ratio, resulting in a wider accessible dynamic range for the measured variable. Comparing the polarographic with the spectrophotometric method of studying association equilibria, errors of cornparable magnitude are indicated (22). (22) K. Conrow, G . D. Johnson, and R. E. Bowen, J. AmeraChem. Soc., 86, 1025 (1964).
RECEIVEDfor review July 17, 1969. Accepted June 18, 1970. Presented in part at the 157th National Meeting, American Chemical Society, Minneapolis, Minn., April 1969. Work supported in part by the Petroleum Research Fund through Grant No. PRF 1396-G2.3. Funds for commter time Provided by the University of Georgia Computer Center are gratefully acknowledged.
A Complexometric Titration for the Determination of Sodium Ion James D. Carr and D. G . Swartzfager Department of Chemistry, University of Nebraska, Lincoln, Neb. 68508 A method for the direct complexometric titration of sodium ion with CyDTA in the presence of other alkali metal ions, alkaline earth metal ions, transition metals, and rare earth metal ions is described. The method is accurate within 2% for sodium ion concentrations as low as molar and utilizes a sodium ion specific electrode for end-point detection. The stability constants for the 1:l complexes of sodium and potassium with CyDTA are determined to be 2.5 =t0.4 X lo4 and 33 + 2, respectively. The value of the pK4 of CyDTA is determined to be 13.17 0.08.
*
1 :1 complex of measurable stability with potassium (7). Since complexes of CyDTA are usually more stable by at least an order of magnitude than those of d,l-PDTA (8), the possibility of appreciable complexation between potassium and CyDTA was also investigated. The stability constant of sodium-CyDTA is measured potentiometrically and that of potassium-CyDTA is calculated indirectly. Kxacg
+ C Y D T A - ~ NaCyDTA-3 KKC~ K+ + CyDTAKCyDTA-
Na+ THERECENT DEVELOPMENT of the sodium ion selective electrode offers a fast, convenient, and relatively inexpensive method for the determination of sodium. The technique, however, suffers from the variation of the sodium ion activity with solution composition. In this work a method for the direct complexometric titration of sodium ion in the presence of excesses of other alkali metals, alkaline earths, transition metals, and rare earth metal ions is described. The method is sensitive to concentrations at least as low as molar with accuracy and relative precision of less than 2%, utilizing a sodium ion electrode as the means of endpoint detection. A variation on the technique also affords a method for the titration of lithium ion utilizing sodium ion as an indicator. Various other chemical schemes have been proposed for sodium analysis but many are imprecise and require tedious and frequent standardization for reliable results. The method described employs trans-l,2-diaminocyclohexane-N,N,N’,N’-tetraacetic acid (abbreviated here as CyDTA or Cy, abbreviated elsewhere as DCTA) as the complexing ligand. The sodium complexation of the aminocarboxylate multidentate ligands has been illustrated in several contexts in the past, but usually as a handicap to be overcome rather than as a useful analytical reaction (1-6). Recently it has been demonstrated that d,l(l,2-propylenedinitri1o)tetraacetic acid (abbreviated as d,l-PDTA) forms a (1) R. J. Kula, D. T. Sawyer, S. I. Chan, and C. M. Finley, J. Amer. Chem. SOC., 85, 2930 (1963). (2) J. L. Sudmeier and C. N. Reilley, Inorg. Chem., 5, 1047 (1966). (3) R. J. Kula and G. H. Reed, ANAL.CHEM., 38, 697 (1966). (4) J. D. Carr, K. Torrance, C. J. Cruz, and C. N. Reilley, ibid., 39, 1358 (1967). ( 5 ) G . Schwarzenbach and H. Ackermann, Helv. Chim. Acta, 30, 1798 (1947). (6) V. Palaty, Can. J. Chem., 41, 18 (1962). 1238
0
(1) (2)
