Recent Developments in Titrimetry Papers presented at the Seventh Annual Summer Symposium sponsored by Division of Analytical Chemistry and AnaZgtz iCuZ C h r n i e t r g , Minneapolis, Minn., June 1 8 and 19, 1954
Current Status of Analysis by Titration PHILIP J. ELVING University o f Michigan, A n n Arbor, Mich.
Despite, or perhaps because of, our advances in analytical instrumentation, titrimetric methods of analysis seem to be increasing in value and in use. Titration itself is fundamentally a process in which a solution of known reactivity or chemical equivalency in respect to the desired constituent is added to a sample containing the latter until all of the desired constituent present has reacted. Titration consequently requires four items: satisfactory reactions, titrants of known reactivity, means of measuring the amounts of titrant used, and ways of detecting the equivalence point in the reaction. This is illustrated by the titrimetric determination of calcium in lead alloy by the addition of standard 1%antimony-lead pellets. Current trends in development and application dong the four areas indicated are briefly reviewed. Some of the possibilities of titration in nonliquid systems are indicated.
I
N T H E contemporary extensive application of instrumentation to analytical methods and techniques, there is a tendency on the part of some chemists to regard as old-fashioned those approaches to chemical methodology symbolized by the expression, “test tube and buret.” However, the process of measurement by titration which the buret symbolizes is still a flourishing solution to analytical problems. The scope and use of the buret or its equivalent are actually increasing, rather than decreasing. This is largely due to the inherent advantages of measurement by titration: simplicity, rapidity, possible specificity, and wide applicability and adaptability. The analytical operation of titration has been greatly favored in recent years by a more comprehensive view of the chemistry of the titration reaction and by the instrumentation of the process itself. The former has resulted in the development of new titrants and accessory reagents, and in a more considered use of media for titration, while the latter has increased the means of detecting the equivalence point and has indicated the possible complete automatization of the titration process. There is increasing awareness that water is not the only medium for titration and that even a liquid-liquid reaction system is unnecessary. Recent reviews of titrimetric methods of analysis have included those applicable to inorganic determinations by Rodden and Goldbeck (81, %), and to organic substances by Smit,h, Shriner, and coworkers (83-85). The standard reference work in English by Kolthoff and Furman (21) is being revised by Kolthoff and Stenger (88). The basic principles of electrometric methods are reviewed in Lingane’s monograph (24). The extended use of 1676
electrochemical analytical methods has been briefly reviewed by Cruse (6). A sizable volume (26) appeared in 1948 devoted to the use and applicability of one titrimetric solution, the Karl Fischer reagent. Another extensive monograph (8) covered the use of organic reagents in gravimetric and titrimetric analysis. NATURE OF A TITRATION
I t will be useful in surveying the current trends in titrimetric methods of analysis to consider exactly what is implied in such an analytical situation; an attempt must first be made to answer the questions of what is done and what is required in a titration. Operationally, we have a solution containing a sample of the desired constituent, which solution may be the result of certain preliminary treatments necessary to prepare the desired constituent or its equivalent for reaction with the titrant. The titrant is usually added to the sample solution from a buret until the completion of reaction of the constituent to be measured with the added titrant is detected. Essentially, a measurement has been made which is based on chemical reactivity; from the amount of titrant used and its equivalencv to the desired constituent, the amount of the latter present can be calculated. The operation of titration consequently presupposes four necessities: (1) a satisfactory reaction between the constituent to be measured and the titrant-e.g., a reaction which is rapid, reproducible, and complete; (2) a titrant of known reactivity or chemical equivalency in respect to the desired constituent; (3) a means of measuring the amount of the titrant used-e g., a buret; and (4)a suitable means of detecting the equivalence point-Le., the stage a t which a stoichiometric or empirically reproducible reaction between titrant and constituent has occurred. Obviously, the first, second, and fourth items are usually interrelated and cannot often be considered separated from each other. The essential nature of the four items is well emphasized in a procedure developed for the determination of calcium in lead, which is an enlightening example of the versatility of the titration approach to analytical problems. This procedure is worthy of consideration in some detail, as it seems to be virtually unknown to analytical chemists. TITRATION OF CALCIUM IN LEAD ALLOYS
