to compensate for the amounts of H3D- and HD-3 present. Curves from 1.0 and 8.4M potassium hydroxide solutions of the dye are also included in Figure 6. Species 5 should be pre- dominant in the 1 . O M potassium hy- droxide solution, and species 6 should be predominant in the 8.4M potassium hydroxide solution. The circles mark- ing the various points of intersections between the different curves show the isosbestic points.

The data for the four principal dye species given in the curves in Figure 6 can be used with the four ionization constants to calculate an approximate absorption spectrum for any dye solu- tion having an acidity in the range from 10.35N hydrochloric acid to a pH of approximately 12. The color system associated with the dye is therefore

defined completely for any acidity that is likely to be used in analysis.

ACKNOWLEDGMENT

The author is greatly indebted to Ludwig Fusser, General Dyestuff Co., 435 Hudson St., New York 14, N. Y., for supplying the uncut sample of acid Alizarine Garnet RA from which the reagent used in this study was prepared. She is also indebted to Charles Kinser, Geological Survey, for the thermogravi- metric data summarized in Figure 1.

LITERATURE CITED

(1) Am. Aseoc. Textile Chemists and Colorists, “Colour Index,’’ Vol. 3, 2nd ed., p. 3058, No. 14290, Lowell Tech- nological Institute, Lowell, Mass., 1956.

(2) Bailar, J. C., Jr., Callis, Clayton, J . Am. Chem. SOC. 74, 6018 (1952).

(3) Britton, H. T. S., “Hydrogen Ions,”

Vol. I, 4th ed., Chapman & Hall, London, 1956.

(4) Drew, H. D. K., Dunton, F. G., J. Chem. SOC. 1940,1064.

(5) Drew, H. D. K., Landquist, J. K., Ibid., 1938, 292.

(6) Fletcher, M. H., ANAL. CHEM. 32, 1827 (1960).

(7) Freeman, D. C. Jr., White, C. E., J. Am. Chem. SOC. $8,2678 (1956).

(8) Fusser, Ludwig, General Dyestuff Co., New York private communication.

(9) Powell, W. A., Savlor, J. H., ANAL. CHEM. 25,960 (1953):

(19) Robinson, R. A,, Stokes, R. H., Electrolyte Solutions,” Butterworths,

London 1956. (11) Schubert, Leo, doctoral thesis, Uni-

vereity of Maryland, 1954. (12) White, C. E., Hoffman, D. E.,

Magee, J. S., Jr., Spectrochim. Acta 9, 105 (1957).

RECEIVED for review June 30, 1960. Accepted September 19, 1960. Publica- tion authorized by the Director, U. 8. Geological Survey.

Theoretical Study o the Reaction between 2,2’,4’- droxyazobenzene-5-sulfonic Acid an Zircon i u

MARY H. FLETCHER

e/ . S. Geological Survey, Washingfon, D. C.

b Zirconium reacts with 2,2’,4’-tri- Rydroxyazobenzene-5-sulfonic acid in acid solutions to form two complexes in which the ratios of dye to zirconium are 1 to 1 and 2 to ’1. Both com- plexes ure true chelutes, with zir- conium acting as a bridge between the two orthohydroxy dye groups. Appar- ent equilibrium constants for the reac- tions to form each of the complexes are determined. The reactions are used as a basis for the determination of the active component in the dye and a graphical method for the determina- tion of reagent purity is described. Four absorption spectra covering the wave length region from 350 to 750 mM are given, which completely define the color system associated with the reactions in solutions where the hydro- chloric acid concentration ranges from 0.0064N to about 7N.

HE dye, 2,2’,4’-trihydroxyazoben- zene-5-sulfonic acid, showed promise

as a possible reagent for the determina- tion of zirconium (19). This paper is concerned with the theoretical studies pertaining to the reaction between zirconium and the dye, and presents the fundamental data that would be the basis for any specific application of the reaction,

Throughout this paper, the con- ventional terminology of the first

paper ( la ) is used. As before, hydrogen ion concentrations are expressed as activity values. The concentrations of other substances are given as moles and refer to moles per liter. P is used for the fraction of active component in dye (or the purity of dye) that has been dried at 150’ C. and considered to be anhydrous. Until the value of P is determined, most of the dye con- centrations and the constants that depend upon its value are expressed in terms of P, so that they all refer to pure anhydrous dye.

As the sulfonic acid group of the dye is always ionized at any acidity where a reaction occurs between the dye and zirconium, and as the sulfonic acid group does not take part in the reaction with zirconium (1, l l ) , equilibrium constants are expressed in terms of the ionized form, HID-.

For convenience, zirconium has been treated as a monomeric, simple quad- rivalent ion rather than as a polymeric, zirconyl, or hydrated species. Unless i t is specified otherwise, chloride com- plexing has been disregarded, as i t has been assumed that the effects of chloride complexing are small in relation to the effects of changes in acidity or zir- conium or dye concentrations.

REAGENTS A N D APPARATUS

2 4 ‘,4 ’-Trihydroxgrazobenzene-5- sulfonic Acid. The same purified

reagent prepared for the study of the dye (19) was used here. The purified dye was dried at 150’ C. and weighed by difference, as i t is hygroscopic.

Zirconium Chloride Stock Solution. Acidity 0.830N in hydrochloric acid, 1 ml. = 19.89 mg. of ZrOz. High purity zirconium nitrate (2.2675 grams) from the Fairmont Chemical Co., 60 Ferry St., Newark 5, N. J., was moistened with water, and 10 to 20 ml. of concentrated hydrochloric acid added. The resulting solution was evaporated to dryness on a steam bath. Several more portions of hydro- chloric acid were added and evaporated to dryness. Finally 11 ml. of concen- trated hydrochloric acid was added and the mixture was heated until the salt dissolved. Then 10 ml. of water was added, and the solution was heated again and filtered through a fine paper. The filtrate was made up to a volume of 50 ml., and analyzed to determine its acidity and its zirconium content.

