taining high W/Ti ratios. Hydrolytic precipitation of the titanium proved to be a simple and effective separation tech- nique. Adjustment of the pH of the dissolution medium to 12 (in the presence of fluoride to keep the tungsten in the acid solution) quantitatively precipitated the titanium with insignificant coprecipitation of the tungsten. Results of the analyses of synthetic mixtures of titanium and tungsten and two alloy samples are given in Table 111. Several experiments indicated that, in this manner, titanium can also be quantita- tively separated from molybdenum.

ACKNOWLEDGMENT Impurity analyses of the titanium metal were carried out

by J. W. Fischer, R. Lim, J. R. Stevens, and E. G. Walter.

RECEIVED for review December 14,1970. Accepted February 16, 1971. This work was performed under the auspices of the U. S. Atomic Energy Commission. Reference to a com- pany or product name does not imply approval or recom- mendation of the product by the University of California or the U. S. Atomic Energy Commission to the exclusion of others that may be suitable.

Determination of Formation Constants of Copper( II) Complexes of Ethane-1-hydroxy-1,l-diphosphonic Acid with a Solid State Cupric Ion-Selective Electrode

Hiroko Wada and Quintus Fernando Department of Chemistry, University of Arizona, Tucson, Ariz. 85721

The acid dissociation constants of ethane-l-hydroxy- 1,l-diphosphonic acid, (H4Y), and the formation con- stants of the copper(l1) complexes, CuY2-, CuHY-, and CuH2Y, have been determined in aqueous solution at 25 OC at an ionic strength of 0.1. The values of these concentration constants that were obtained potentio- metrically with a solid state cupric ion-selective elec- trode have been confirmed by potentiometric measure- ments with a glass electrode and by a spectrophoto- metric method. On the basis of the formation constant measurements, it has been proposed that the copper (11) complex has a six-membered chelate ring struc- ture.

ETHANE-~-HYDROXY-~ ,1-DIPHOSPHONIC ACID, (EDPA), is a polydentate ligand which forms soluble complexes with most metal ions and selectively precipitates thorium(IV), scandium (111), and the lanthanides from acid solutions ( I ) . A method for the selective determination of thorium(1V) has been proposed, in which the formation of a soluble binuclear ternary complex of thorium(1V) has been postulated ( I ) . If the oxygen donors on one phosphonic acid group in the EDPA molecule participate in metal complex formation, mononuclear and binuclear complexes containing four- membered metal chelate rings will be obtained. If the oxygen donors are from two different phosphonic acid groups in the same EDPA molecule, six-membered chelate rings will be formed. In addition to four- and six-membered rings that can be formed, a variety of neutral and protonated metal chelates may also be present in solution.

To assess the usefulness of EDPA as an analytical reagent it is important to recognize the different types of complexes that are obtained when solution parameters such as acidity and ligand concentration are varied. A study of the metal complex equilibria involving copper(I1) and EDPA was undertaken therefore, as part of a systematic study of poly- dentate ligands of the same type. This particular system was chosen since it seemed feasible to determine the con- centrations of various species in solution by at least three

methods that complement each other: the free copper(I1) ions in solution could be determined potentiometrically with a solid state cupric ion-selective electrode, the hydrogen ions that are released upon complex formation could also be determined potentiometrically with a glass electrode, and, finally, the concentration of a copper(I1) complex that is formed in solution could be measured spectrophotometrically. This approach should yield reliable complex formation con- stants which could be used as a basis for deducing the kinds of metal complexes that might be expected in solution.

