V O L U M E 28, NO. 10, O C T O B E R 1 9 5 6 reference value. The correction, which can be determined erperimentally or calculated from Faraday's law, is subtracted from the observed titration time to obtain the corrected titration time. Table 111 shows typical corrections. Parasitic currents in the indicator circuit are minimized by the cell geometry shown in Figure 1 and by mounting the electrode assemblies on opposite sides of the titration cell. The generator cathode is isolated from the solution to prevent liberated hydrogen gas from being swept into the solution. Traces of hydrogen reduce or even reverse the current flow in the indicator circuit just before excess bromine is generated. The diffusion current measured by the indicator electrodes is shown in Figure 2 to be proportional to the concentration of bromine in the titration cell. The proportionality constant depends upon the cathode area, applied voltage, effective thickness of the diffusion layer around the cathode, and the diffusion coefficient of bromine. With the cell assembly described, the cathode area and applied voltage are constant. The effective thickness of the diflusion layer is influenced greatly by the rate of electrolyte flow past the cathode. Therefore, to provide reproducible lesults, the electrode geometry is fixed and the stirring rate i* maintained constant. To maintain a constant diffusion coefficient of bromine, cell temperature must be held constant. The bromine concentration needed for a given indicator current doubles when the cell temperature decreases from 25' to 5' C. Between 20" and 30" C , fluctuations of 0.2" C. can be tolerated during a titration and no temperature control is needed; a t 5' C., control within 0.1' C. is required to minimize end point drift. Although bromination is often carried out a t low temperature3 to discourage substitution, the very small amount of bromine present a t the end point limits it. Results a t both temperature;. usually agree and operation a t low temperature is normally not required. Compounds harder to brominate can be rapidly titrated to a single end point by increasing the bromine concentration; under these conditions, substitution may be a problem and low temperature operation may be justified. This method for determining bromine addition is accurate for measuring small amounts of unsaturated hydrocarbons It is rapid and well adapted to routine laboratory use. Arrangement3
1555 Table 11. Thiophene in Sample, P.P..\I.
Effect of Thiophene
Calcd.
Bromine Indev ~Found
0 40 200
20 0 20 0 20 0
20 0 20 1 20 4
20 1 20 0 20 6
0 40 200 300
100.0 100.0 100 0 100.0
100.0 100.1 101.5 104.4
100.1 100 0 101 7 103. d
Table 111.
Typical Dilution Corrections
Sample Volume, 1\11.
Generation Current, .\la.
Correction, Seconds
0.5 0.5
2.0 2.0
are being made to make the titrator commercially available under license. A continuous recording bromine index titrator that can titrate a flowing plant stream is under development. LITERATURE CITED
( I ) Braae, B., ANAL.CHEW21, 1461 (1949). (2) Dubois, H. D., Skoog, D. A., Ibid.,20, 624 (1948); Am. SOC.
Testing Materials, ASTN D 1169-52T. (3) Francis, A. W., Ind. Eng. Chem. 18, 821 (1926). (4) Johnson, H. L., Clark, R. A., AXAL.CHEM.19, 869 (1947). (5) Kolthoff, I. M.,Bovey, F. A , , Ibid., 19, 498 (1947). 16) Leisev. F. A..Ibid.. 26. 160i (1954). (7) Lewis, J. B., Bradstreet, R. B., IND.ENG.CHEM.,ANAL. ED. 12,387 (1940). (8) Myers, R. J., Swift, E. H., J . A m . Chem. SOC.70, 1047 (1948). (9) Sease, J. W., Niemann, C . , Swift, E. H., ANAL. CHEM.19, 197 (1947). (10) Shaffer. P. A , Briglio, A , Brockman. J. A., Ibid., 20. 1008 (1948). (11) Wilson, G. E., J . Inst. Petroleum 36, 25 (1950). RECEIVED for review December 17, 1955. Accepted J u n e 8, 1956. Division of Anall tical Chemistry, 129th Meeting, ACS, Dallaa, Tex.. April 1956.
Amperometric and Potentiometric Titrations of Cadmium with Ethylenediamine Tetraacetate Using Dropping Mercury Electrode as Indicator Electrode NOBUYUKI TANAKA, I. T. OIWA, and MUTSUO KODAMA Department of Chemistry, faculty o f Science, Tohoku University, Sendai, Japan
Amperometric and potentiometric titrations of cadmium have been carried out with ethylenediamine tetraacetate in an acetate buffer at pH 4.2, using the dropping mercury electrode as an indicator electrode. In amperometry, the experimental end points agree with stoichiometric equivalence points only in the solution containing gelatin. In potentionietry at constant current, titration curves are discussed quantitatively from the voltammetric standpoint and a procedure is given to calculate the equivalence points from the experimental end points.