A conventional gravimetric procedure was used on two aliquots for the deter- mination of zirconium. Ammonium hydroxide prepared from tank ammonia gas was used to precipitate the zirconium and the precipitate was ignited to DOa, which was weighed.

The acidity was determined by cal- culation from p H values determined on aliquots of the stock solution that had been diluted 1/26, l/m, l/lm, and with water. The values calculated from these aliquots were consistent and there did not seem to be any appreciable hydrolysis.

W 0 z a m a

m a

0 cn

1.0

0.5

a

0

.85 0 100 2 00 300 6 5 6

C O N C E N T R A T I O N X IO'

Figure 2. for 0.01 N hydrochloric acid solutions

Absorbance differences from blank at 490 mp

A. 103.1 P X 10- Figure 1. Absorbance differences f rom biank at 52.51 X I O W e mole 490 mp for 0.1N hydrochloric acid solutions containing 18.89 P x 1 O-B mole of dye and varying amounts of zirconium

5.m. cell

Zirconium Chloride Working Solu- tions. More dilute zirconium solu- tions were prepared from the stock solution by dilution with water after the addition of a predetermined amount of hydrochloric acid. The amount of acid and degree of dilution were governed by the conditions of each test. However, all working solutions less acid than the stock solution were prepared immediately before use to avoid possible complica- tions from polymerization or hydrolysis of zirconium.

A Beckman DU Spectrophotometer equipped with a Spectrocord recording attachment was used €or all absorption measurements; 1.0-, and 5.0-em. cells were used.

used for pH measurements. A Beckman Model G pH meter was

PRODUCTS OF REACTION AND PURITY OP DYE

The number of complexes, the com- bining mole ratios of dye-zirconium in

these complexes, and P, the fraction of active component in the dyere, were determined in tests where the concentra- tion of either the zirconium or the dye was constant and the concentration of the other varied over a wide range.

Determination of Number of Corn- plexes Fonned. Initial tests u-ere made in 0.1N hydrochloric acid solu- tions. In the first of these tests, the dye concentration was 18.89 P X 10-6 mole and the zirconium concentra- tion ranged from zero to approximately 1.3 X 10-3 mole. Absorption spectra of the solutions for the wave length region between 350 and 750 mp con- sistpd of a family of curves with an iso- absorptive point at 466 to 457 nip. Maximum positive absorbance dif- ference between the zirconium solutions and the blank occurred a t 490 mp, and one curve resulted from all solutions that contained 33 X 10+ or more mole of zirconium.

Table 1. Malar Absorbance Differences (Mixture - Blank) (0.0lN hydrochloric acid, 490 mp, 1-cm. cells)

Portion of Curves in Fig. 2 Used to Calculate Absorbance Curve A Curve B Differenoea AA/mole Zr AA/moIe dye AA/mole Zr AA/mole dye

Horizontal 1.164 x 104 2.110 x 104 . . . P

Zr in large dye in large excess excesa

Rising 2.032 x 104 ... ... 1.082 X lo4 P

Point aL or b~ 1.135 x l o4 1.135 x 104 1.082 x 104 1.082 x 104 P P

Point as or ba 1.901 X IO4 0.951 X lo4 1.912 X 104 0.956 X lo4 P P

28 e= ANALYTlCAL CHEMISTRY

'6 mole of dye and varying amounts of zirconium of zirconium and varying amounts of dye

I-crn. cell

The results of the test are summarized by the data for the wave length 490 mp given in Figure 1. Here, the point of intersection for the dashed lines ex- trapolated from the rising and horizontal portions of the curve show that ap- proximately 18 X mole of zir- conium is consumed in completely cornplexing 18.89 P X mole of dye. A dye-zirconium combining ratio of 1 to 1 is, therefore, indicated €or the complex that forms in the presence of excess zirconium.

In the rising portion of the curve, the absorbance difference from the blank, A-4, per mole of zirconium is 5.297 X lo4; and in the horizontal portion of the curve, AA per mole of dye is 5.040 X 104/P. If the (I + 1) complex is the only product of the reaction and is associated completely in the solutions represented by the rising portion of the curve, these molar absorbance dif- ferences must be equal, If equality is assumed, P has a value of 0.952.

However, in the results from similar tests where the zirconium concentration was constant and the dye concentration varied, the plateau of the curve had a slight positive slope and the curve was still rising n-hen the dye solubility precluded any further increases in its concentration. This continuous rise in the curve suggested the possibility that small. amounts of a second complex were forming in the presence of excess dye. If this occurred in the previous test, P might have a value slightly greater than 0.952. However, as it was impossible to use sufficient con- centrations of dye in 0.1N acid solutions to prove the existence of a second com- plex and recheck the value of P, addi- tional tests were run in 0.01N hydro- chloric acid.

The data from the tests at the lower acidity are given in Figure 2 and Table I. The intersections of lines al and aa

with curve A and of lines bl and bz with curve B mark the points on each curve (Figure 2) that correspond to concentration ratios for apparent moles of dye/mole of zirconium that are 1 to 1 and 2 to 1, respectively. The solutions used to obtain the absorbance data in curre -4 (Figure 2) contained 103.1 P X 10-6 mole of dye and varying amounts of zirconium; those used to obtain the data in curve B contained 52.51 X 10-6 mole of zirconium and varying amounts of dye. All solutions con- tained 0.99 mole of potassium chloride to bring their ionic strength, p, UP to a value of 1. In all cases, t o assure a state of equilibrium, no absorbances were measured until a t least 2 hours after the solutions were prepared.

The most important feature of the data in Figure 2 is the horizontal plateau in curve B. It indicates that a t lorn acidities the reaction that occurs in the presence of excess dye is complete. The reaction that occurs in the presence of excess zirconium also reached corn- pletion, as is shown by the horizontal plateau in curve A . This, however, is no different from the results obtained in more acid solutions (cf, Figure 1). The plateau of curve 4 represents the same (1 + I) complex that was found in earlier tests; the plateau of curve B represents the second complex that was being sought.