EXPERIMENTAL

Synthesis of EDPA. Ethane-1-hydroxy-1,l-diphosphonic acid was prepared by the action of acetic anhydride on phos- phorus acid (2). One mole of solid phosphorus acid and 1.1 moles of acetic anhydride were heated to 100 "C, maintained at this temperature for one hour, and the mixture steam distilled until the distillate was no longer acidic. The oily residue in the distilling flask was dissolved in water, and the pH of the resulting solution was adjusted to a value between 8 and 9 with sodium hydroxide. Ethyl alcohol was added to the solution until a white precipitate of the trisodium salt, EDPA.3Na, was formed. The crude salt was separated and purified by recrystallization from an ethanol-water mixture. The di- and trisodium salts of EDPA were found to be slightly hygroscopic and the free acid and the monoso- dium salt were extremely hygroscopic. An elemental analysis of the trisodium salt indicated that it contained about 8 % water, (Found: C , 8.11%; H, 2.50%; P, 21.13z; Calcd forEDPA.3Na.1.21H20; C, 8.11 z; H,2.56%; P,21.09%). After intensive drying the compound was titrated with a standard solution of (CH&NOH and was found to be 100% pure and free of water and acidic contaminants. The lH NMR spectrum of the compound in D20 exhibited the expected triplet that arises from the methyl protons that are split by two phosphorus atoms. Standard solutions of EDPA were prepared by dissolving EDPA in deionized water and standardizing the solution potentiometrically with stan- dard (CH&NOH.

(1) R. Pribil and V. Veseley, Tulunta, 14, 591 (1967). ( 2 ) B. T. Brooks, J. Amer. Chem. SOC., 34, 496 (1912).

ANALYTICAL CHEMISTRY, VOL. 43, NO. 6, MAY 1971 751

Reagents. All chemicals used were of reagent grade purity. Standard solutions of copper(I1) were prepared from C U ( C ~ O ~ ) ~ and standard EDTA. In this work (CzH&NC104 was used to maintain the ionic strength of all solutions at 0.1.

Apparatus. EMF measurements were made with a Beck- man Model G pH meter. The measurements of pH were made with a Beckman Type E2 glass electrode and a satu- rated calomel electrode calibrated with Beckman buffers. An Orion Cupric Ion Activity Electrode, Model 94-29A, was used together with a double junction reference electrode for measurements of the copper(I1) ion activity in solution. The response of the electrode was checked with standard solutions of copper(I1) ranging in concentration from 5 x 10L3M to 2 X 10PM and was found to be Nernstian. Since it was anticipated that much lower concentration levels of copper(I1) would have to be measured, the electrode was subjected to a more stringent test with solutions containing much smaller concentrations of copper(I1). Errors that are usually encountered in the use of standard solutions of low concentrations that have been prepared by successive dilu- tion of a stock solution will be minimized if an appropriate metal buffer solution is employed to measure the concentra- tion of free copper(I1) ions in solution. This was in effect accomplished by the measurement of the overall formation constant of the complex, CU(NH;)~~+. The value of this constant that was calculated from the potentiometric titra- tion of a solution containing NH4N03 (0.10M) and Cuz+ (0.01M) with standard NaOH using the solid state cupric ion-selective electrode and a reference calomel electrode was 1 0 1 2 . g 6 , which agreed well with the value of 1 0 1 3 . 0 5 that was measured in 2M NH4N03 at 25 “C by a potentiometric method with a glass and calomel electrode (3). As a further test, the formation constant of the 1 : 1 copper(I1)-nitrilo- triacetic acid complex was determined at an ionic strength of 0.1. The pH of a solution that was 1.049 X 10d3M in nitrilotriacetic acid and 0.470 X lOL3M in copper(I1) was varied between 1.3 and e.5 and the potential difference between the solid state cupric ion-selective electrode and a saturated calomel reference electrode was measured. The formation constant of the 1 : 1 complex calculated from these results was 1012.97, which is in good agreement with the values 1012.96 ( 4 , 5), and 1013.10 (6) , that have been reported in the literature. From these experiments it was assumed that the solid state cupric ion electrode could be used to measure copper(I1) concentration levels of the order of 1 O-I1 M.

Potentiometric Determination of the Acid Dissociation Constants of EDPA and the Formation Constants of Copper (11)-EDPA Complexes. The titration apparatus consisted of a water-jacketed 250-ml vessel fitted with a stopper in which appropriately located holes allowed the insertion of a buret, a pair of electrodes, and a nitrogen gas inlet tube. Titrations were carried out in a carbon dioxide free atmosphere by bubbling nitrogen gas slowly through the solution and maintaining an atmosphere of nitrogen gas above the solution. Water from a constant temperature bath maintained at 25 “C was circulated through the jacketed beaker. A solution of carbonate free tetramethylammonium hydroxide (obtained by passing the solution through the anion exchange resin Amberlite XRA-400), was stored under nitrogen in a poly- ethylene bottle; a self-filling buret, filled by using a positive pressure of nitrogen, was used to add the tetramethylammo- nium hydroxide solution to the titration vessel. The tetra- methylammonium hydroxide was standardized with NBS primary standard potassium hydrogen phthalate.