I
S R E C E N T years ethylenediaminetetraacetic acid or its salts have been introduced for titration of various metal ions. Potentiometric, amperometric, and spectrophotometric titrations, as well as titrations with chemical indicators, have been developed. PEibil and Matyska ( 7 ) studied the amperometric titration of cadmium with disodium ethylenediamine tetraacetate using the dropping mercury electrode as an indicator electrode, but gave no details. Adams (1) applied the same titrant to the potentiometric titration of cadmium a t controlled current input using the dropping mercury electrode. However, his approach was purely empirical and involved no mathematical or theoretical treatment. Meanwhile Kolthoff ( 5 ) developed to
ANALYTICAL CHEMISTRY
1556
RA3
P
RPI
RP2
\-
y f
Figure 1.
Schematic diagram of apparatus for potentiometry at constant current
C. Electrolysis cell G. Galvanometer M A . Milliammeter P. Potentiometer Mi-RAE. Resistors of 30, 15, 45, 60, and 75 megohms for constant current supply RPI. R G . 2000 ohms Voltage source for constant current,
RP:.
2.6 t
200 ohms
~
R G , RGs. loo0 ohms
RG3. 5000ohms RG4. 100ohms RFa, RGa. 50 ohms R A . l5ohms RFI. 20 ohms 45-volt dry cell
I
-0.2
1
-0.4
-0.6
-0.8
E,VOLT.vs.
I
I
I
-1.0
-1.2
-1.4
!
S.C.E.
Figure 2. Current-voltage curves of 0.970 X 10-3M cadmium In acetate buffer of pH 4.2 ( P = 0.1) in absence and presence of EDTA A . NoEDTA B. 1 x 10-2M EDTA
Table I. Limiting Currents of Polarographic Wave of Free-Cadmium Measured at Different Heights of Rlercury Column Concentrations, h ' X 103 Total Total cadmium EDTA 1.008 1.008 2.016 2.016 3.024 3.024 6.048 6.048 a
Limiting Current a t -0.700 Volt BS. S.C.E., pa. .It .1t 35.0 c111. 25.0 cm. 0.145 0.15 0.28 0.265 0.45 0.47 0.87 0.85
ii (35.0)a it (25.0) 1.02 1 03 1.02 1.01
ir (35.0) and ir (25.0) mean limiting currents measured a t 35.0 and 25.0
rm. in height of mercury column.
Table 11.
Arnperometric Titrations of Cadmium with EDTA
Concn. of Concn. of Cd in 50 Ml. E D T d Used of Solution, for Titration, M x 103 &I' X 102 [A] Without gelatin 1,008 1.018 1.210 1.018
IDT-& Btoichiometrical
Experimental
Error,
4.95 5.94
5.10 4.95
+3.1 +3.5
%
a great extent the theory of the titration curve of potentiometry at constant current. I t seems north while to reinvestigate the potentiometric titration of cadmium a t constant current with disodium ethylenediamine tetraacetate. I n this study, the amperometric titration of cadmium with ethylenediamine tetraacetate and the effect of the kinetic current on the titration curve are discussed. The potentiometric titration of cadmium a t constant current with ethylenediamine tetraacetate as titrant and the dropping mercury electrode as an
indicator electrode is also studied. The titration curves are analyzed from the theoretical standpoint and a procedure is given for calculating the equivalence point from the observed end point. APPARATUS
Polarography and Amperometric Titrations. A manual polarograph (6) was used for the measurement of all currentvoltage curves and also for the amperometric titrations. The current was measured by means of a 10,000-ohm resistance and potentiometer. The dropping mercury electrode had an n~ value of 2.85 mg. sec.-l and a drop time, 1, of 3.20 seconds, being measured in air-free 0 . l d l potassium chloride solution with opeii circuit a t 35.0 cm. of mercury column a t 25.0' C. All currentvoltage curves given in this paper are corrected for residual current, unless otherwise stated. Potentiometric Titration at Constant Currents. An instrument similar to that used by Adams ( 1 ) was constructed as shown in Figure 1. I n order to increase the accuracy of the potential measurement, an ordinary pH-meter or vacuum tube voltmeter was replaced by the potentiometer and the combination of UX-54 type vacuum tube (corresponds to the FP-54 type of vacuum tube in the United States) and galvanometer. The latter was used as an indicator galvanometer. The constant current n-as supplied from the 45-volt dry cell and resistors of 30 to 225 megohms (RA1-R&, Figure 1). As the voltage sourcc provides 45 volts, the current passing across the electrodes varies 0.274 per 0.1-volt shift of potential (IO). The indicator electrode ryas the same dropping electrode used in the amperometric titrations. A saturated calomel electrode was used for the reference electrode. Semimicroburets of 5-ml. and 10-ml. capacity were used for both amperometric and potentiometric titrations. Purified nitrogen was passed through the solution to remove dissolved oxygen before the measurement of current-voltage and titration curves and also after every addition of titrant during the amperometric and potentiometric titrations. A11 polarographic measurements and titrations were carried out a t 25.00" =t0.01" C. REAGENTS