Molar absorbance differences for the two complexes are given in Table I. Thcy are the values that were calculated from the horizontal regions of curves A and B (Figure 2 ) . As the value for the (1 + 1) complex was calculated from the dye concentration, i t is expressed in terms of P. Nevertheless, i t is clear that the values are different, the con- stant for the second complex being 1.82 P times greater than that for the (1 + 1) complex.

This large characteristic difference betn-een the molar absorptivities of the two complexes made it relatively easy to identify the predominant species of complex in the various solutions and to estimate the completeness of the reac- tions. For example, consider the molar absorbance differences in Table I that a ere calculated from different regions of the curves in Figure 2.

All the values calculated from the rising portion of curve B and from points al and bl are close enough to the one from the horizontal section of curve A t o show that the (1 + 1) complex was essentially the only species in the solutions when the zirconium concentra- tion was equal to or greater than the dye concentration. Analogously, the values per mole of zirconium calculated from the rising portion of curve A and from points a2 and bs are close enough to the one from the horizontal portion of curve B to show that the second com- plex was the predominant species in

solution when the dye concentration was 2 or more times greater than the zirconium concentration.

In solutions where the (1 + 1) com- plex is the only species present, the degree of reaction may be determined by division of the molar absorbance dif- ference per mole of minor component by the value of the fully associated complex. As the zirconium concentra- tion was equal to the apparent dye concentration in the solutions cor- responding to points al and bl, dye was the minor component; horn-ever, if 0.952 is used as a first approximation for the value of P, the zirconium excess would be equivalent to only 4.9 X 10-6 mole at point al and 2.5 X a t point bl. Yet these small concentra- tions were very effective in driving the reaction towards compl6tion. As evidence of this, calculations indicate that 97.5 and 93.0% of the total dye were complexed a t points a1 and bl, respectively.

As the dye-zirconium ratio is 1 to 1 in this first complex, small amounts of excess dye would be as effective as small amounts of excess zirconium in driving the reaction toward completion. As a consequence, there was virtually no uncombined zirconium in the solutions that are represented by the regions of the curves that extend from about mid- way between a1 and a2 to a2, and from midway between bl and bz to bz. Here, essentially all the zirconium was com- bined in one or the other of the coni- plexes.

In such instances where all zirconium is complexed, the fraction of zirconium combined in the (2 + 1) complex may be calculated according to the following equation : Fraction of zirconium as (2 + 1) complex

A absorbance/mole of zirconium for solution

A absorbance/mole of zirconium for (2 -( 1) complex

Calculations made in this way, using 0.952 as an approximation for P , indicate that 76.4 and 77.87, of the zirconium were combined in the (2 + 1) complex in the solutions corresponding to points a2 and bz where the true concentration ratio of dye-zirconium was not quite 2 to 1. When the con- centration ratio was about 3 to 1, however, the absorbance differences fell on the plateau of curve B and on the linear rising section of curve .4 (Figure 2), which showed that virtually all the zirconium was now in the ( 2 + 1) complex. This indicates 2 to 1 as the combining ratio for dye-zirconium in the second complex. This is substan- tiated by agreement between calculated and experimental absorbance data in later sections of this paper.

Knowledge of the dye-zirconium combining ratios for t.he two complexes

and of their molar absorbance differences from the blank made id possible to re- evaluate P by an independent method using the data obtained in 0.01N hydrochloric acid solutions.

Determination of Active Component in Dye. The following terminology is used: For the present, IZr(H3D- - &+)]+*-", [Zr(HSD- - nH+)2]+2--2n, and B will be used as formulas for the (1 + I) complex, the (2 + 1) complex, and the dye, respectively; and B, which is used for the dye blanks, will represent the total of all uncombined dye forms present in the solution; el, E ~ , and eB will be the molar absorp- tivities of the (1 + 1) complex, the (2 + 1) complex, andthedyeasmeasured against water as the reference solution; (e1 - eB) will be the molar absorbance difference from the blank for the (1 + 1) complex as measured with a dye blank for the reference solution; and (a-2eB) will be the molar absorbance difference between the (2 + 1) complex and its blank as measured with a dye blank for the reference solution.

The values for (€1 - EB) and (E%-

2 4 for the wave length 490 mp and a pH of 2 are given in Table I and

lo4 and 2.110 x lo4, are respectively. The value fo: eB was deter- mhed from the dope of a curve which related absorbance and dye concentra- tions of solutions that contained various amounts of dye but no zirconium, and the value of was determined from the slope of a similar curve obtained from solutions that contained a large excess of zirconium and varying amounts of dye. The value of f 2 mas calculated from the other constants. At a pH of 2,

-; eL is

""* P

0.4544 X lo4 EB is equal to P

- A absorbance/niole of zirconium-for (1 + i) complex

- A absorbance/mole of zirconium for (1 + i) complex

independent of pH: and is equal to 1*6182 lo'; e2 is also independent of

p~ and is equal to (2.110 x 104 + 0'9088 lQ4). A11 these values are for P a wave length of 490 mp and ail refer to 1-cm. cells.

Using the foregoing terminology, preliminary equations that are adequate for the present discussion may be written. Equation I applies to the formation of the (1 + 1) complex, and Equation 2 applies to the conversion of the (1 + 1) complex to the (2 + I) complex.

Zrf4 + HaD- F? [Zr(HaD- - nH+)] +3-n 4- n H + (1)

[Zr(HsD- - nH+)] +a-n + HaD Ft [Zr(H3D- - nH+)*] 4 a - W + n H + (2)

VOL 32, NO. 13, DECEMBER 1960 0 1

C O N C E N T R A T I O N X IO6

nlarged section from Figure 2

The valences assigned to the complex ions in these equations represent the net difference between the positive charge on the zirconium and the negative charge on the dye radical.