The situation demanding analysis arose in connection with the development of a lead alloy suitable for the long-life stand-by batteries needed in telephone systems, and is best described by BOUton and Phipps ( 4 ) , who devised the successful analytical 8 0 1 ~ tion:
V O L U M E 2 6 , NO, 11, N O V E M B E R 1 9 5 4 Lead-calcium alloys were suggested for use as storage battery grid material some years ago, but commercial development has been retarded seriously by the difficulty of calcium control. While the limits of calcium content are rather broad, they must be adhered to, since an excess of calcium causes rapid growth of the positive plates and too little calcium is accompanied by inferior physical properties. Using chemical methods, hours of skillful analytical work are required to determine the calcium content of a melt prior to casting, and further hours are needed to determine the rate of change of calcium content as casting proceeds. A method will be described in this paper wherqb calcium determinations can be made “on the spot” with hlgg accuracy, by personnel unskilled in analytical methods, in a matter of minutes. This procedure eliminates calcium control difficulties and removes a major obstacle to commercial fabrication of lead-calcium storage batteries. Analytical Solution. The method devised involved an imaginative solution based on the general nature of a titration. The reaction utilized was the fact that calcium and antimony form a solid phase insoluble in lead. The phase has a composition approximating Sb7Cas. The titrant n-as a lead alloy containing 1% of antimony. The titrant was measured by molding the antimony-lead alloy in pellets of known weight, so that actual measurement simply involved counting the number of pellets added to the sample. The detection of the equivalence point in the reaction depended upon the striking differences in surface appearance of lead alloy containing very low percentages of calcium. Lead containing 0.004% calcium exhibits a brilliant luster equivalent to that of a Inercury pool, which appears dark under oblique illumination ewrpt a t the edges. Lead containing 0.008% calcium has a suifnce which is almost completely covered by a gray film, while lend containing 0.006% calcium has an appreciable gray film on the surface. Procedure. Known amounts of sample are removed from the manufacturing kettle using ladles which hold a definite volume of sample. Varying numbers of pellets corresponding to the range of calcium content expected are added to the different ladles and the mixtures are stirred for a few seconds. The contents of the ladles are chilled by being poured into molds and the surface appearances are noted; the end point is taken to be a faint trace of gray corresponding to an untitrated calcium residual of 0.005%. The calcium percentage is then read from the linear calibration curve between amount of antimony added -1 e., number of pellets-and per cent of calcium. The preckion is within &0.002% in the range up to 0.11% calcium; the method is applicable in the range of 0.005 to 2% calcium. This method may well serve as the prototype for the development of other methods of nonferrous alloy analysis, based on the euistence of the numerous intermetallic compounds described iri the literature. CURRENT TRENDS IN TITRIMETRY
Contemporary developments and trends in measurement by titration can now be considered on the basis of the prerequisites for a titrimetric procedure. No attempt has been made to be all-inclusive, but dominant features and promising lines for future rrsearch are stressed. REACTIONS
Neutralization Titration in Nonaqueous Medium. Non:tqueous media have long been used in titration. especially in the determination of acidity in oils. The important change in recent years in the use of such media has been the recognition of the possibilities inherent in the use of so-called nonreactive and reactive media t o enhance and to differentiate degree of acidity. Although the study of superacidity by Conant, Hall, and others served to make chemists aware of the use of media of different degrees of acidity, the revelation of the analytical possibilities apparently date from the 1948 paper in ANALYTICAL CHEMISTRY by Moss, Elliott, and Hall ( 2 7 ) on the use of ethylenediamine as a solvent for the titration of acids. The general area of acidbase titration .in nonaqueous media has been outlined by Fritz in a recent monograph ( 9 ) , and current developments have been reviewed by Riddick ( 2 9 ) .
