ACKNOWLEDGMENT
sion current corresponding to Br03- represents a difference, iBrOJ= iobserved - iBrOa-.In the presence of perbromate, the diffusion must be measured by subtracting the charging current of the electrolyte alone from the current in the presence of bromate or perbromate. The polarographic method is rapid and quite suitable for the determination of perbromate in the presence of bromate.
The authors thank E. H. Appelman of the Argonne National Laboratory for the solution of potassium perbromate. RECEIVED for review August 6, 1970. Accepted November 25,1970.
Polarimetric Studies of Alkali Metal Ion Complexes of I-PropylenediaminetetraaceticAcid James D. Carr and D. G . Swartzfager Department of Chemistry, University of Nebraska, Lincoln, Neb. 68508 RECENTLY, SEVERAL REPORTS have appeared on the formation of weak 1 : 1 complexes between the alkali metal ions and the aminocarboxylate multidentate ligands: ethylenediaminetetraacetic acid ( I ) , d,I-propylenediaminetetraacetic acid (abbreviated d,l-PDTA) ( 2 , 3 ) and trans-l,2-diaminocyclohexaneN,N,N',N'-tetraacetic acid ( 4 ) . In the case of the potassium complex of d,l-PDTA, evidence of a chelated structure has been obtained via the NMR vicinal coupling constants of the ethyleneic protons. The stability constant of the complex was reported to be 1.5 at 100 "C and 5.7 at 35 "Cinextremely high ionic strength media ( p > 3) (3). Although such small interactions are usually quite difficult to observe under conditions where the information is most useful (lower temperature and ionic strength), this is not the case when optically active PDTA is employed. It has been well established that the optical rotatory properties of dissymmetric molecules are, in many cases, extremely sensitive to changes in conformation, solvation, and changes of a chemical nature. In the case of I-propylenediaminetetraacetic acid (abbreviated here as IPDTA or L), changes which occur upon complex formation are accompanied by a large change in the optical rotation. This provides a convenient and accurate method of monitoring the formation of these weak complexes. EXPERIMENTAL Apparatus. Polarimetric measurements were performed at 365 mp in a 10-cm cell thermostated at 25 'C in a PerkinElmer Model 141 polarimeter. All p H measurements were made with a Corning Model 12 expanded scale p H meter. Reagents. All solutions were prepared with deionized water and stored in polyethylene bottles. The anhydrous I-propylenediaminetetraacetic acid was prepared by the method of Dwyer and Garvan ( 5 ) . A 0.5% aqueous solution of the active acid gave a specific rotation of -50.0" at the sodium D line. Stock solutions of the cations sodium, potassium, cesium (Alfa Inorganics), and tetramethylammonium (Southwestern Analytical) were prepared from their respective hydroxides. Solutions of lithium and tetraethylammonium (1) G. Anderegg, Hela. Chim. Acta, 50, 2333 (1967). (2) J. L. Sudmeier and A. J. Senzel, ANAL.Cmw, 40, 1693 (1968). (3) J. L. Sudmeier and A. J. Senzel, J. Amer. Chem. SOC.,90, 6860 (1968). (4) J. D. Carr and D. G. Swartzfager,ANAL.CHEM., 42,1238 (1970). ( 5 ) F. P. Dwyer and F. L. Garvan, J. Amer. Chem. SOC.,81, 2955 (1959).
hydroxide were prepared via ion exchange of their chloride salts. All cation stock solutions were checked for the presence of sodium and potassium impurities by flame photomwere etry. Corrections, which were never greater than made for these impurities whenever necessary. Procedure. Working solutions were prepared volumetrically from the stock solutions. The initial concentration of I-PDTA was about 2.0 X 10-2 molar. After the alkali metal ion was added (in the hydroxide form), the ionic strength was adjusted to 0.5 with tetramethylammonium hydroxide which gave an initial p H of about 13.4. The optical rotation of the solution was determined as the pH was lowered by the addition of concentrated HCI. The observed molar rotation was then calculated according to Equation 1 after the total concentration of the active species was corrected for dilution.
5z,
[Cl'lobs = where
=
&be
b
=
c =
Cl'obs/bC
the observed rotation (degrees) cell length (centimeters) concentration (moles per liter) RESULTS AND DISCUSSION
The effect of a large excess of each of the cations on the observed molar rotation over the pH range from 1.5 to 13.5 is illustrated in Figure 1. Since the observed molar rotations in the presence of both tetramethylammonium and tetraethylammonium were identical within experimental error over the entire pH range, it is assumed that these cations do not interact with 1-PDTA. The behavior in the high pH region (9 t o 13.5) is generally consistent with the known complexation of lithium, sodium, and potassium; however, there is some indication that cesium is also being complexed or is in some way interacting with the active ligand. This interaction proved to be too small to measure quantitatively. The effect of varying the potassium ion concentration on the observed molar rotation in the high pH region is shown in Figure 2. Assuming that the species KHLZ- is nonexistent, the. constraints on the system are represented by Equations 2-5.
(3) ANALYTICAL CHEMISTRY, VOL. 43, NO. 4, APRIL 1971
583
-6
3
7 /---
I
i
-4t
i
g2[
L
1
c
i
" 1
t-
"r
20 '
I
i
E
o?
