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
Present address, Hercules Powder Co , Wilmington, Del
ANALYTICAL CHEMISTRY
1680 considered in addition to the very real uncertainty involved in the location of the already poorly defined inflection point. Because in a photometric titration, a property is determined which is directly, rather than logarithmically, proportional to the concentration of the substance being measured, i t was reasoned that a sharp break might be observed in those systems where the change in hydrogen ion concentration would ordinarily be too small. The high sensitivity of the photometric method makes it attractive a priori for the titration of very dilute solutions and the present work was undertaken to establish the general utility and accuracy of the method for the determination of weak acids aa well as the stringency of the fundamental limitations. THEORY
In order to predict the charactefistics of the photometric titration curves of typical weak acids, calculations were made using hypothetical compounds over a representative range of concentrations and dissociation constants. For convenience it was assumed that the hypothetical compound was colorless in the undissociated form and colored in the ionized or neutralized state.
Figure 2. Theoretical Photometric Titration Curves for Monobasic Acids of Various pK Values at a Concentration of 10-4M
The fraction ionized was computed by u-ell-known methods and plotted against the fraction already added of the strong base necessary for neutralization. The quadratic expression for the hydrogen ion was solved explicitly and suitable corrections for hydrolysis were made as necessary. The plot of fraction in the ionized form against added base is seen to be equivalent in form to the plot of absorbance against added base, assuming Beer's law to hold. I n view of the discussion (3) of the errors introduced by high absorbance measurements, it can be seen that limitations in accuracy derived from the fraction ionized curve are not removed by titration a t a higher extinction coefficient. The fraction ionized curve is a true indication of the inherent limitations of the method.
I n Figures 1 and 2 are shown the theoretical photometric titration curves for weak monobasic acids of various strengths a t concentrations of and M . Figure 3 shows how the titration curve of an acid of K A = 1 X 10-6 varies with concentration. It is seen from these curves that there is a limit to how strong a titratable acid may be as well as a limit to how weak. The liniiting factor in the first instance is the dissociation of the acid in the original solution: Clearly a strong acid could not be titrated, as it would be completely in the ionized form to begin with and no color change would take place during neutralization. On the other hand, the titration fails if the acid is so weak that the reaction is considerably short of completion a t the equivalence point or with 100% excess of titrant. On both accounts the scope of the method definitely decreases with decreasing concentration. A definite break can be located, as a rule, if the product CKA is equal to or greater than lo-** and the addition of reagent is carried 100% beyond the equivalence point. If CKA is no appreciable break is obtained even with a very large ewes8 of reagent. I n the titration of acids weaker than K A = 10-7, the points fall more and more below the initial straight line as the equivalence point is approached, thus tending to decrease the slope and give a high result. The incompleteness of the reaction after the equivalence point and even upon addition of excess reagent tends, however, to counterbalance the low slope prior to the equivalence point and thus brings the end point, which is taken as the intersection of the two straight lines, into good agreement with the equivalence point. I n the titration of such very weak acids, points taken near the beginning of the titration are of the most value in determining the slope of the straight line to be extrapolated for the end point. With highly dissociated acids, on the other hand, measurements close to the equivalence point should be used to determine the straight line before the end point. The most dilute solutions which can be titrated effectively would seem to be about 10-bM. At dilutions greater than this, the hydrogen and hydroxyl ion concentrations from the dissociation of water become comparable to the concentrations obtained from reactant and titrant and no sharp change results a t the equivalence point. The calculations above are based on the assumption of titration in aqueous medium. Similar considerations would apply to titra-
1681
V O L U M E 26, N O . 11, N O V E M B E R 1 9 5 4 tions in solvents such as acetic acid and butylamine if the appropriate equilibrium constants were known. I n aqueous solution, the titration of acids which are ordinarily a little too strong to give a good end point may be often aided by adding alcohol or dioxane. The addition of a solvent which lowers the dielectric constant of the medium decreases the effective strength of the acid being titrated. Mixtures of Acids. If an acid which is colorless in both the ionized and un-ionized forms is titrated with a weaker acid colored only in the ionized form, a photometric titration curve with two breaks would be expected. The accuracy with which the two equivalence points may be located will depend on the absolute and relative strengths of the two acids and their concentrations. The effect of the difference in ionization constants for two weak acids in equal concentrations is shown for some typical cases in Figure 4. As the two acids approach each other in strength, a larger and larger proportion of the first is left untitrated a t the first equivalence point, while simultaneously a larger and larger proportion of the second is titrated before the first equivalence point. The two straight lines meanwhile merge into a single curve with no clearly delineated break and in the limit when the two ionization constants are the same, a single straight line results. As the difference in strength of the two acids diminishes, the first end point becomes increasingly premature as well as difficult to locate. The problems connected with locating the second equivalence points are essentially those encountered in the titration of a single weak acid. Obviously, the same considerations apply to the titration of successive stages of dissociation of a polyprotic acid as to the titration of mixtures of acids.