1677 This topic, because of its importance in contemporary analytical chemistry, has been carefully considered in the present symposium on titrimetry. The important topic of the interpretation of the data obtained in measurements made in nonaqueous media is considered by Grunwald (IS) with emphasis on the evaluation of potentiometric data. Although there are still some who feel that it is enough if a specific analytical method works, most analytical chemists would prefer to be able to identify the physical basis for their data in order the better to evaluate the limitations and applicability of the method. The pressing problem of the selection of the medium for a particular titration is discussed by Fritz ( I O ) ; such a choice is often the pivotal factor in the development of a new analytical procedure. The amazing development in the last few years of titration in nonaqueous medium is well emphasized by the discussions of the general applicability of such titration by Riddick (SO) and of the more specific applicability to pharmaceuticals by Wollish, Pifer, and Schmall (36). It would seem worth while to investigate other types of titrimetric reactions in nonaqueous media. In particular, the use of complex-forming solvents, such as formamide and ethylenediamine, may aid in securing specificity in redox, precipitation, or complexation titrations. Mechanism of Redox Reactions. Oxidation-reduction reactions have long been used as the basis for titrimetric methods of analysis. However, their extensive applicability and general usefulness have been occasionally marred by the presence of undesirable error-producing side reactions. This situation is being improved by the increase in our knowledge of the nature of oxidation-reduction reactions through the studies of the mechanisms and kinetics of redox reactions by Duke, Kolthoff, and others. One particularly interesting area is that of the mechanism of induced reactions-Le., of a reaction between a substance preeent in the solution and the titrantwhich occurs only when a desired reaction between another substance in the solution and the titrant occurs. Kolthoff (20)has presented a detailed account of the general cause and mechanism of such reactions. TITRANTS
Obviously, the introduction of new reactions for titrimetric measurement may involve the simultaneous introduction of new standard titrants or the popularization of heretofore infrequently used reagents-e.g., the increased use of sodium methoxide and of perchloric acid as standard reagents in neutralization titrationin nonaqueous media. One of the more influential developments in titrimetry has been the increased use of complexation and precipitation methods of titration due to the introduction of versatile chelating agents which can be more or less readily modified to accomplish specific objectives. The outstanding example is probably ethylenediaminetetraacetic acid and its salts and derivatives, the introduction of which has revolutionized the analytical chemistry of calcium and magnesium, and has had a profound influence on the analytical chemistry of many other metallic elements. In addition to use as titrants, such chelating agents have been of tremendous help in increasing the specificity of titration methods by their ability to serve as masking agents or sequestrants fof ions that might interfere in the desired reaction. The use of chelating agents in titrimetric methods of analysis is reviewed by Martell and Chaberek ( 2 5 ) . MEASUREMENT OF THE TITRANT
The developments in the measurement of the titrant have been relatively few, except for a considerable number of ingenious solutions to the problems of the mechanical addition and measurement of volumes of the order of a few microliters or less of titrant. Such devices are well described in Kirk’s monograph ( 1 7 ) on ultramicromethods.
ANALYTICAL CHEMISTRY An outstanding development of tremendous importance for remote analytical work, as well as for the usual bench-type research and control analysis, has been the instrumentation of the addition and measurement stages of the titration. The basis for this development and its potentialities are well summarized by Carson’s review of automatic methods of titration ( 5 ) . Coulometric Titration. One influential development has been in the measurement of the titrant by measurement of the quantity of electricity required for the generation of sufficient titrant to react with the desired species or the equivalent measurement of the time required for generation of the titrant a t constant current flow. This approach to the means of introducing and measuring the titrant is the basis of coulometric titration, in which the titrant is electrolytically generated a t constant current flow and the equivalence point is detected amperometrically, potentiometrically, or otherwise. The time required for titration is then a measure of the amount of reagent consumed. This technique obviously presupposes 100% current efficiency in the operation. In some cases the substance to be determined may be directly transformed by the passage of