures of propanol, butylamine, or dioxane were titrated with copper or zinc nitrate in dimethylformamide (128). Photometric end-point detection was used. Titrations with zinc show only one break, but those with copper show two, corresponding to 1:l and 1:2 copper-chelate complexes. Tributylphosphate, tributylphosphine oxide, and dihexyl sulfoxide can be titrated witK tin(1V) chloride or bromide or titanium(1V) chloride as Lewis acids in anhydrous 1,2-dichloroethane with malachite green as indicator (188). An unusual titration based on the formation of ion pairs between barium ions and Cr042-, MOO^^- or HW04- in 9:l acetone-water has been reported (122). A spectrophotometric end point using Nitchromazo at 650 nm was found satisfactory. Zirconium and hafnium could be determined by titration in the same way of the ZrFs4- and H ~ F Bcom~plexes in 1:l acetonitrile-water to form Ba2MFs ion pairs (123).Molybdenum and tungsten can be masked with hydrogen peroxide. MISCELLANEOUS Procedures for the purification of propylene carbonate were compared through analyses by gas chromatography and ultraviolet spectrophotometry, and through measurements of electrical resistivity ( 5 7 ) .Water and propanediol influence the high voltage conduction of propylene carbonate only at high concentrations. A method for the estimation of acetaldehyde in glacial acetic acid by gas chromatography is sensitive down to a part per million (184). ACKNOWLEDGMENT The assistance of V. Melnychuk in the preparation of this review is gratefully acknowledged.
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X-Ray Diffraction C. E. Pfluger Department of Chemistry, Syracuse University, Syracuse, N. Y. 132 10
This review presents a general overview of the field of x-ray diffraction with emphasis being placed on the directions in which applications and research in the areas of instrumentation, analysis, powder methods, topographic methods, determination of molecular structure, etc., have been going, rather than presenting a comprehensive listing of all references in which x-ray diffraction was utilized. To do so would have been a formidable task as the use of x-ray diffraction methods in solving problems in chemistry, materials science, geology, industry, etc., is extremely widespread, as becomes obvious after even a rather superficial scan of the literature. This review covers the period of January 1974 through December 1975, mainly by the appearance of an abstract during this time, although several journals were independently scanned. It is sincerely hoped that 362R
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no work of new and fundamental importance has been omitted. The year 1975 marked the death of William Coolidge, several months after his lOlst birthday. Society owes Dr. Coolidge a debt of gratitude as it was the results of his fundamental research on making tungsten ductile which made possible his invention of the hot-cathode x-ray tube which bears his name, launched an electronics era based on the electron tube, and revolutionized the lamp industry. A number of books dealing with various aspects of x-ray diffraction have appeared during the last two years; however, those books dealing with a specific area of x-ray diffraction will be mentioned in those sections discussing these areas. Likewise, a rather large number of review articles have appeared, each dealing with a specific field or