0 2
1 F
$+2? O
j
G
I
t
i
44L
*6\
'
1
7
8
9
I
,
10
11
12
13
14
PH
Figure 1. Effect of a large excess (0.35M) of each of the various cations on the observed molar rotation of I-PDTA (about 2.0 X
Figure 2. Effect of varying the potassium ion concentration in the high pH region
A , sodium; B , a mixture of sodium and cesium; C, potassium; D, lithium; E, cesium; F, both tetraethylammonium and tetramethylammonium
Concentration of potassium: A , 0.420M; B, 0.271M; C, 0.210M; D, 0.151M; E , O.121M; F, 0.061M; G , 0.01045M; H, 0
Fj
+ F, = 1
[K+I = [KIT - [LITF, where Ffand F, are identified as follows: Fj
i ~ 4 - 1
=
+
[ ~ ~ 3 - 1
[L]T
Utilizing Equations 2-4 and Equation 8,
+
[aloha = [ ~ I ~ F I[alcFc
l4
(8)
which relates the observed molar rotation at a given pH to the molar rotations of the free ligand [a]!(taken as the observed molar rotation in the presence of tetramethylammonium ion), and the complexed ligand [a], at the same pH, the following expression was derived. (9)
where the quantity Z is the inverse of the conditional stability constant (10) and F, is expressed in the following terms:
Utilizing Equations 9 and 11, the values of [a],and Z were calculated at several values of the hydrogen ion concentration with the aid of a computer program by an iterative least 584
ANALYTICAL CHEMISTRY, VOL. 43, NO. 4, APRIL 1971
!dc//j
I
12-
1 I I 1 -
1
2
3
C.3
4 5 x 10"
6
7
8
9
Figure 3. Plot of Equation 10
squares procedure involving successive approximations for
[ah. The values of Z determined in this way for data on the potassium system are plotted against the hydrogen ion concentration (Figure 3), which according to Equation 10 is a straight line with a slope of l/KKLK( and an intercept of ~ / K K L The . values of pK4 and K K Lwere determined to be 11.01 + 0.02 and 8.06 + 0.08, respectively. The same procedure was applied in the case of sodium ion as for potassium. The values of pK, and KN&Lwere found to be 11.01 + 0.05 and 3.56 + 0.44 X lo2,respectively. Utilization of the same procedure for lithium was impractical because of the high stability of the complex. Instead, a mole ratio plot was constructed (Figure 4) at a pH of 13.2 and
-77
,
,
,
I
I
I
A
i
t/
,
0
C2
*5 Y *67
, 06
04
,
1
,
00 10 12 14 16 18 moles of L I/ mole of I-P DTA
1
I
20
22
l
l
24
Figure 4. Mole ratio plot for complexation of lithium at a pH of 13.2. The concentration of I-PDTA at the equivalence point is 1.972 X ~~
1
~
Table I. Values of M
=
[CUI, for the Alkali Metal Complexes
0.5, T
Species LiL3NaL3KL3CSH~L KH2L'L4- (pH 13.4) HL3- (pH 8.4) HzL*- (PH 4.4)
'-
=
25 "C, X = 365 m p
[a](1-deg/cm-mole) -2.32 -6.06 -8 0 -7.9 -5.0 f5.81 -2.78 -3.51
K L ~ L = 1.02 X lo4 K N ~ L= 3.56 f 0.44 X 10' KKL = 8.06 i 0.08 K C ~ H=~ L 5.07 f 0 4 K K H ~ L= 6 . 2 3~ 0 . 8
the stability constant was calculated by conventional procedures to be 1.03 X lo4. The values of for the alkali metal complexes are presented in Table I. The effect of the various alkali metal ions on the observed molar rotation at low p H is illustrated in Figure 1. Initially this interaction was thought to follow the same sequence of reactivity as was observed at high pH, Le. Li > Na > K > Cs. However, this was inconsistent with the behavior in the presence of the tetraalkylammonium cations, which suggested the opposite sequence (Cs > K > Na > Li). T o clarify the situation, the observed molar rotation as a function of pH was determined in the presence of a mixture of both sodium and cesium ion. Curve B, Figure 1, shows that the molar rotation resembles that of sodium a t high p H and cesium at low pH. These results indicated that the observed effect, though not necessarily the reactivity, follows the second sequence.
Figure 5. Effect of varying the cesium ion concentration in the low pH region Concentration of cesium: A , 0.391M; B, 0.191M; C, 0.OS5M: D,0.01047M
For lithium and sodium, the observed effects were too small to allow quantitative calculations. The effect of varying the cesium ion concentration is shown in Figure 5. Assuming that the stoichiometry of the complex is 1 : 1, it can be shown that Equations 4, 5,8,9, and 11 still apply. The quantity 2 is now a rather complicated function of the hydrogen ion concentration involving the acid dissociation constant of I-PDTA, the stability constant of the unprotonated complex, and the equilibrium constants which relate the various possible forms of the complex (CsL3-, CsHL2--,and CsHH2L1-). However, the observed effects indicate that the interaction is predominantly with the diprotonated form of the ligand. Thus if the quantity 2 is evaluated at a pH of 4.4, where the species H2L2- represents greater than 9 8 z of the total free ligand concentration, then 2 simply reduces to the inverse of the stability constant of the complex (CsHL-). The values of K C ~ Hand ~ LK K H ~were L determined to be 5.7 + 0.4 and 6.2 i 0.8, respectively. The values of [ale for the two complexes are given in Table I. These results do not allow any definite conclusions to be drawn regarding the sequence of reactivity of the alkali metals with 1-PDTA at low p H or the nature of the interaction between the metal and the ligand.
RECEIVED for review August 19, 1970. Accepted November 30, 1970.
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