To evaluate P, sections of curves A and B (Figure 2) were replotted on a larger scale in Figure 3. A tangent was drawn to curve A in the region between points al and azJ and another was drawn to curve B in the region between points bl and bz. Each of the tangents passes through or within 1% of the experimental pointe over a short region of curve A or B , I n these regions, the Corresponding solutions contained a mixture of the two complexes but virtually no unconlbined zirconium, and the linearity of the curves indicates that any changes in the fraction of the dye complexed here were no greater than the experimental errors (IS). Therefore, for the purposes of this discussion, the fraction of dye complexed will be considered constant, and will be denoted by R with a subscript a or b added to designate the data of curve A or B. The relationships between the concentrations of the complexes, zir- conium: and dye in all these solutions are given in Equations 3 and 4. Moles (2 + 1) complex 4- moles (1 + 1) complex = total molea of zirconium (3) 2 X niolea ( 2 + 1) complex +

moles (1 + 1 ) complex = RP (apparent moles of dye) (4)

In the system corresponding to tangent A , the concentration of dye was constant and the concentration of !&conium varied. Therefore, in ac- cordance with Equations 3 and 4, increasing concentrations of zirconium resulted in corresponding increases in the total concentration of the two complexes, but the latter could be achieved only if the resulting mixtures contained increasing fractions of the

1 e ANALYTICAL CHEMISTRY

1.2

I . o

\ 0 . 6

0 . 4

-1.5 -1.0 -0.5 0 0.6 1.0

- L O G a"+

Figure 4. of varying acidities containing 12.10 X of dye and 13 1.3 X 1

Absorbances at 429.5 mp for solutions mole

mole of zirconium 5-cm. cell

( I + I) complex and decreasing fractions of the (2 + 1) complex. Each mole of dye participating in the reactions could combine with either 0.5 mole of zir- conium to form 0.5 mole of the (2 + 1) complex or with 1 mole of zirconium to form 1 mole of the (I + 1) complex, As a consequence, the net effect to the system from each I-mole increase of zirconium was a 2-mole increase of the (1 4- 1) complex and a 1-mole decrease of the (2 + I) complex. The correspond- ing change in the absorbance difference from the blank for the system would, therefore, be equal to [2(e1 - E B ) - ( E Z - 2 E B ) I J and also to the slope of tangent A. The slope of the tangent had a value of 0.304 X IO4. These theoretical and experimental values for the change in absorbance difference per mole increase in zirconium were equated in Equation 5 and the proper constants substituted to give an expression which was solved for P. 2(el - - (E2 - 2SB) = 0.304 x lo4

( 5 )

- 1.164 X lo* 2 x P

2.110 X 10' = 0.304 X IO4 P = 0.9644

As all zirconium was combined here, R,, the fraction of dye complexed, need not be considered.

In the system represented by tangent B, the Concentration of zirconium was constant and the concentration of dye varied. In accordance with Equation

3, the total moles [ (2 + 1) complex + (1 + 1) complex] were constant and equal to the Zirconium concentration. Increasing the concentration of dye in these solutions resulted in the convcr- sion of the (I + 1) complex to the (2 + 1) complex according to the re- action given in Equation 2. The change in the absorbance difference from the blank corresponding to each 1-mole increase in the dye concentration of this system would be equal to R $ [ ( E ~ - 2 e ~ ) - (e, - E B ] ] and also to the slope of tangent B, which has a value of 0.8736 X lo4. These theoreti- cal and experimental values were equated in Equation 6, the proper constants were substituted, and the resulting expression was then simpised.

0.8736 X lo4 (6) Rbpl(€2 - 2eB) - (€1 - €E)] =

1.164 x 104 - ~ ~ ~ C 2 . 1 1 0 x 1 0 4 - -- P-I - 0.8736 X lo4

+ 0.5517 0.4140 p=- Rb

The simplified expression related P and Rb. When 0.9644, the value found for P from tangent -4, was substituted in this equation, ab had a value of 1.003, indicating that the concentration of uncombined dye in the solutions was negligible. Assuming this to be true and letting Bb equal 1, P was found to be 0.9657. Averaging the three ex- perimental values (0.952, 0,954, and

I .o

0.8

0.6

0.4

-1.0 -0.5 0 0.5 1.0 1.5

- L O G aH++-(+ p H

Figure 5. Absorbances at 429.5 my for solutions of varying acidities containing 10.03 X 1 O-e mole of dye and 20.00 X 1 Om6 mole of zirconium

5-cm. cell

W u z a m 1.0 a

m a a

0 v)

0.5

1.0 1.5 2.0 2 5

P H

Absorbance differences from reference Figure 6. at 490 mp for solutions of varying acidities

A. 309.7 X 10-6 mole of d y e 6. 309.7 X 10-6 mole of dye + 30.00 X 10-6 mole of

zirconium Values are for 1-cm. cells, measurements were made in 0.5-cm. cells. Reference solution, 184.07 X IO-eM d y e solution a t p H 2.02

0.966), a mean value of 0.961 was obtained for P. This mean value will be used throughout the rest of the paper.

This value for P was substantiated by the results of the thermogravimetric data presented in the first paper ( l a ) , and later, after equilibrium constants were determined for the zirconium-dye reaction, i t was possible to check the original assumptions which were made in devising the tangent method for the determination of P. The equilibrium constants were used to calculate the components that would be present in 0.01N acid solutions similar to the ones used for the determination of P. According to these calculations, un- combined zirconium should be virtually absent from solutions corresponding to the tangent regions of curves A and B (Figure 3), and the variations in the concentrations of uncombined dye in the central region of each tangent should amount to no more than *1 to 2 X mole. As the error introduced by these differences would be no greater than the errors in measurement, i t was safe to assume the absence of un- combined zirconium and negligible changes in the concentration of un- combined dye. Similar calculations for 0.LV acid solutions indicated that virtually all of the zirconium should be complexed in the solutions correspond- ing to the rising section of the curve in Figure 1 and that no more than 1 to 2% of the total zirconium should be combined in the (2 + 1) complex in any of the solutions corresponding to the central and upper portions of the rising section of this curve. As this amount of the (2 + 1) complex would cause errors in the value of P no greater

than 0.5 to 1.5%, it was considered proper to include 0.952, the value found for P from the data in Figure 1, when calculating the mean value for P.