l
0
l
.2
I
l
b
1 1 1 1 l .6 .e Froci ion Ti tro led
1
1.0
1
1
1.2
1 I
Figure 3. Theoretical Photometric Titration Curves for Monobasic Acids of pK 5.0 at Various Concentrations
It has been shown theoretically ( 1 ) that no inflection appears a t the first equivalence point in the potentiometric titration curve unless the ratio of the first to the second ionization constants is greater than 16; in fact, difficulty is encountered in locating the break a t a ratio of 100 and the ratio must be greater than several thousand to give good results. The photometric titration method, on the other hand, gives an easily located end point in lO-3M solutions with a ratio of ionization constants of only 100
and would seem to offer much greater accuracy and sensitivity in the simultaneous titration of two weak acids. I n principle, several weak acids could be determined in a single titration if their strengths and light absorption characteristics differed suitably. With the limitations that the ionization constants must be gyeater than 10-12, the practical limit on the number determinable is probably three or at the most four. For example, it would be 10-6, and expected that acids with ionization constants of 10-9 could be titrated with an accuracy within 2 to 3% in 10-8M solution. One would be fortunate indeed to find such an ideal c u e in actual practice.
Figure
.SO1
4
,f
THEORETICAL TITRATION CURVE OF TWO WEAK ACIDS I N THE SAME SOLUTION WHERE THE TITRATION IS CARRIED OUT AT THE WAVELENGTH AT WHICH THE ANION OF THE SECOND ACID ABSORBS ALL AT A CONCENTRATION
-4special case of the successive titration of acids of differing strengths is the determination of a strong and a weak acid in admixture. The weak acid must undergo a color change and serves not only as its own indicator but as the indicator for the end point of the strong acid as well. .4s shown below, it is possible to determine traces of strong in weak and weak in strong acids as well as comparable quantities of each. The considerations involved in the choice of an indicator substance for a photometric titration are somewhat different from those pertaining to a conventional visual titration. I n the latter, the indicator ordinarily passes through its color change (approximately 50% conversion) in the close vicinity of the pH of the equivalence point. For a photometric titration it is desirable to have an indicator which does not begin its color change until the close vicinity of the equivalence point, and usually a relatively large quantity of indicator is added, so that the whole amount is not converted. Thus, for the titration of a strong acid with a strong base, thymol blue (pK = 9.0) rather than bromothymol blue (pK = 7.1) would be chosen. With macro concentrations of reagents, the difference would probably not be noticeable, but with very dilute solutions and small volumes as in microtitrations, the choice of the proper indicator is important. The automatic cancellation of the “indicator blank” by photometric titration is an important advantage in microtitrations, where ordinal ily indicator blanks are relatively large. For the titration of very weak colorless acids (pK 7 to 9 ) it i q often very difficult to find suitable indicator substances. A4different approach to the indicator problem may sometimes he used. In it, an indicator acid of known concentration and the same ( 3 ~ 0 . 5pK unit) strength is added. On titration, the two acids are neutralized simultaneously, a single curve being obtained. The difference between the total acidity and the known number of equivalents of indicator added is the titration value of the
1682
ANALYTICAL CHEMISTRY
sample. An example of this is the use of 2,4dinitrophenol as an indicator in the titration of 10-4Llrm-hydroxybenzoic acid. EXPERIMENTAL
All titrations were performed, unless otherwise indicated, in a Beckman Model B spectrophotometer, modified as indicated (3). I n the titration of dilute solutions, carbon dioxide was excluded with a n atmosphere of nitrogen. The titration beaker had a capacity of 150 ml. and a 5.000-ml. microburet was used for addition of titrant.