Disodium ethylenediamine tetraacetate (EDTA) of analytical reagent grade (Waka Pure Chemical Industries, Ltd.) n-as puri-
V O L U M E 28, NO. 10, O C T O B E R 1 9 5 6
1557
ficd b y recrystallization ( 2 ) . The stock solution of 13)TA was 0.1 .I/ and standardized with the staridardiaed calcium solution, a magnesium chloride solution Ileing used as the back-titrant and Eriochrome Black T as indicator ( 4 ) . The cadmium sulfate solution \vas standsrdized against the EDTA solution (3). Other chcmiri& used were d l analytical rwgen t grade. EXPERIM EiYTA L AND DISCUS SIOS
Current-Voltage Curves. The current-valtage curves of 1 X l O - 3 N cadmium, measured in acetate buffer of pH 4.2 in the a l m n c e and presence of EDTA4,are shoim in Figure 2 . The ionic strength of the sripporting electrolytes was adjusted to be 0.1 ii-ith potassium nitrate. I n the presence of EDTA no well-defined imve !vas obtained. The reduction potential \vas sliiftetl to more negative potential and the limiting current, though not well defined, was markedly decreased. To learn hoiv the current-voltage curves of cadmium change in the course of titrution with EDTA, the cnrrent-voltage ciirves of the mixtures or cadmium and EDTA in various proportioris were also measured. As seen from curve R in Figrire 3, the mixture of cadmium and EDTA a t the ratio of exactly 1 to 1, which corresponds to the mixture a t the equivalence point, gives a polarogram with a amall reduction current of free cadmium ion. This agrees with the findings by Adams, who measiired the current-voltage riirves of the sume mixture of equimolar concentrations ( 1j. The waves corresponding to the reduction of free cadmilim ion \vere further studied. Those limiting currents were measured a t the different heights of mercury column, with the results given in Table I. Upon the addition of O . O O l ~ o gelatin, the limiting ciirrents of the reduction of free cadmium ion were markedly srippresred (Figure 4j. It was also found t h a t the presence of gelatin affects the reduction Tave of the cadmiiim-ethylenediamine tetraacetate complex. Figure 5 indicates the currentvoltage curves of the mixture of 1 X 10-3M cadmium and 101'30 KDTA in the presence of 0.001 to 0.01% of gelatin. Adams mentioned, in his report, that the reduction wave of free cadmium ion obtained with the mixture of 1 X 10-3M cadmium :tiid 1 x l O - 3 M E D T h in acetate buffer of pH 4.2 is due t o the 1)resence of the free cadmiiirn ion Jvhich forms by dissociation of
the complex. Ilouxver, calculation of the concentration of free cadmium ion present in the solution indicated that the concentration of the free ion which is in equilibrium lrith the complex a t pH 4.2 is much smaller than ivoiild be expected from the limiting current of the polarogram. According to Schn-arzenbach, the dissociation constants of ethylenediaminetetraacetic acid are given as 1.996 for pK,, 2.672 for pK2, 6.161 for p&, and 10.262 for pI& a t 0.1 ionic strength a t 20' C. ( B ) , and the stability constant of the cadmium comples is 16.4 for log R (4). The concentration of free cadmium ion uould be onl\- l,!l!l X 10-6.l.11 in
- 0.6
-0.5
-0.7
E ,VOLT.vs. S.C.E.
-0.8
-0.3
Figure 4. Effect of gelatin on free cadmium wave of 2 X l O - 3 M cadmium ethylenediamine tetraacetate In acetate buffer of pH 4.2 ( p = 0.1) A . Without gelatin B . With 0.001 % gelatin
i", 6.0 5.0
z
W
I
I
I
3.0
+ -
if
z ~
2.0
I 1
-0.8
-1.0
-1.2
E , 70LT.v~. S.C.E.
-1.4
Figure 5. Effect of gelatin on polarographic waves of 1 X 10-3M cadmium ethylenediamine tetraacetate Figure 3.