DETERMINATION OF NUMBER OF ORTHO- HYDROXY GROUPS IN DYE PARTICIPATING IN

REACTION WITH ZIRCONIUM

Before it was possible either to write the final equations for the reactions between zirconium and the dye or to calculate values for the equilibrium constants, it was necessary to evaluate n in Equations 1 and 2. This involved finding out whether one or both of the dye orthohydroxy groups react with zirconium. The determination was made by a method similar to those used by many other workers (3, 6, 8, 14, 17, 19-22, 24, g6, 27) from absorbance and acidity data from four series of solutions; in each series, the dye and zirconium concentrations mere constant but the acidity varied.

I n the first and second series of solutions, the zirconium concentration was greater than the dye concentration and the dye-zirconium mole ratios were small enough to ensure that only the reaction of Equation 1 occurred. In the third and fourth series of solu- tions, the dye concentration was greater than the zirconium concentration and the dye-nirconium mole ratios were large enough to ensure that, at the acidities used, only the reaction of Equation 2 occurred. In all tests, sufficient potassium chloride was added to each solution having an acidity less than 1-$4 (based on the concentration of hydrochloric acid added) to raise it5 ionic strength, p, to a value of 1. NQ absorbance measurements were made

until at least 2 hours after preparation of the solutions, to assure that equi- librium had been established. -4s a further control, absorbance measure- ments were always made on a series of blank solutions that contained all reagents except zirconium, and also on solutions that contained either fully associated (1 + 1) or (2 4- 1) complex whenever measurements were made on the dye-zirconium mixtures in any of the four series of solutions.

The absorbance and acidity data from these tests are given in Figures 4 through 7 and the results are 5um- marized in Figures 8 and 9. TO sim- plify calculations, absorbance values were read from the curves in Figures 4 through 7 a t intervals of 0.1 pH or -log a=+ units, and these values were used to calculate the components that would have been present in solutions having these acidities. The wave length 429.5 mp was selected to obtain the data in Figures 4 and 5 because it is the isosbestic wave length for the dye forms HJI and H3D-. Thus, a fairly constant blank was obtained for these tests in strong acid, whereas a wave length of 490 mp would have given blanks showing variations as great as or greater than those found for the zirconium-dye mixtures.

Calculations from the data in Figures 4 and 5 to determine the concentrations of the different components in the solutions where the reaction was that indicated by Equation 2 , were based on the following relationships: [Total zirconium) =

[(I + 1) complex] + [uncombined zirconium]

[uncombined dye] [Total dye] = [(I + 1) complex] t

[(HBD-)] = [uncombined dye] X . .

0.794 L .794 + an+!

VOL 32, NO. 13, DECEMBER 1960 e 1831

I I f

1.2 c w 1.0 0 z d 00 0. 8 a 0 v) 0.6 a

0.4

0 . 2 0.6 I . 0 1.5 2.0

--LOG a,,++l- p H

Figure 7. varying acidities A. 90.29 X mole of dye 6. 90.29 X 10-8 mole of dye f 30.00 X 10-6 mole of zir- conium. 1 -cm. cell

Absorbances at 490 mp fer solutions of

where 0.794 is K., for the dye, and brackets denote concentrations except for the hydrogen ion, where activities are used. L! Absorbance from the blank for any solu-

tion = ((el - e g ) [ ( l + I) coniplex])

Fraction of dye aa (1 4- 1) comalex = adsorbance (mixture- - blank)

(61 - EB) (total dye)

Once the components of the different solutions were determined, the loga- rithms for the different concentration mole ratios for (I + 1) complex/(H3D-) were plotted us. -log ( c u i in Figure 8 where curve A has a slope of 2.24 and curve B has a slope of 2.19. The equilibrium for the reaction in these solutions may be expressed by the equation,

which may be rearranged and put into Iogarithmic form to become

[Zr(HsD- - nH+) + E - * ]

(HID-) Log - - --?z log QH+ + log (Zr+4) + log K,,

Thus, in accordance with the loga- rithmic expresaion, the slopes of the curves in Figure 8 would be equal to n, if the concentration of uncombined zhooniurn was constant. This condi- tion was met closely enough by the data in curve A as the dye-zirconium ratio in the corresponding solutions was 1 to 11; but, in the solutions that provided the data for curve B, the dye-zirconium ratio was only 1 to 2. As a consequence, complex formation in these solutions caused m appreciable change in the concentration of the uncomplexed zir- conium. However, the slope of curve B can be corrected to adjust for these changea Lo give a value for n by aub- tracting a correction factor that is equal

9 832 e ANALYTICAL CHEMISTRY

(3 0 -I

- 1.5 I I I I 1 1 l 1 l 1 1 1 I I I I I I

-1.0 -0.5 0 0.5 1.0

-LOG a H +

Figure 8. Logarithmic plot for determinalion of number of orthohydroxy dye groups that react to form ( 1 + 1 ) complex A. 12.10 X 10-8 mole of dye 4-131.3 X 10-6 mole of

E . 10.03 X 10-6 mole of dye f 20.00 X 10-6 mole of zirconium

zirconium

to A log (Zr+4) per unit of -log aa+ or pK. When this is done, the cor- rected value for n as obtained from the slope of curve B is 2.45. Thus, the values (2.24 and 2.45) found for n indicate that both of the dye ortho- hvdroxv u o u m react with zirconium to

and the equilibriumexpression becomes:

(8 1 [Zr (HD j +] aa2 +

Knl = [HID-] [ZI-+~]