1
.500-
I
0
Iy
Potasslum Blphthalcte Buffer ~ H = 3 (Colorless) 9
-
mlr
330
370
410
450
490
530
1
I
570
610
650
Figure 5. iibsorption Spectrum of 3.6 X 10-5M p-Nitrophenol in .4cid and Basic Forms Beckman Model B spectrophotometer, 1-cm. Corex cells
Sodium hydroxide solutions, O . l J 1 , were prepared by dilution of 50% sodium hydroxide, previously centrifuged to remove sodium carbonate, with carbon dioxide-free water, and standardized against Bureau of Standards potassium acid phthalate. These solutions, stored in waxed bottles and protected from atmospheric carbon dioxide, were observed to keep their titer to within 1 part per thousand for 6 months. Inorganic chemicals used were C.P. or reagent quality. Organic chemicals were Eastman Kodak Co. white label and were purified by recrystallization unless titrimetric assay indicated 99% purity or better. pNitrophenol was recrystallized from water and toluene and dried in vacuo over magnesium perchlorate and paraffin wax, giving a product which assayed over 99.5% purity.
It seemed evident that for systems in which little or no curvature was t o be expected in the titration curves, the titration results should be both precise and accurate. This situation holds in the majority of oxidation-reduction reactions reported in the literature and for acid-base titrations in the optimum range of ionization constants and concentrations To verify the reliability of the method under more or less ideal conditions, the series of titrations listed in Table I was performed. Twenty-five-milliliter portions of 0.11307.U potassium acid hthalate were titrated under nitrogen with standard sodium ydroxide, 25.00 ml. of 0.01119M being added by pipet, and the titration was completed with 0.01119.11 reagent added by microburet. Four samples were run potentiometrically using a Beckman Model G p H meter-glass electrode assembly and the equivalence point was located by plotting the second derivative of the titration curve. Five samples were then run in the same manner, except that phenolphthalein was added and the end point determined photometrically by measurement of the increase in absorption in 553 mp.
E
The tlvo methods are seen to agree to within 0.3 part per thousand with excellent precision, as measured by the standard deviation, for each. Because no problem seemed involved in the titrations under highly favorable circumstances, attention was shifted to the
Table I. Potentiometric and Photometric Determination of End Point in Titration of 0 . l M Potassium Acid Phthalate with Hydroxide Potentiometric
Photometric
25.250 25.253 25.252 25,254
25.252 25.262 25.25Q 25.2% 25.261
25.252
25.239
Av. Std. dev.
0,002
0,004
examination of the more difficult systems which would require pressing the method to the limit of its applicability. Highly dilute solutions, mixtures of weak acids of similar strength, mistures of strong and weak acids in extreme ratios of concentrations, and dilute solutions of acids with unfavorable ionization constant$ were therefore studied. Titration of Weak Acids. The compounds selected for these studies were, for the most part, substituted phenols, inasmuch as they provided a graded series of acids of differing strengths and convenient absorption characteristics. The strong absorption of the phenolate ions (Figures 5 and 6) in the short wave visible and near ultraviolet was used to follow the course of the neutralizations. Figure 7 shows a typical photometric titration curve for 0.0043234 m-nitrophenol a t 528 mp vith sodium hydroside. Since this is a rising curve with an end point in the high absorbance range, the conditions are least favorable for high accuracy. On the same axes is shown the potentiometric titrat,ion curve.