Current-voltage curves of (4.970 X cadmium
10-3.11
I n acetate buffer of pH 4.2 ( p = 0.1) in presence of various concentrations of EDTA A. 5 0 7 ~ B . 10070 C . 101% of equivalent amount for cadmium
In acetate buffer of pH 4.2 with slight excess of EnTA -_
A . 0.001% E . 0.002% C . 0.003% D . 0.005% E. 0.01~0of gelatin Residual current not corrected
ANALYTICAL CHEMISTRY
1558 the solution containing 1 X 10-3M cadmium and 1 X 10-3M EDTA. The authors' explanation of the wave corresponding to the reduction of free cadmium ion is that the complex dissociates on the surface of mercury to form the free cadmium ion in the course of electrolysis. Consequently, the currents must be kinetic in nature. This is supported by the experimental results obtained a t the different heights of mercury column (see Table I ) and those obtained by the addition of gelatin (see Figure 4).
ethylenediamine tetraacetate-cadmium complex, 0.0170 of gelatin was added to the supporting electrolyte. Typical examples of the titration curve obtained a t three different values of controlled current are given in Figure 7 . As expected from the theoretical consideration ( 5 ) , potential jumps occurred before the equivalence points in all titrations. The deviation from the stoichiometrical end point depended on the initial concentration of the cadmium and also on the applied current. The deviation is greater with decrease in the initial concentration of cadmium and with increase of the current applied. The amount of titrant required for the indicator electrode to obtain a value of -0.700 volt us. S.C.E. was taken as the experimental end point. I n Table I11 the observed end points determined from the titration curves are listed with the deviation from the equivalence point, &,bsd.
t r
0 -0.90 4 -"O
" -0.80
P
1 Figure 6. Amperometric titration curves of 50 ml. of 1.211) X 10-3M cadmium with EDTA In acetate buffer of pH 4.2 ( p = 0.1) A . Without gelatin B . With 0.001% gelatin Equivalence point indicated by arrow
VOLUME OF EDTA ADDED, M I . This suggests that both amperometric and potentiometric titrations must be carried out in the presence of suitable amounts of gelatin. Amperometric Titrations. Cadmium was titrated amperometrically with EDTA a t -0.7 volt us. S.C.E in acetate buffer of p H 4.2 containing a desired amount of potassium nitrate necessary to make the ionic strength 0.1. Typical examples of the titration curve obtained in the absence and presence of gelatin are given in Figure 6. Both curves are corrected for dilution effect. The results of the titration obtained are listed in Table 11. As seen in Figure 6 and Table 11, satisfactory agreement between experimental end points and equivalence points was obtained when the solution contained 0.001% of gelatin. On the other hand, when the titrations were carried oiit in the absence of gelatin, the experimental end points were somewhat greater than stoichiometrical ones because of the kinetic current due to the dissociation of the complex. Potentiometric Titrations at Constant Current. The potentiometric titrations of various concentrations of cadmium were carried out a t constant current in acetate buffer of p H 4.2. The ionic strength of the solution was adjusted to 0.1 with potassium nitrate. Considering the appearance of kinetic current and the characteristics of the reduction wave of the
Figure 7.
Potentiometric titration 'curves of 50 ml. of 2.036 X 10-3iM cadmium with 0.1008M EDTA at constant current pa. 2 io 0.5 1.0 pa. 1.5 pa. ia
io
Equivalence point indicated by arrow
For the calculation of the amount of titrant required theoretically, the sensitivity of the electrode, IC, is defined as id
=
kC
or
where i d is the diffusion current of cadmium in microamperes in acetate buffer of pH 4.2 with ionic strength 0.1 and C is the con-
1559
V O L U M E 28, NO. 10, O C T O B E R 1 9 5 6
Table 111.
Initial C0ncn.a of Cd, C, .Tf X 103
Potentiometric Titrations of Cadmium with EDTA at Constant Current E D T A Required, Ml.5 TheoretA t eq. ically At obsd. point, (calcd. from end point, ueq. eq. l’), u vobsd.
0.5 pa. 2.39 2.40 4.95 4.94 1.00 1.02 2.53 2.54 5.08 ...
be applied to the calculation of the initial concentration of the substance titrated. From Equation 3, C is expressed aR
c
i - i
= “ I
k
x -V T.’f
v
+$
(4)
Deviation, ‘I1. Autheor.c
Avob8d.d
ia =
0.514 1.028 2.056, 5.140 10.28
2 56 5.10 1.02 2.55 5.10
0.16 0.16 0.02 0.02
...