(3) C . G. Spike and R. W. Parry, J. Amer. Chem. Soc., 75, 2726

(4) G. Schwarzenbach and R. Gut, Helc. Chim. Acta, 34, 1589

(5) G. Schwarzenbach, G. Anderegg, W. Schneider, and H. Senn,

(6) T. Moeller and R. Ferrlis, Inorg. Chem., 1, 55 (1962).

( 195 3).

( 1956).

ibid., 38, 1147 (1955).

A standard solution of the ligand was introduced as a solution of the ditetramethylammonium salt into the titra- tion vessel, tetraethylammonium perchlorate was added to maintain the ionic strength at 0.1, and the resulting solution was titrated with standard perchloric acid for the determina- tion of ~ K z . Values of pK3 and pK4 were determined by the titration of the di- and tritetramethylammonium salts, re- spectively, with standard (CH3)4NOH solution. The value of pK1 is too low to be measured potentiometrically with a glass electrode. The pH meter readings were converted into [H+] values (hydrogen ion concentrations) by using a correction factor that was calculated from the titration curve of perchloric acid with tetramethylammonium hydroxide at the same ionic strength of 0.1. Hence, the constants obtained are concentration constants and are valid at an ionic strength of 0.1, and EDPA concentration of 0.01M.

The complex formation constants were calculated from the potentiometric titration data obtained with an Orion solid state cupric ion-selective electrode and a saturated calomel reference electrode. The solutions used in the measurements consisted of copper(II), EDPA, HC1o4, and ( C Z H ~ ) ~ N C ~ O ~ to maintain a constant ionic strength of 0.1. Titration of these solutions was carried out with standard (CH3)4NOH solution. The method for calculating the acid dissociation constants and the complex formation constants from the titration data are described in the next section.

Equilibrium constants for the addition of a proton to the species CuY 2- and CuHY- were obtained potentiometrically by the measurement of the hydrogen ion concentrations in solutions containing C U ( C ~ O ~ ) ~ , EDPA, and (C2H5)4NC104, when titrated with standard (CH3)4NOH solution. The method, therefore, is tantamount to the determination of the acid dissociation constants of CuHzY and CuHY-.

RESULTS

The dissociation of the free acid may be represented as follows:

HO OH OH -0 OH OH \ I / kl \ I / kz o=p-c-p=o O=P-c-P=O + / I \ / I \

HO CHI OH HO CHB OH W4Y) (H3Y-) -0 OH 0- -0 OH 0-

\ - I / ks \ I / k4 O=P-C=P=O - 7 O=P-c-P=O + HO CH, OH

/ I \ -0 CHB OH

/ I \ (HY3-)

-0 OH 0-

W 4 - )

The following equations were used to calculate the acid dissociation constants from the potentiometric titration data.

where all the concentration terms are expressed in moles/l., and C y is the molar analytical concentration of EDPA, and [B+] = [(CHEJ~N+]. The acid dissociation constants that were obtained from Equations 1 and 2 by a linear least squares method are listed in Table I.

752 ANALYTICAL CHEMISTRY, VOL. 43, NO. 6, MAY 1971

Table I. Acid Dissociation of Complex Formation Constants of Cu-EDPA at 25 "C and Ionic Strength 0.1

Acid Dissociation Constants of EDPA

( 2) 2.31 6 .99 10.93 Method" Pkn Pks Pk4

Formation Constants of Cu-EDPA Complexes Cu : EDPA

ratio log KE& log K:Ly log K& (1) 1: 10 4 .80 7 .47 11.84

Protonation Constants of Cu-EDPA Complexes Cu : EDPA

ratio log K&H~Y log K ~ H Y 1 :3 4 . 3 6 .8 1:lO . . . 6 . 4

( 2)

( 4) 1:lO 4 . 3 6 . 6 (3)

a Method: (1 ) Potentiometric determination with solid state

(2) Potentiometric determination with glass elec-

(3) Spectrophotometric determination. (4) Calculated from Equations 31 and 32.

cupric ion selective electrode.

trode.