Zr+4 +- H,D- [Zr(HD)+] f 2H+ (7) tions of the different components in the

1 .O 1.5 2.8 P H

Figure 9. Logarithmic plot for determinaiion of number of orthohydroxy dye groups that react to form (2 + 1 ) complex A. 30.00 X mole of zirconium +309.7 X 10-8 mole of

B . 30.00 X 10-6 mole of zirconlum f 9 0 . 2 9 X'10 -6mole of dY e

d y e

solutions where the reaction was that indicated in Equation 2 were based on the following relationships: [Total zirconium] =

[Total dye] = 2[(2 + 1) complex] + (HaD-) = (uncombined dye) X

[(2 + 1) complex] + [(I + 1) complex]

[(l + 1) complex] + [uncombined dye]

0.794 (0.794 + a=+>

where 0.794 = K,, for the dye, A Absorbance from the blank for any solution =

(e2 - 2€B) i(2 + 1) complex1 + (€1 - EB) [(I + 1) complex1

Combination of the first and last of these equations gives an expression for the concentration of the (2 + 1) com- plex : [(2 + 1) complex] =

[ A absorbance (mixture - blank)] - [(total zr) (€1 - EB)]

Using these equations, calculations were made to determine the concentrations of the different components in the solu- tions. Then, in a manner similar to the one used for the (1 4- 1) compIex, the logarithms of the different concentration

(62 - 2€B) - (E1 - €B)

- [(2 + 1) complex] [(I + I) complex] were mole ratios for

plotted in Figure 9 as a finction of either the calculated value for -log UH+ or measured pH. The slope of curve -4 is 1.84 and the slope of curve B is 1.69. As the logarithmic expression for these ratios is

--n log + I&-(H~D-) + log K.,

the slopes of the curves will be equal to n, if the concentration of (H,D-) is constant. This condition is met closely enough by the data in curve A because the dye-zirconium ratio was 10 to 1 in the solutions used to obtain the data. However, the dye-zirconium ratio was only 3 to 1 in the solutions used to obtain the data for curve B, and as a result, complex formation caused ap- preciable changes in the concentration of (HsD-). But the value of the slope of this curve can be corrected in a manner similar to that used for curve B, Figure 8, to adjust for these changes and give a value for n. When this is done, a value of 1.91 was found for n as determined from curve B. Thus, the two values for n, 1.84 and 1.91, indicate that both of the orthohydroxy groups in the dye react with the two unsatisfied valences of the zirconium in the (1 + 1) complex to form the (2 + 1) complex. Accordingly, Equa- tion 2 may be rewritten as: Zr (HD)+ f HaD- Ft Zr(HD)a+ + 2H+

(9)

and the equilibrium for the reaction may be expressed as:

Both of the complexes formed in the reactions are true chelates, with the zirconium acting as a bridge between the orthohydroxy groups in the dye, In the (1 + 1) complex, the dye satisfies two of the zirconium primary valences and fills three of its coordination posi- tions. Although zirconium has a CO- ordination number that ranges from 6 to 8, zirconium is shown with only three of its coordination positions filled in the proposed structural formula for the (1 + 1) complex, because this represents that part of the structure that has been definitely established. The single positive charge on this complex represents the net difference between the two unsatisfied positive valences of the zirconium and the negative charge on the sulfonic acid dye group. It does not imply any association between the zirconium and the sulfonic acid group. Similar structures have been proposed before; Drew and Fairbairn (10) were the first to describe lakes of this type where the metal in the chelate exhibits a residual ionic valency, and they have pointed out that this is a general occurrence among the chelates of the o,o'-dihydroxyazo compounds.

In the ( 2 + 1) complex, the dye satisfies all four of the zirconium primary valences and fills six of its coordination positions. The double negative charge is due entirely to the two ionized sulfonic acid dye groups.

Isolation and analysis of the two complexes, or determination of their charges, would further elucidate the nature of these complexes. However, possible structures for those portions of the structures that have been estab- lished are :

r -I+

These structures are similar to those found by many other workers (1, 8, 4, 9-11, 16, as) for complexes formed h the reactions between different metals and o,o'-dihydroxyazo compounds.

CHLORIDE DEPENDENCE

Absorbance and pH data from a series of 0.01N hydrochloric acid solu- tions that contained 35 x 10-6 mole of dye, 10 x 10-6 mole of zirconium, and 0 to 2.0 moles of potassium chloride showed that the reaction between the (1 + 1) complex and the dye to form the (2 + 1) complex is independent of the concentration of the chloride ion. Similar data from a series of 0.1N hydrochloric acid solutions that con- tained 20 x 10-8 mole of both dye and zirconium and zero to 2 moles of potassium chloride as well as data from a series of 0.01N hydrochloric acid solutions that contained 35 X mole of dye, 10 X 10-6mole of zirconium, and 4.5 to 6.5 males of lithium chloride showed that decreasing amounts of (1 + 1) complex formed with increasing amounts of chloride. Considered as a whole, these data indicate that neither of the dye-zirconium complexes contains chlorine and that chloride ion is liberated in the reaction between zirconium and dye to form the (1 + 1) complex. The latter would be expected if the zirconium-dye complexes contain no chlorine and a weak zirconium- chloride complex dissociates as zirco- nium and dye react to form the (1 + 1) complex. A plot of

(1 + 1 complex) a=+* log (uncombined airconium) (HaD-)

os. -log (Cl-) for the last two series of solutions is shown in Figure 10. The upper portion of this curve, which corresponds to the solutions that con- tained potassium chloride, has a slope of about 0.34, and the lower portion, which corresponds to the solutions that contained lithium chloride, has a slope of about 4. However, calculations from pH measurements on the solu- tions yielded hydrogen ion activity co- efficients ranging from 6.3 to 15.6 for the solutions that contained lithium chloride, and the mean activity co- efficients for lithium chloride solutions in pure water range from 1.7 to 3.0 (23, Table 9, p. 285, and Table 19, p. 489) a t the concentrations used here; af a result, the chloride dependence shown in Figure 10 is so exaggerated for the lithium chloride solutions that it would be difficult to interpret the lower part of the curve in a quantitative manner.