0.15 O,l5 0 0.01
Table IV. Calculation of Initial Concentrations of Cadmium from Observed End Points
...
Concn. of Cd Added, ,M x 103 0.5140 1.028 2.056 5.140 10.28
i o = 1.Opa.
0.514 1.028 2.056 5.140 10.28
2.55 5.10 1.02 2.55 5.10
2.08
0.514 1.028 2.056 5.140 10.28
2.55 5.10 1.02 2.55 5.10
1.78 4.30 0.94 2.47 5.03
2.09 4.65 0.98 2.50 5.05
0.47 0.48 0.04 0.04 0.04
1.5 pa. 1.75 4.30 0.94 2.45 5.00
0.77 0.80 0.08
4.62 0.98 2.51 5.06 ia =
0.08 0.08
O.4fi
0.45 0 04 0.05 0.05
Concentration of Cd Calculated with Equation 4 0.5 pa. io = 1.0 pa. io = 1.5 pa. Error. Error, Error, .v x 103 .I{ x 1 0 3 % M x loa % 0.5153 +O 3 0 5153 f O 3 0.508.5 -1.1 1.028 0 1.036 +o 8 1.028 o 2.059 f0.2 2 0% 0 2.04g -0.3 5.134 -0 2 5 134 -0.1 5 085 -1.1 ... .. 10 26 -0.2 10.23 -0.5 io =
0 80 0.80 0.08 0.10 0.10
Initial volume 50 ml. Concentrations of EDTA used for titrations were 0.01008 and 0.1008.1.1. See Equation in text. d Difference between amount required a t equivalence point and a t observed end point. a
b
centration of cadmium in moles per liter. When a solution of V ml. in initial volume containing C mole per liter of cadmium in initial concentration is titrated in constant current of i, microampere with the ethylenediamine tetraacetate solution of the concentration of c mole per liter, the amount of the ethylenediamine tetraacetate, v ml., required when the potential of the indicator electrode is equal to -0.700 volt us. S.C.E. can be expressed as
I n actual calculations, the amount consumed a t the observed end point may be introduced into v in Equation 4. In Table IV the concentrations of cadmium calculated from the observed end points are given, which are in good agreement with the concentration present. This fact, in turn, clearly indicates that the potentiometric titration a t const,ant current can be applied even to solutions of fairly low concentration, if the concentration is calculated from the relation given by Equation 4. ACKNOW LEDGBIENT
The authors would like to express their gratitude to I. M. Kolthoff for his suggestion that this study be carried out. They also thank the Ministry of Education for the financial support of this research. LITERATURE CITED
Adams, R. N.,ANAL.C H m f . 26, 1933 (1954). Blaedel, W. J., Knight, H. T., Ibid., 26, 741 (1954). Flaschka, H., 2. anal. Chem. 138, 332 (1953). Ishidate, M., Chem. Times 5 , 66 (1951). Kolthoff, I. M., ANAL.CHEM.26, 1685 (1954). Kolthoff, I. M.,Lingane, J. J., “Polarography,” vol. 1 , p. 297, Interscience, New York, 1952. (7) Piibil, R., hlatyska, B., Collection Czechoslov. Chem. Communa.
(1) (2) (3) (4) (5) (6)
or
v =
V ( C k - (i, - ir)} { ck (is - i,) 1
+
where i, means the residual current of the supporting electrolyte a t -0.700 volt us. S.C.E. expressed in microamperes. The values calculated for v with Equation 1 under various experimental conditions are given in Table 111. Since the amount of reagent required a t the equivalence point, v e 4 . , is veq.
the theoretical deviation, relation,
16, 139 (1951).
( 8 ) Schwarzenbach, G., Ackermann, H., Heh. Chim. Acta 30, 1798 (1947); 31, 1029 (1948). (9) Schwarzenbach, G.,Freitag, E., Ibid., 34, 1503 (1951). (10) Tanaka, Nobuyuki, Japan Analyst 4, 640 (1955). RECEIVED for review March 2, 1956. Accepted J u n e 20, 1956.
cv
= -
Atheor.,
can be calculated from the
(3)
The theoretical deviations calculated from the above relation are also given I,, Table 111. Apparently, the agreement between &heor. and A w e d . is satisfactory. For the practical titration the abovementioned relation can
Colorimetric Determination of Silicon in LowAlloy and Carbon Steels-Correction In the article on “Colorimetric Determination of Silicon in LowAlloy and Carbon Steels” [ANAL.CHEM.21, 589 (1949)] on page 590, first column, third paragraph, the eighth line should read: “a reference curve is constructed a t 740 mp.” U. T. HILL