100

mv

The polydentate ligand, EDPA, can form a variety of com- plexes with copper(I1). In a solution containing copper(I1) and about a tenfold excess of the ligand the variation of [CuZ+] (which is proportional to the measured potential difference between the solid state cupric electrode and the reference electrode) with pH is shown in Figure 1. In the vicinity of pH 3, where HzY2- is the predominant species of the ligand, the curve flattens out and it is reasonable to assume that the predominant complex species that is present in solution is CuH2Y. This assumption was verified by the calculation of the complex formation constant, K::YHzy, from EMF measurements in solutions that had a pH range from 3.5 to 2.0. The complex formation constant, KEiZ2Y, is defined by the equation:

-

-

Let the total concentration of EDPA that is not bound in the complexes be represented by Cy', and the side reaction coeffi- cient by CY^,^(^), where

(4)

The term LHzY2-] can be eliminated from Equations 3 and 4 to give :

p c u * + = -log pz:"> ~ + log K : & ~ - log a H z y ( H ) ( 5 )

where p cu2+ = -log [CUZ+I, (6)

If the measured potential difference between the Orion solid state cupric ion electrode and the reference calomel electrode is E millivolts, the relation between E and p Cuz+, obtained from the Nernst Equation is:

E' - E p CU" = ___ at 25 "C

29.6 (7)

E' is a constant, the value of which depends on the standard electrode potential of the solid state cupric ion electrode, the liquid junction potential, the potential of the saturated calo-

- loot I 1 I I I

6 8 PH

2

Figure 1. Effect of pH on the potential of the solid state cupric ion-selective electrode (us. SCE)

CcU = 8.90 X 10-4M; Cy = 1.10 X 10-ZM; ionic strength = 0.1

me1 electrode, and the activity coefficient of the copper(I1) ions in solution.

If only one complex species, CuH2Y, is present in solutions of pH < 3.5, Equation 5 predicts that a plot of p Cuz+ us. log a H 2 y ( H ) should give a straight line of slope -1 and y-

. The con- CCuHnYl

intercept equal to log K : , & ~ - log ~

CY' centration terms, [CuHzY] and Cy' were readily calcu- lated from the initial concentration of Cuz+ and the EDPA, assuming stoichiometric formation of the CuHzY complex

was constant in the pH range [CuHzY]

and that the term log ~

C Y ' 3.5 to 2.0, when CY^^^(^) varied from 0.09 to 0.64. In this pH range a plot of p Cu2+ us. log aH2Y(H) gave a straight line of slope -1 and log K:,&y calculated from the y-intercept was 4.80. A typical set of data for the calculation of log KE&y is given in Table 11.

In the regionin which pH > 3.5, the complex CuHzY would be expected to lose protons and form the species CuHY- and CuY2-. The formation constants of these two complexes are defined by:

H Y [CuHY-] [Cu2+] [HY KCuHY = ~~

and

Y [CUY 2-1

[CU~+I [Y 4-1 KCUY = (9)

and the side reaction coefficients C Y H ~ ( H ) and CY^(^) are given by :

If Cy' represents the concentration of uncomplexed EDPA, Equations 12 and 13, which are analogous to Equation 5 , can be derived for the calculation of log KCHUYHY and log G U Y .