In Equation 8 for K , , the term (2W4) is used for all zirconium not complexed by the dye. If all zirconium not complexed by the dye is present as

VOL 32, NO. 13, DECEMBER 1960 0 1833

? , I L I I- ::I 3.0

- L O G (GI-)

Figure 10. Chloride dependence

0. 0.1 N HCI + KCl; 20 X 10-6 mole of dye and zirconium X. 0.01N HCI + LiClr 35 X moleof d y e a n d 10 X mole

of zirconium

(ZrCl+S) (zr+4) (CY) = K*) and ZrCl+* and

then the true equilibrium constant, KI, might well be represented by the expression

[ Zr (HD) +] a=+* - (Zr f4) (H3D -)

IZr(HD) + ] ~ F I + ~ [ K , ( C ~ - ) $. I)] (Zrf4 + ZrCl+a) (H,D-)

- K1 =

K.,[K,(CI-) f 11

where the individual species are properly identified.

Connick and McVey (6) found a value of about 2 for K, and stated that it might be about 30% higher if an im- purity in the zirconium they used were eliminated. A value of about 1.5 would be required by the data from the upper portion of the curve in Figure 10, A value of 1.5 dictates that logarith- mic plots for solutions with no added chloride salts such as curve A in Figure 8 should have a slope somewhat greater than 2 but less than 3. As the actual slope of curve A on Figure 8 was 2.24, the data in Figure 8 and 10 are in general agreement.

It is possible that the data obtained in this study might be interpreted by assuming that Zr+* and ZrCl+3 ions are in equilibrium with other simple ions or with polymeric forms. Con- siderable attention has been directed by Connick and McVey (6), Connick and Reas (7) , Kraus and Johnson (16, 18), and Zielan and Connick (68) toward determining the true nature of zirconium in aqueous solutions. They have shown that the principal species is monomeric in very dilute zirconium solutions in I to 2M acid, but they all found polymers in less acid solutions. In view of their work, the zirconium species in the solutions used in the present work remains in doubt. However, the fact that the (2 + 1) complex forms in 0.01N

1834 e ANALYTICAL CHEMISTRY

3 . 5

3 . 0

2 . 5

2 . o

1 5

I . o

0 . 5

0

350 4 0 0 4 5 0 500 5 5 0 6 0 0 6 5 0

W A V E L E N G T H - M I L L I M I C R O N S

Figure 1 1 . Absorption spectra representing color syste? associated with reaction between zirconium and 2,2',4 - trihydroxyazobenzene-5-sulfonic acid

hydrochloric acid certainly substan- tiates the supposition that byhatever the nature of zirconium in these solu- tions, it is in equilibrium with some simple form such as Zr+4 or ZrClf3.

EVALUATION OF APPARENT EQUILIBRIUM AND STABILITY CONSTANTS

Because of the uncertainty regarding the nature of zirconium in the solutions used in this study, and as no attempt mas made to determine thermodynamic constants. values for apparent equi- librium constants were calculated for the reactions as expressed in Equations 7 and 9 according to Equations 8 and 10 from the concentrations of the com- ponents (activities for hydrogen ion) found in the solutions represented by the curves in Figures 8 and 9. Values were calculated also from other tests where the concentrations of the acid and of either the dye or zirconium were constant and one of the latter was varied. In all cases, the concentrations of acid, dye, and zirconium were such that, in each test, essentially only the reaction of either Equation 7 or 9 occurred. In the tests where the acidity was constant the concentrations of dye and zirconium mere selected to give mixtures in which the concentrations of all the components varied over v-ide ranges in each series of solutions. Absorbance data for these tests are not given here, but pertinent details of the tests are summarized in Tables I1 and 111, where the values for the first

and second apparent equilibrium con- stants are given.

In accordance with the nature of concentration constants, the individual values found in the different tests varied somewhat with the concentra- tions of the reactants; however, the range of values for each test was not too great and was comparable to the range covered by the different values given in Tables I1 and 111. The first column in each table gives the average of all the individual values from each test. The other values are individual values for mixtures frequently chosen as representative of equilibrium conditions. The averages of all values in each table. K,, = 1.96 X lo5 and K,, = 23.2, should be good "apparent" constants that are sufficiently accurate for use in calculations of a practical nature. They have been both useful and satisfactory in predicting the com- ponents in diff erent dye-zirconium- acid mixtures and, in many cases, they could have been used safely to eliminate tedious laboratory work.

Stability constants are useful for comparisons of different complexes and therefore have been calculated for the two chelates. The constant, 81, for the formation of the (1 + 1) complex ac- cording to the reaction in the equation. Zr+4 + e Zr(HD)+ is

1.42 X le1@

VOL. 32, NO. 13, DECEMBER 1960 * 1835

The constant, 82, for the formation of the (2 + 1) complex according to the reaction in the equation, Zr(HD)+ + HD*- Zr(HD)-2 is

1.68 X

The over-all constant, So, for the formation of the (2 + 1) complex ac- cording to the equation Zrf4 + 2HD-s Zr(HD)2-2, is

2.39 X 10s‘

COLOR SYSTEM ASSOCIATED WITH DYE- ZIRCONIUM REACTIONS

Low absorbance differences from the blank were obtained for zirconium-dye mixtures that contained excess zir- conium as in the series used to obtain the data in Figure 4 and curve A , Figure 8, whenever the solution acidity was even slightly lower than pH 2.2. It is believed that these low absorbance differences were the consequence of a decrease in the concentration of re- active zirconium which resulted from its polymerization or hydrolysis. Tihat- ever the cause, a p H of 2.2 was the lowest acidity used for any of the work reported here.

A pH of 2.2 as the lower limit of the useful acidity range assures that ion- ization of the uncombined dye will proceed no further than the first stage and that HaD and H3D- will be the only dye forms present in measurable amounts. Thus, the two dye forms and the two complexes are the only com- ponents of the color system associated with the reaction between zirconium and the dye. As a consequence, molar absorption spectra for these four sub- stances (Figure 11) describe the color system as completely as the equilibrium and ionization constants of the dye describe the reaction.