Table 11. Direct Photometric Titration of Dilute Solutions of Substituted Phenols with Sodium Hydroxide Phenol p-Bromo p-Nitro m-Nitro p-Bromo 10 -4 2,I-Dinit ro p-Nitro m-Nitro 10 - 5 2,4-Dinitro p-Nitro n = number of titrations.
di 10 - 2 10 -3
PK
Q ? 7 0
n 2
8 3
21 8
8 3 3 4
2
9 2 3 9 7 0
i o
2 3 2
2 2
d v . Error.
70
-0 6 -2.3
-0.7 -0.5 -0.7
. ++ s3 . 00
--I2
-+
13
Table TI summarizes the results on a number of phenols. Good results are obtained with acids as weak as even p-bromophenol (which has a strength comparable to boric acid) in solutions as dilute as 10-3.11. At a concentration of 10-41W, errors of several per cent were obtained with the acids having ionization constants
I-
.os0 L
I
n 0I
Potassium Biphthalate Buffer p H :3 9 (colorless1
In N ~ ~ H P O ~ - N D Buffer OH pn:ii 3 ( y e l ~ a u i
330
370
410
450
430mu 530
Figure 6. Absorption Spectrum of 3.6 X 10-sAM rn-Nitrophenol in Acid and Basic Forms Beckman Model B spectrophotometer, 1-crn. Corex cells
1683
V O L U M E 2 6 , NO. 11, N O V E M B E R 1 9 5 4
to the fact that in the vicinity of the end point, the first, acid is incompletely titrated and the second is already beginning to be titrated. Because of the relative magnitudes of the absorbance indices, this results in a fortunate compensation of errors and gives a somewhat more exact result than should theoretically be espected with such a small difference in ionization constants. ntiornetrically on t h e Mixtures of Strong and Weak Acid. The determination of a strong acid in the presence of a weak acid and vice versa is often difficult by ordinary means. If the weak acid undergoes a change in absorpFigure 7 t,ion characteristics on neutralization, the TITRATION OF 100ml O F 4 32 x 10-3fi r n - N I T R O P H E N O L UNDER N I T R O G E N phot'ometric titration technique may be used with advantage in the location of the first end point. When mixtures of Theoretical end point .= 3.54ml. hydrochloric acid and p-nitrophenol in I I I I I I I I I I various ratios were t,itrated with sodium 0 6 ,8 1.2 1.6 2D 2.4 2.8 3.2 3.6 40 4A 4.8 hydroxide at a wave length where the ml. 0 120 N NaOH phenolate ion absorbed (480 mp), two breaks were observed. When there is a large excess, the hydrochloric acid may be determined with high equal to 10-5 or lev, while a t 10-zAII,the limit of the method apaccuracy, the phenol serving as an indicator. I n l O - 3 M solupears to have been reached as far as direct titration is concerned. tions, the titration of equimolar mistures gives results of about Easily identifiable breaks were obtained in the 10-6Af solutions, the same accuracy as was observed for mixtures of weak acids suggesting that, it might be possible to use the method with an wit,h well separated ionizat,ion constants. A trace-e.g., 1%empirical calibration factor to allow for the difference between the of weak acid in a strong acid is determined readily by prior titraobserved end point and the true equivalence point. Keedless to tion of the strong acid with relatively more concentrated sodium say, ext,reme care is needed to avoid carbon dioxide and other hydroxide until neutralization of the 11-eak acid has just begun or chance interference a t these concentration levels. Photochemiis just about to begin (as noted from the behavior of the spectrocal decomposition of p-bromophenol solutions by ultraviolet light photometer on the addition of small increments of titrant). The was observed t o be a disturbing factor in the titration of 10-3M titration is then continued with more dilute hydroxide and the solutions, unless precautions were taken to minimize exposure. This factor should be kept in mind whenever organic compounds are titrated in t'he ultraviolet. .4R Mixtures of Weak Acids. Nixtures of acetic acid with p- and 3 23 m-iiitrophenol were titrated in 10-3.11 solutions a t a wave length where the phenolat,e ions absorbed. The first end point, corresponding to the end of the acetic acid neutralization and the beginning of the phenol titration, was characteristically a litt'le low, but excellent results were obtained for the second end point, corresponding to the total acidity. Table I11 shows these results, together with those on mixt,ures of p-nitrophenol and m-nitrophenol.
t B,
y
Table 111.