[CuHY-1 p cuz+ = -log {c,-} +

ANALYTICAL CHEMISTRY, VOL. 43, NO. 6, MAY 1971 753

Table 11. Potentiometric Data for Determination of Formation Constants of Cu-EDPA Complexes with a Solid State Cupric Ion-Selective Electrode at 25 "C and an Ionic Strength of 0.1

C,, = 8.90 X 10-4Mand Cy = 1.10 X 10-ZM

mV p Cu2+ PH log ( Y H ~ Y ( H ) mV P Cu2+ PH logCYHY(H) rnV p Cu2+ pH log CYY(H)

138 5.17 2.16 0.64 108 6.18 4.59 2.38 135 5.27 2.32 0.52 103 6.35 4.81 2.16 30 8.82 6.94 4.34 132 5.37 2.40 0.47 99 6.49 4.96 2.02 26 8.95 7.09 4.13 128 5.51 2.54 0.38 92 6.79 5.20 1.78 20 9.16 7.24 3.93 127 5.54 2.73 0.28 88 6.86 5.36 1.63 13 9.39 7.46 3.68 123 5.68 2.82 0.23 83 7.03 5.48 1.52 3 9.73 7.69 3.36 121 5.74 3.06 0.12 78 7.20 5.62 1.38 -8 10.10 8.04 2.94 1 20 5.78 3.25 0.09 76 7.26 5.73 1.28 - 23 10.60 8.60 2.36

- 30 10.84 8.80 2.16

log Kgf&y = 4.80 log K C H U ~ ~ ~ = 7.47 log K&y = 11.84

Between pH 4.6 and 5.8, a plot of p Cu2+ us. log a H y ( H ) gave a straight line of slope -1, and the value of log KCHUYHY calculated from the y-intercept was 7.47. Similarly, between pH 6.9 and 8.8, a plot of p Cu2+ us. log Q ~ ( ~ ) gave a straight line of slope -1 and the value of log KZUy calculated from the y-intercept was 11.84. In both cases the concentration

[CuHY-] [CuY2-] ratios -7 and ___ were assumed to be constant

CY CY' and their values were obtained from the initial concentra- tions of copper(I1) and EDPA and the assumption that the predominant metal complex species in solution was CuHY- in the pH region 4.6 to 5.8 and CuY 2- in the pH region 6.9 to 8.8. Table I1 gives typical sets of data from which log KE:HY and log KgUy could be calculated.

Two methods were used to confirm the validity of the com- plex formation constants that were obtained by the use of the solid state copper electrode. The formation of the species CuHY- and CuY 2- involves a loss of protons, and it should be possible, in principle, to determine the successive formation constants of these species by the potentiometric titration of solutions, made up of Cu(C104)2, EDPA, HClOd [and (C2H6)4NC104 to keep the ionic strength at 0.11, with (CH&NOH using a glass-saturated calomel electrode pair. The equations that were used for the calculation of these formation constants are derived below.

Under the solution conditions that were employed for the potentiometric measurements with a glass and saturated calomel electrode, the following concentration terms can be neglected: [Cu2+], rn3Y-1, [Y4-], [H+] and [OH-].

Cy = [CUHY-] + [CUY '-1 + [HzY '-1 + [HY '-1 (14)

C,, = [CUHY-] + [CUY'+] (15)

Subtraction of Equation 15 from Equation 14 gives:

C y - Ccu = [H;Y2-] + [HY3-] = [HY3-]{1 + [T} (16)

The charge balance equation in the system is given by:

[B+l = [Clod-] + 2[HzYz-l + 3[HY3-] + [CuHY-1 + 2[CuY2-] (17)

where

[C104-] = 2ccu. (1 8)

The concentration of CuHY- obtained from Equations 14, 16, 17, and 18 is given by Equation 19, and the concentration of CuY2- obtained from Equations 15 and 19.

CY - ccu [CUHY-] = 2Cy + 2Ccu -

The equilibrium constant, KZuHY, defined by:

[CuHY-I [CUY 2-1 [H+] KkHY =

can now be calculated from the following equation obtained by substituting for [CuHY-] and [CuYz-] from Equations 19 and 20 in 21.

In a region of lower pH where the complex species CuHzY predominates, the concentration terms [Cu2+], [HYa-l, [Yd-], and [OH-] can be neglected and the equilibrium con- stant KguHlY can be obtained from the analogous Equations 23-29.