current, avoiding the need for a chemical titrant. Coulometric titration is well suited for the measurement of exceedingly minute amounts of material and for procedures involving automatic and remote control. For example, it has been used in an apparatus for the automatic determination of sulfur dioxide and other sulfur compounds in air. I n the Titrilog manufactured by Consolidated Engineering, a sample of air or other gas is periodically taken and analyzed for oxidizable compounds by titration with electrolytically generated bromine; the equivalence point in the titration is detected by a polarized electrode arrangement. The strip-chart recorder records the sulfur compound-e.g., sulfur dioxide-content of the air; other gases in air which react with bromine will obviously also be recorded as sulfur dioxide. By the use of preliminary absorbers and suitable bypass arrangements, several quantities can be recorded--e.g., total sulfur content, total sulfur less hydrogen sulfide, and total sulfur less hydrogen sulfide and mercaptans. Coulometric processes have been reviewed by DeFord ( 7 ), Furman (11), and Lingane (24). DETECTION OF EQUIVALENCE POINT
I n view of its importance, it may be worth while to attempt characterization of the equivalence point. I t is the stage in a chemical process a t which a stoichiometric or empirically reproducible reaction has been completed. The end point is some observable phenomenon which may be associated with the occurrence of the equivalence point, such as the change in color of the test solution or the appearance of an inflection point in the plotted record of an electrical property of the test solution versus volume of titrant added. I n the interests of precision and accuracy, it is most desirable that the end point and equivalence point coincide. End points may be based on any means of indicating the completion of a reaction-e.g., through observation or measurement of depletion of one reactant or of appearance of an excess of another reactant. I n general, any property of a solution may be used which exhibits a definite change a t the equivalence point. Added indicators are usually preferred because of the ’simplicity of visual end-point detection. However, under various more or less well-known conditions, indicator methods may be inconvenient, inaccurate, or perhaps even unavailable. Nonindicator methods of detecting the equivalence point are legion. Among the many types of titration which are readily recalled are the following: conductometric, potentiometric, amperometric, capacitimetric, radiometric, cryometric, calorimetric or thermometric, refractometric, viscometric, photometric or spectrophotometric, sonic, and stalagmometric. The essential difference in these types is in the means of equivalence-point detection.
Usually the most difficult part of any titration is to know vihen to stop. Recognition of some external feature, the socalled end point, which would hopefully coincide with the equivalence point, has been an important objective in analytical research for the past century. The development of acid-base and redox indicators to cover the usable range of equivalence-point pH and potential is familiar to all chemists, as is that of adsorption indicators for precipitation titrations. The increased application in the past half-century of electrical methods for following titration reactions has not only served to establish new means for end-point ascertainment, but has also been of inestimable value in helping to elucidate the nature of many reactions. Electrometric Methods. Although conductometric titration a t audio-frequencies is a t present but little used, a development of the past decade based on the use of megacycle frequency oscillator circuits seems to offer considerable opportunity, for investigation as a means of equivalence-point detection, especially in millimolar solution. Because the instrument response can by proper choice of oscillator circuit and sample cell be used to follow changes in capacity as well as in resistance, in which ionic concentration is a prime factor, the applicability to organic reactions involving nonionic species may markedly increase the types of reactions suitable for titrimetric measurement. .4n added potential advantage of the high frequency oscillator circuits is that insulated cells are commonly used-Le., the electrical connections are made to the outside of the cell rvith no contact between sample solution and electrodes. Critical reviews of the present state of our knowledge of megacycle frequency oscillators as applied to equivalence-point detection have been presented by Blaedel ( 2 ) and Hall (14, 15) and their coworkers, by Blake (S), and by Reilley and McCurdy (28) Currently, the most commonly used electrometric methods of equivalence-point detection involve potentiometric and amperometric techniques with a group of other techniques including various so-called polarized electrode methods, the “dead-stop” end point, etc. Kolthoff (19) proposes a classification of all these methods based on the presence or absence of current flow and