Other alkali metal ions (except lithium) form much weaker complexes than does sodium and do not interfere with the titration. Alkaline earths, transition metal ions, and rare earths form much stronger complexes than sodium and may be titrated first to a visual or conventional potentiometric end point prior to the sodium end point. Though not directly demonstrated in this work, the tetraanion of CyDTA appears to be the only species which reacts with sodium ion to an appreciable extent. In order to have a large fraction of the total CyDTA species present as the tetraanion, the solution pH must be maintained considerably above the pK4 of CyDTA [calculated from the accepted best value (9) and ionization enthalpy (8) to be 12.29 at 25 “C, p = 0.1 with KNOB]. Potassium hydroxide, potassium orthophosphate, cesium hydroxide, and piperidine, all were used to raise the pH to these values without introduction of substantial sodium impurity. EXPERIMENTAL
Apparatus. All potentiometric measurements involving the sodium ion specific electrode (Corning Model No. 476210) were made with a Corning Model 12 expanded scale pH meter, The titrant was introduced with a 2-ml capacity Gilmont micrometer buret. When simultaneous pH measurements were required, a Sargent Model LS pH meter equipped with a Corning semimicro combination electrode was employed. Solutions and Reagents. All chemicals used were reagent grade whenever possible. The CyDTA was obtained from ~~
~
(7) J. L. Sudmeier and A. J. Senzel, ANAL,CHEM., 40, 1693 (1968). (8) L. G. Sillen and A. E. Martell, “Stability Constants of Metal Ion Complexes,” Special Publication No. 17, The Chemical Society, London, 1964. (9) G . Anderegg, Helv. Chim. Acra, 46, 1833 (1963).
ANALYTICAL CHEMISTRY, VOL. 42, NO. 11, SEPTEMBER 1970
10.0
8.0
3.5
P N ~ m
6C
-2
X
T 54.0
3.0
2.0
2.5
0.0
0
I
I
I
I
1.0
3.0
5.0
70
~
1.o J.5 moles CyDTA/mole Ne
0.5
~
1
0
I ~
Figure 2. Plot of Equation 7
Figure 1. Effect of varying pH on the titration curve at zero potassium ion concentration pH: (1) 13.10; (2) 12.80; (3) 12.50, (4) 12.24, (5) 12.02[CyDTA] = 0.112 M ; initial [Na+] = 5.5 X lO-3M
the Aldrich Chemical Co. and used without further purification. It was recognized that both potassium and cesium hydroxide (Alfa Inorganics) contained sodium as an impurity ; the level of sodium present in potassium hydroxide was taken as reported 0.05%, the impurity level in cesium hydroxide was determined by flame photometry to beO.l%. Results were corrected for these impurities whenever necessary. Standard solutions of sodium and lithium ion were prepared by direct weighing of their chloride salts. All CyDTA solutions were prepared by the addition of the appropriate base (CsOH, KOH, or piperidine) to the tetraacid until a pH of 12 to 13 was achieved and were standardized by titration of a standard calcium solution. Procedure. When quantitative measurements of the stability constants and the fourth acid dissociation constant of CyDTA were performed, the response of the sodium ion electrode was calibrated with two standard solutions of sodium chloride in a pH and ionic strength medium similar to that in which the measurements were being made. A slope of 58 mV per concentration decade was observed as opposed to the expected theoretical value of 59.1 mV. No appreciable effect on the electrode response was observed when potassium ion was present at a concentration of 0.1M even at the lowest sodium ion concentrations (approximately 10-4M). Also no effect was observed on changing the pH within the region under investigation. All quantitative measurements were performed in a thermostated cell at 25 OC and ionic strength was adjusted to 0.10 with cesium nitrate. Initial solution volume was 15.0 ml. The sample solutions were prepared by volumetric addition of the appropriate standard solutions and the pH was adjusted with the base corresponding to the cation of the CyDTA titrant. Titrations performed in the presence of calcium, copper, or blood serum were first titrated to the visual murexide end point in a weak ammonia solution. The pH was then adjusted with CsOH or piperidine and the