C y = [CUHY-] + [CUH~Y] + rnsY-1 + [HzYz-l (23)

Ccu = [CUHY-] + [CUHZY] (24)

754 ANALYTICAL CHEMISTRY, VOL. 43, NO. 6, MAY 1971

DISCUSSION

The first dissociation constant of the tetraprotic acid (EDPA), CH3C(OH)(POaH&, is too large to be measured potentiometrically; the three successive dissociation con- stants that have been measured are well separated (Table I). This simplifies the problems that are encountered in complex formation studies with copper(I1) since only two, or at the most, three anionic species of the ligand will have to be taken into consideration over a reasonably wide pH range. It has been shown experimentally that in the pH range 6.9 to 8.8, the predominant metal complex species that is present in solution is CuYz-, which has a formation constant of 1011.8*. This formation constant is much greater than the constant that would be expected if a four-membered chelate ring was formed. The metal chelate, CuY2-, probably has a more stable six-membered ring configuration.

0 0- \ /

HO P-0

Table 111. Spectrophotometric Data for the Determination of log KZuHY at 25 "C and Ionic Strength 0.1

A Absorbance at 1 cy x 103

255 nm [H+] x 10- (ec"Y2-.Cc" - A ) 0.228 0.339 8.64 0.259 0.708 10.3 0.276 1 .oo 11.4 0.298 1.48 13.4 0.326 2.63 17.2 0.350 4.17 22.7

ccu = 1.38 x 10-4~ ; cy = 1.70 x 1 0 - 3 ~ .

[CUHY-] = [B+] - Cy - Ccu + [H+] -

E KCuHzY =

The equilibrium constants in Equations 22 and 29, obtained from measurements with a glass and saturated calomel electrode, are related to those in Equations 8 and 9, obtained from measurements with the solid state cupric ion-selective electrode. The relationships are:

(32)

The constants obtained are summarized in Table I. An examination of the absorption spectra of solutions

containing Cu2+ and EDPA in a 1 :10 ratio showed that a marked change in the absorbance at 255 nm occurred in the pH region 7.5 to 6.0. The potentiometric data obtained in this pH region indicate that the species CuY+ and CuHY- are the important copper(I1) complex species present in the solution. Consequently, it should be possible to measure the equilibrium constant KguHY by a spectrophotometric method. Table I11 shows the variation of absorbance with pH in a solution containing Cu2+ and EDPA in a ratio 1 : 10. The value of log KgUHY was calculated from a plot of

us. ~ where A is the measured ab- ( C C u . E C u Y 2 - - A ) W+I' sorbance and eCuY2- is the molar absorptivity of CuYz-. This value of log KEuHy is included in Table I for purposes of comparison with the rest of the tabulated equilibrium constants.

H H Y K C ~ H Y = KcuHy/K&y.k4

1 CY

c u \

/ \ / 'C/

H3C P-0 / \

0 0-

This chelate can add two protons successively to give the com- plex species, CuHY- and CuH2Y. The addition of a proton to the dianion, CuY 2-, should take place more readily than the addition of a proton to the monoanion, especially if there is some degree of delocalization of the negative charges in the metal chelate. This is reflected in the formation con- stants of CuHY- and CuHzY as well as in the protonation constants of these two complexes (Table I). The maximum meta1:ligand ratio employed in this work was 1 :lo. Under these conditions, no insoluble complexes of copper(1I) were formed. It was observed, however, that if the metal: ligand ratio was decreased to about 2 : 1, precipitation occurred, probably due to the formation of a binuclear complex. It would be of interest to determine the structure of the insoluble copper(I1) complex, especially since it has been proposed that the insoluble thorium(1V) complex forms four-membered chelate rings with this ligand (I).

RECEIVED for review December 2, 1970. Accepted February 11, 1971. This work was supported by U. S. Atomic Energy Commission Grant No. AT(11-1)-1654.

Correct ion High Sensitivity Internal Reflection Spec t roelec t roc hem i st ry for Direct Monitoring of Diffusing Species Using Signal Averaging

In this article by Nicholas Winograd and Theodore Kuwana [ANAL. CHEM. 43, 252 (1971)] the following credit should be added on page 259, column 2:

The authors acknowledge the financial support of the National Institutes of Health (GM14036) and the National Science Foundation (GP9306).

ANALYTICAL CHEMISTRY, VOL. 43, NO. 6, MAY 1971 755