Photometric Titration of Mixtures of Weak Acids, 10-3M Acids
First Acetic Scetic p-Nitrophenol
Second p-Sitrophenol rn-Sitrophenol m-Sitrophenol
KdKz 174 3200 20
Error in E n d Points, First Second -2.5 0.0 -2.5 0.0 -1.3 fl.1
I n the latter instance, the ratio of ionization constants is only 20, so that no break would be expected in the potentiometric titration curve. As may be seen in Figure 8, the p-nitrophenol end point may be located photometrically by extending t,he initial straight portion of the first branch of the curve to intersect the estension of the straight portion of the m-nitrophenol titration, and good results are obtained in the determination of both compounds. -4lthough both are yellow in the basic form, a satisfactory curve is obtained by working a t 545 mp where the absorbance index (extinction coefficient) of the m- isomer is far greater than that of the p - isomer. T h a t the observed curve is not displaced more above the two t,heoretical straight lines than it is can be ascribed
mi U s 7
Figure 8.
NoCH
Photometric Titration of a Mixture of W e a k Acids
50 ml. of 0.0219 Mp-nitrophenol and 50 ml. of 0.0213 M m-nitrophenol with 0.667 M sodium hydroxide at 545 mp. Theoreticalp-nitrophenol end point 1.62 ml.; theoretical total acidity equivalent t o 3.22 ml.
1684
ANALYTICAL CHEMISTRY
titration curve of the weak acid is developed. If the f i s t end point were overshot slightly in the addition of the concentrated titrant, it may usually be located with sufficient accuracy by extrapolation of the weak acid line back to the axis.
Table IV. Photometric Titration of Mixtures of Hydrochloric Acid and p-Nitrophenol Av. % Error in HC1 M
PNP,
M
Ratio
End P o i n t HC1 PNP
Table IV shows some of the results on p-nitrophenol-hydrochloric acid mixtures. Especial care must be taken to eliminate or correct for any carbonate present in the sodium hydroxide used €or the titration of a large amount of strong acid prior to the determination of a small amount of weak acid. Unless removed, the carbon dioxide produced will be titrated simultaneously with any colored weak acid having an ionization constant comparable to those of the nitrophenols, and high results will be obtained. The presence of 0.1% carbonate in the 0.9M sodium hydroxide used to neutralize 0.1M hydrochloric acid in a 100 to 1 mixture with p-nitrophenol was sufficient to raise the error in the phenol titration from a consistent +3% to a consistent +9%. If the weak acid is not volatile, the carbonate error may be avoided by boiling out the carbon dioxide after the neutralization of most of the strong acid. If the weak acid is also volatile, a blank must be run. Titrations with Matched-Strength Indicators. The determination of the carbonate blank on sodium hydroxide illustrates a novel type of indicator titration. If two weak acids, one colored and the other colorless, having the same or very similar ionization constants, are titrated in a mixture, the photometric titration curve will evidently be analogous to that of the colored acid alone, but with a diminished absorbance index. Thus, if a known quantity of a colored weak acid is added to an unknown quantity of a colorless acid of the same or slightly greater strength, and the mixture is titrated, the concentration of the unknown acid may be determined by difference. I n this way, traces of carbonate in sodium hydroxide may be determined. The hydroxide is neutralized with a minimum of shaking and exposure to the atmosphere by a slight excess of strong mineral acid (preferably perchloric or hydrochloric), a known amount of p-nitrophenol is added to give a concentration of about O.OOlM, and the mixture ik titrated with dilute, standard alkali. For best accuracy, the titration should be compared with that obtained when the carbon dioxide is boiled out after the addition of hydrochloric acid and before the addition of the pnitrophenol. The potentialities of the matched-strength indicator technique were explored using 2,4dinitrophenol as the indicator for mhydroxybenzoic acid and pnitrophenol as the indicator for the dihydrogen phosphate ion. Table V shows