on the number of indicator electrodes used. Such a clascification should not only remove ambiguity and confusion, but should result in a more rational and rewarding use of electrometric methods in titrimetry. Photometric Methods. Photometric detection of the equivalence point by following the change in radiant energy absorption has certain advantages in many cases-e.g., in slow or incomplete reaction in the region of the equivalence point. This heretofore only slightly used end-point technique is critically discussed by Goddu and Hume (12). Other Methods. Many physical properties other than those susceptible to electrometric or photometric measurement have been used to follow titrations and to locate the equivalence point. Obviously, any physical property m-hich, when plotted against the amount of titrant added, shows a change in slope or an inflection point a t the equivalence point is potentially a means of estimating end points. For example, thermometric measurement of the heat of reaction has been successfully used for a large number of analytical situations-e.g. ($3). The use of added internal indicator compounds is by no means a t an end. Some especially interesting work has been done on the development of redox indicators of high potential and of fluorescent indicators suitable for precipitation reactione. Iiolthoff (18) reviewed indicator development several years ago. TITRATION IN NONLIQUID MEDIA
Chemists almost inevitably associate titration with the addition of one liquid or solution to anothrr, although other systems are possible, as was exemplified in the method described for the determination of calcium in lead alloys. The present author believes that one profitable direction of investigation of titration
V O L U M E 2 6 , NO. 1 1 , N O V E M B E R 1 9 5 4 methods is that involving reaction in nonliquid-liquid systems. A provocative example of the possibilities is evident in the description by Katz and Barr (16) of gas-gas titrations, in which pressure is the value measured. The apparatus uses such currently available items as magnetic stirring, corrosion-resistant valves, and sensitive pressure-measuring devices. The technique is applicable to any sufficiently rapid gas reaction in which the number of moles of product gases differ from the sum of the moles of reactant gases. Among the reactions described by Katz and Barr are the addition of fluorine to paraffin mixtures for the determination of methane, the determination of olefins by titration with chlorine, and the titration of fluorine in gaseous snniples with ethylene. Another suggestive type of titration which has too long been overlooked by chemists is the titration of a solid with a gas. I n a series of phase rule studies on proteins, Bancroft (1) described the measurement of amino groups in a protein sample by adding hydrogen chloride gas to a sample container of constant temperature and volume. The steps in the resulting diagram of equilihrium hydrogen chloride pressure versus amount of hydrogen chloride added per unit mass of the solid indicated the number of different types of amino groups present as related to their relative base strength. Carboxyl groups in the same samples could be similarly titrated with dry ammonia gas. I t is readily apparent how such nieasurementq can be used to obtain valuable analytical information on various types of both solid and liquid samples, including complex materials such as natural products nnd polymeric substances.
1679 (8) Flagg. J. F., “Organic Reagents Used in Gravimetric and
Volumetric Analysis,” Kew York, Interscience Publishers, 1948. (9) Fritz, J. S., “Acid-Base Titrations in Nonaqueous Solvents,” Columbus, Ohio, G. Frederick Smith Chemical Co., 1952. (10) Fritz, J. S., ANAL.CHEM.,26, 1701 (1954). (11) Furman, N. H., Ibid., 22, 33 (1950); 23, 21 (1951). (12) Goddu, R. F., and Hume, D. N., Ibid., 26, 1679 (1954). (13) Grunwald, Ernest, I b i d . , 26, 1696 (1954). 114) Hall. J. L.. Ibid.. 24. 1236 (1952). (15) Hall, J. L., Gibson, J. A., Critchfield, F. E., Phillips, H. O., and Seibert, C. B., Ibid., 26, 835 (1954). (16) Kata, S., and Barr, J. T., Ibid., 25, 619 (1953).
(17) Kirk, P. L., “Quantitative Ultramicroanalysis,” New York, John Wiley & Sons, 1950. (18) Kolthoff, I. M., ANAL.CHEY.,21, 101 (1949). (19) Ibid., 26, 1685 (1954). (20) Kolthoff, I. M., Second .4nnual Anachem Conference, hssoci-
ation of Analytical Chemists, Detroit, Mich., May 3, 1954. (21) Kolthoff, I. M., and Furman, N. H., “Volumetric Analysis,” New York, John Wiles & Sons, 1929. (22) Kolthoff, I. M., and Stenger, V. -4.,“Volumetric A4nalysis.” Sew York, Interscience Publishers, Vol. I (1942). . . Vol. I1 (1947). Vol. I11 (in preparation). Linde, H . W., Rogers, L. R . , and Hume. D. N., h . 4 ~ C. m x . 25, 404 (1953). Lingane, J. J., “Electroanalytical Chemistry,” New York, Interscience Publishers, 1953. hlartell, A. E., and Chaberek, 8.. A s a ~ .CHEY., 26, 169% (1954).
lIitchel1, J., and Smith, D. 11.. “.%quametry,” New York, Interscience Publishers, 1948. lIoss, h1. L., Elliott, J. H., and Hall, R. T.. ANAL.CHEM.,20, 784 (1948).