response of the sodium ion electrode monitored to determine the sodium end point which was taken as the inflection point of the titration curve or the maximum in the first derivative curve. The accuracy of the sodium titration therefore depends upon the accuracy of the pre-titration. A small relative error in the pre-titration of a large amount of heavy metal will cause a large relative error in a subsequent sodium titration. RESULTS AND DISCUSSION
Stoichiometry of the Complex. Although the inflection point of the titration curve occurs at a molar ratio of sodium to CyDTA equal to one, the possible existence of a 2 :1 complex (Na2CyDTA2-) of measurable stability still remains. In order to determine if such a species is present, CyDTA was titrated with sodium ion. A plot of millivolts us. -log([NaIT - [CyIT)in the region where the 1 :1 complex is at least 98% formed (150 to 250% titration) gave a straight line with a slope of 58.2 mV indicating that any 2 : 1 complex is either nonexistent or extremely weak. Stability and Acid Dissociation Constants. The effect of the solution pH (adjusted with CsOH) on the titration curve is illustrated in Figure 1 . Assuming that cesium does not form a complex with CyDTA and that the species NaHCyDTAZ- is nonexistent relative to NaCyDTA 3-, the constraints on the equilibrium system can be represented by Equations 3-6. (3)
(4) [CYIT= [CY4-1
+ [HCy3-l + [NaCy3-l
(5)
+ [NaCy3-l
(6)
1 N a l ~= [Na+]
ANALYTICAL CHEMISTRY, VOL. 42, NO. 11, SEPTEMBER 1970
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*I 1
w
n
90
0.
50
I
0.5 1.o moles CyDTA/mole N d
1.5
Concentration of potassium: (1) 0.0, (2) 1.5 X 10-2M,(3) 3.8 X lO-%V, (4)7.9 X 10-2M. [CyDTA] = 0.112M; initial [Na+] = 5.5 X 10-*M
Using these Equations the following expression is derived by substituting Equations 3 and 4 into Equation 5 , rearranging, and substituting Equation 6 and rearranging further.
(7)
where: A =
+
[Na+l([Cyl~- [ N a l ~ iNa+l) [Nab - [Na+l
I
I
I
0.8
1n.2
1e 6
ml CyDTA
Figure 4. First derivative curve of sodium ion titration. p H = 12.6 (piperidine), initial [Na+] = 5.5 X 10-3M; [CyDTA] = 0.112M
Figure 3. Effect of varying potassium ion concentration on the titration curve a t a constant pH of 12.00
[H+l = A K ~ K N-~ K4 c~
I
04
(8)
The quantity A can be shown by substitution of Equation 6 and then 4 into Equation 8 to be equal to the inverse of the conditional stability constant of sodium-CyDTA. The only experimental quantity required to calculate A from Equation 8 is ma+] which is obtained from the potentiometric data at
each of six points in the region of 130-200% titrated on each of the titration curves shown in Figure 1. The relative standard deviation of the values of A from a given titration curve was never greater than 3.6% and was limited by the accuracy of the response of the sodium ion electrode. A plot of IN+] VS. A yields a straight line with a slope of K4K~.cyand an intercept of minus K4 (Figure 2). The values of log K N ~ c ~ and pKc which were obtained from a weighted linear least squares analysis of Figure 2 are, respectively, 4.40 f 0.08 and 13.17 f 0.08 where the uncertainty is one standard deviation calculated by the least-squares program. The effect on the titration curve of varying the potassium ion concentration when the pH is held constant is shown in Figure 3. In this case the system can be characterized by employing the same arguments as before with Equation 5 modified to include the species K Q 3 - and the addition of the following new constraints.
Table I. Results of Titrations
0
b
Moles Na+ added X lo6
Moles Na+ found X lo6
PH
9.78 9.83 10.05' 9.83 9.83 11.2 10.05 12. lb
9.67, 10.0 9.78 10.00,9.83,9.94 10.0 10.0 11.4 10.4 11.9
12.6 12.7 12.6 12.6 12.6 13.0 12.6 12.6
Base Piperidine Piperidine Piperidine Piperidine Piperidine CsOH Piperidine Piperidine
Moles Li+ added X lo4
Moles Li+ found X lo4
9.34
9.27
12.7
Piperidine
Unknown to operator until values had been reported. By flame photometry.
