1559
V O L U M E 28, NO. 10, O C T O B E R 1 9 5 6
Table 111. Potentiometric Titrations of Cadmium with EDTA at Constant Current Initial C0ncn.a of Cd, C, .Tf X 103
E D T A Required, Ml.5 TheoretAt 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
In 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., H e h . 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 June 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