Reilley, C. N., and McCurdy, R. H., I b i d . , 25, 86 (1953). Riddick, J. A , , Ibid., 24, 41 (1952); 26, 77 (1954). Riddick, J. A., Division of Analytical Chemistry, AMERICAN CHEMICAL SOCIETY, Seventh Annlytical Symposium, Minneapolis, Minn., June 18 and 19, 1954. Rodden, C. J., I b i d . , 21, 163 (1949); 22, 97 (1950). Rodden, C. J., and Goldbeck, C. G., Ibid., 24, 102 (1952). Smith, W.T., and Buckles, R. E., Ibid., 23, 66 (1951); 24, 108
LITERATURE CITED (1)
Bancroft, W. D., and Barnett, C. E., J . Phus. Chem., 34, 449
(1930). (2) Blaedel, W. J., llalmstadt, H. V., Petitjean, D. L., and iinderson, W. K., -4N4L. CHEM.,24, 1241 (1952). (31 Blake, G. G., “Conductometric iinalysis at Radio-Frequency,” London, Chapman & Hall, 1950. (41 Bouton, G. hl., and Phipps, G. S., Trans. Electrochem. Soc.. 92, 305 (1947). ( 3 ) Carson, W. K.,Division of Analytical Chemistry, AMERICAN
CHEMICAL SOCIETY, Seventh Snalytical Symposium, Minneapolis, Minn , June 18 and 19. 1954. ( G ) Cruse, IC,Angezc. Chem., 65, 232 (1953). ( 7 ) DeFord. D. D., ; 1 ~ 4 CHEJI., ~. 26, 133 (1954).
(1952).
Smith, W.T., and Shriner, R. L., I b i d . , 21, 167 (1949); 22, 101 (1950).
Smith, W. T., Wagner. W.F., and Patterson, J. h l . , I b i d . , 26, 155 (1954).
Wollish, E. G., Pifer, C. W.,and Schmall, Ll., Ibid., 26, 1704 (1954). RECEIVED for review July 29, 1954. -4ccepted August 6 , 1954.
7th Annual Summer Symposium-Developments in Titrimetry
Photometric Titration of Weak Acids ROBERT F. GODDU1
and
DAVID N. HUME
D e p a r t m e n t of Chemistry a n d Laboratory for Nuclear Science, Massachusetts Institute o f Technology, Cambridge 39, Mass.
Photometric titration for the determination of weak acids (or bases) which differ in light-absorption characteristics in the ionized and un-ionized forms has been studied both theoretically and experimentally. Satisfactory end points are obtainable only if the product of ionization constant and concentration is equal to or greater than at concentrations of 10-5iM and above. The titration of various substituted phenols is used to demonstrate the capabilities and limitations of the method in the determination of weak acids individually, in mixtures, and in the presence of strong acids. The photometric titration method has advantages over potentiometric methods w-hen determinations are made in highly dilute solutions and with very w-eak acids.
A
SY method for the determination of weak acids in aqueous
solution is limited in its scope by two fundamental requirements: r h e substance to be determined must be appreciably stronger than water as an acid, and the concentration must be appreciably larger than the concentration of hydrogen ions from the water. A number of authors ( 2 , 4 ) have estimated the limitations of the potentiometric method and their findings have been summarized by Kolthoff and Furman (.5). Rollpr (6) in particular has estimated that there will be an inflection point in the potentiometric of p H titration curve of a weak acid with a strong base only if the product of the concentration, C, and the ionization constant, K , is greater than 27 times the dissociation constant of water (about 3 X 10-13). Furthermore, for values of CK smaller than lo-” there is a significant difference between the inflection point and the true equivalence point which must be 1
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