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ANALYTICAL CHEMISTRY, VOL. 42, NO, 11, SEPTEMBER 1970
Other metal ions present
Caa+(16.0 X mole) Cu2+( 6 . 3 X mole) Caa+( 8 . 0 X mole) Cas+ (54.2 X 1 0 - 6 mole) K+, Cas+, Mga+-pigeon blood serum
"'1
I
I
I
1
I
1
rnv
L mi CyDTA Figure 5. Typical titration curves of sodium ion with piperidinium Cy DTA (1) No other metal ions present, (2) in the presence of Ca+* (0.010 M),(3) in the presence of C U +(0.004M) ~
(9)
+
[KIT = [K+l [KCy3-1 (10) These relationships lead directly to the following Equation
+
K K C=~ [AKN,C~ - (1 H+/K4)1[K+l-' (11) A is defined as before. Using the values of K 4 and KN~Q. previously determined, the value of K K Cwas ~ calculated by successive approximations to be 33 f 2. It should be noted at this point that the value of pK4 reported in this work is substantially larger than that reported earlier (9). This is due to the fact that in the previous work potassium nitrate was employed for ionic strength control without consideration of complex formation between potassium and CyDTA which leads to a low apparent pK4 value. Determination of Sodium. As shown in Figure 1 the titration of sodium ion with cesium-CyDTA at a sufficiently high pH (roughly, pH > 12.5) easily allows end-point detection with a relatively high degree of accuracy and precision. A typical first derivative curve used to select an equivalence point is shown in Figure 4. The high cost of CsOH and the difficulty encountered with its sodium impurities make it a less desirable reagent than might appear at first glance. Several other inorganic bases such as potassium ortho phosphate and potassium hydroxide were used initially but proved to be unsuitable for analytical titrations due to the high potassium ion concentration they afford. The organic base piperidine meets the requirement of supplying a high enough pH and is virtually free from sodium and potassium impurities. Piperidine is a relatively poor complexing ligand so will have little effect on other equilibria. As seen in Figure 5 and from the results in Table I, the use of piperidine (1-2 molar) allows end-point detection within an acceptable limit of uncertainty
0
I
2.0
I
4.0
ml CyDTA
I
I
6.0
8.0
Figure 6. Titration curve of lithium ion using sodium as indicator even in the presence of excesses of other metal ions. No quantitative attempt was made to correlate piperidine with CsOH because of the difference in solution composition. Determination of Lithium. As mentioned earlier, it is possible to employ sodium ion as an indicator for the determination of lithium. A typical titration curve is shown in Figure 6 and results are presented in Table I. The only drawback to this method is that sodium is usually present as a substantial impurity in lithium and must be determined independently. This however can be accomplished to a sufficient degree of accuracy by a direct potentiometric measurement with the sodium ion electrode prior to the titration if the sodium impurity is less than 10%. It is worth noting that care must be taken, when pretitration of other metal ions in the solution is performed with the aid of visual indicator, that a ground mixture of the solid indicator with sodium chloride or potassium nitrate (sometimes the usual commercial form) is not employed. CONCLUSIONS The sodium ion titration presented has many advantages over existing chemical schemes. It is accurate, rapid, direct, and by utilization of a constant flow buret and the proper electronic circuitry should be completely amenable to automation and the recording of first derivative curves. The reagents are easily prepared from commercially available materials and are relatively inexpensive when piperidine is used to adjust the pH. ACKNOWLEDGMENT Our thanks are extended to Dr. G . A. Vidaver for the sample of pigeon blood serum.
RECEIVED for review March 2,1970. Accepted June 29,1970. Financial assistance from the National Science Foundation Departmental Science Development Grant fNSF-GU-2054 is gratefully acknowledged.
ANALYTICAL CHEMISTRY, VOL. 42, NO. 11, SEPTEMBER 1970
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