some of the results. The concentration of indicator acid was approximately equal to that of the acid being determined unless otherwise indicated. The correction for the indicator acid is reduced if a low concentration of an indicator with a high absorbance index is used. Thus, for pnitrophenol, when titrated a t the wave length of its absorption maximum, a 10+M solution requires only a 1%correction in the titration of a 10-3M solution of a colorless acid. While in principle any indicator acid of acid strength equal to or less than the substance being determined may be used in the titration a t the total acidity, some ratios of the two ionization constants are much more favorable than others. If the two constants are closely matched, a curve characteristic of the titration
of a single acid is obtained. If the two are sufficiently dissimilar, two distinct breaks are obtained, as in the titration of acetic acid and p-nitrophenol. For intermediate ratios of ionization constants so much curvature may result that extrapolation of the final end point is uncertain. Titration of a Weak Acid with a Weak Base. The titration of a weak acid with a weak base is in many respects analogous to the successive titration of two weak acids and therefore the use of the photometric titration technique might be expected to be advantageous. Secondary amylamine (pKe = 3.5) was used to titrate p-nitrophenol ( ~ K A= 7.0) in 0.001M solution. The titration curve had the same appearance as the curve of the titration of p-nitrophenol with a strong base. Five titrations gave a mean value of 2.85 ml. of 0.1N amine with a standard deviation of 0.02 ml. from the mean and an error of 0.05 ml. The precision and accuracy are comparable to those found for titration with a strong base. Titration of pnitrophenol with sodium borate led to low results and a nonlinear titration curve. This may be attributable to a secondary reaction between the phenol and the boric acid formed. I n general, however, no difficulty is to be expected if the weak acid and base do not undergo secondary reactions. One would expect satisfactory end points in IO-3-W solutiolis if the weak acid differs in strength from the conjugate acid of the weak base by about a factor of 100 in ionization constant
Table V.
Titration of Weak Acids with Matched-Strength Indicators
Acid m-Hydroxybenzoic HIPOIHnPOi a Indicator concentration
Concn.,
M
0.0001
0.001
0.001
Indicator 2,4-Dinitrophenol p-Nitrophenol p-Xtrophenol‘
Error, % hl.0
2t2.0 +0.8
10-jM.
Titration of Weak Bases with Strong Acids. The same general principles apply to the titration of weak bases with strong acids as to the titration of weak acids with strong bases. Relatively little exploratory work was done, but 10-8 and 10-4M chromate solutions were titrated without difficulty using 0.1 and 0.01M hydrochloric acid at wave lengths of 425 and 370 mp. Some titrations were made of 5 x 10-4M p-toluidine solutions in 1-butanol with 0.1M aqueous perchloric acid a t 289 mp in a Beckman DU spectrophotometer. The standard 1-cm. Beckman cell mas used as the titration beaker; titrant was added from a microburet with manual stirring. Good results were obtained with fresh amine solutions on the subtraction of a small strong baee blank, but high results mere obtained if the amine were allowed to stand in butanol for more than 2 hours. ACKNOWLEDGMENT
This work was supported, in part, by the U. S. Atomic Energy Commission through the M.I.T. Laboratory for Suclear Science. The authors are indebted to the Procter & Gamble Corp. for a fellowship for Robert F. Goddu. LITERATURE CITED (1) Auerbach, Fr., and Smolcsyk, E., 2. physik. Chem., llOA, 65 (1924). (2) Eastman, E. D., J. Am. Chem. Soc., 47, 332 (1925); 56, 2646 (1934). (3) Goddu, R. F., and Hume, D. N., ANAL.CHEM.,26, 1740 (1954). (4) Kilpi, S., 2. physik. Chem., 172A, 277; 173A, 427 (1935). (5) Kolthoff, I. hi., and Furman, N. H., “Potentiometric Titrations,” 2nd ed., Xew York, John Wiley & Sons, 1931. (8) Roller, P. S., J . Am. Chem. SOC.,50, 1 (1928); 54, 3485 (1932); 57, 98 (1935). RECEIVED for review July 29, 1954. Accepted September 27. 1954.