The absorption spectra in Figure 11 are the molar absorbances that would be obtained from the four substances if each were measured in pure solution in I-em. cells against water. As the (2 + 1) complex can be obtained only in the presence of excess dye, the values for its molar absorbances were calculated from absorbance differences for the complex and the absorptivity of the dye, but all

1836 e ANALYTICAL CHEMISTRY

of the other values were calculated directly from absorbances measured in pure solutions. All values are in- dependent of pH; the effect of the acidity is to determine the relative proportions of these four substances in any given zirconium-dye mixture.

The curves in Figure 11 are useful in selecting the most advantageous condi- tions for specific applications of the reaction. These curves give all of the information needed to estimate the sensitivity of the color reaction a t any wave length between 380 and 750 mp for hydrochloric acid solutions of any acidity in the range from 0.0064N to about 7137. The relative fractions of E D and HSD-, for any acidity in the useful range, are calculated from K,,, the first ionization constant for the dye. The molar absorbance of the dye, EB, for the mixture of the two dye forms is then calculated from the fractions of the two dye forms and their respective molar absorbances a t the desired wave length. Combination of eB with the molar absorbances of the two com- plexes for the same wave length gives (ee-2es) and ( E , - E ~ ) which are meas- ures of the sensitivities for the two complexes-Le., they would be the slope of standard curves for the deter- mination of zirconium. The concentra- tion of uncombined dye required to yield the desired product or mixtures of products a t the selected acidity can then be calculated from the equilibrium and ionization constazts.

In practice, the requirements of analytical methods are varied and the procedures dwised are governed by such factors as the sensitivity required, the nature of the material t o be analyzed, and the nature and quantity of other ions associated Rrith the one to be determined. Frequently, a single re- action or a single reagent may be used for the solution of a variety of problems as well as the basis for a number of analytical proceduresI provided proper acidities and wave lengths are chosen and masking agents are used where feasible.

An attempt has been made in this study to obtain the fundamental data pertaining to one reaction and i t s color manifestations and to present it in a generalized form, so that later, for any specific application, conditions can be changed a t wiil and the outcome predicted with confidence without the necessity of repeating the basic work. It is hoped that the reaction will find other applications than the deterniina- tion of zirconium in pure solutions.

ACKNOWLEDGMENT

The author is greatly indebted to Ludwig Fusser, General Dyestuff Co., New York, for supplying the uncut sample of acid Alizarine Garnet E4 from which the reagent used in this work was prepared.

LITERATURE CITED

(1) Bailar, J. C., Jr., Callis, C. F., J . Am. Chem. SOC. 74, 6018 (1952).

(2) Beech, W. F., Drew, H. D. K., Ib id . , 603, 608 (1940).

(3) Britton, H. T. S., “Hydrogen Pons,” Vol. I, 4th ed., Chapman & Hall, London, 1955.

(4) Callis, C. F., Nielsen, N. C., Bailar, J. C., Jr., J. Am. Chem. Sac. 74, 3461 (1952).

(5) Chaberek, S., Martell, A. E , Ibid. , 74, 5052 (1952).

(6) Connick, R. E., McVey, W. H., Ibid., 71, 3182 (1949).

(7) Connick, R. E., Reas, William, Ib id . , 73, 1171 (1951).

(8) Diehl, Harvey, Lindstrom, Frederick, ANAL. CHEW 31, 414 (1959).

(9) Drew, H. D. IC., Dunton, F. G., J . Chem. Soc. 1940, 1064.

(10) Drew, H. D. I<., Fairbairn, R. E., Ib id . , 1939, 832.

(11) Drew, H. D. K., Landquist, J., Ib id . , 1938, 292.

(12) Fletcher, h1. H., A N ~ L . CHEV, 32, 1822 (1960).

(13) Harvey, A. E., Jr., Manning, D. L., J. -472. Chem. Soe. 72,4488,(1960).

(14) Hildebrand, G. P., Reilley, C. N., A x - 4 ~ . CHEM. 29, 258 (1957).

(15) Johnson, J. S., Iiraus, K. A., S. Am. Chem. SOC. 78,3937 (1956).

(16) Jonassen, H. B., Cook, M. M., Wilson, J. S., Ib id . , 73, 4683 (1951).

(17) Koltz, I. M., Loh Ming, W. C., Ib id . , 75, 4159 (1953).

(18) Kraus, K. A., Johnson, J. S., Ibid. , 75, 5769 (1953).

(1t) Martell, A. E., Calvin, Melvin, Chemistry of the Metal Chelate

Compounds,” Prentice-Hall, New York, 1952.

(20) Newman, Leonard, Hume, D. N., J . Am. Chem. Sac. 79, 4571, 4576, 4581 (1957).

(21) Neyman, Leonard, LaFleur, W. F., Brousaides, F. J., Ross, A., Ib id . , 80,4491 (1958).

(22) Newman Leonard, Quinlan, K. P., Ib id . , 81, 54b (1959).

(23) Robinson, R. A., Stokes, R. H., “Electrolyte Solutions,” Butterworths, London, 1955.

(24) Schwarzenbach, G., Analyst 80, 713 (1955).

(25) Sullivan, J. C., Hindman, J. C., J . Am. Chem. Sac. 74,6091 (1952).

(26) Venkataraman, K., “The Chemistfy of Synthetic Dyes,” Vol. I, Academic

Press, New York, 1952. (27) Waterbury, G. R., Martin D. S.,

Jr., J. Am. Chem. Sac. 75,4161 (1953). (28) Zielan, A. J., Connick, R. E., Ibid. ,

78, 5785 (1956).

RECEIVED for review June 30, 1960. Accepted September 19, 1960. Publica- tion authorized by the director, U. S. Geological Survey.