difficult to create specificity of a complexing agent for only one or two metal ions. Such a specificity could probably be achieved only by closely meeting the steric requirements of the ion in question. The following compound is a n example showing how specificity might be obtained. Ethylenediamino-bis(acety1acetone) (EDAA) : (-CH?-N=C-
I CH,
CH=C-O)2-2
ing from cis-diaminocyclohexane. We get the following stability series for any metal:
is especially adapted to four coordination sites around a metal ion forming a planar square. Complex formation takes place with special ease with K'i+2, PdL2, Pt+2, and C u t 2 . The cations with a n octahedral sphere form EDAA complexes with two further unidentate ligands in trans- position to each other, this being the constitution, for instance, for cob:tlt(II)-EDAA, the two unidentate ligands being water molecules. By replacing EDAA with 1,2 - diaminocyclohexane - bis(acety1acetone) (DCAA), strain is created within the complex becausp of steric difficulties to make the three chelate rings coplanar. The DCAA complexes are less stable than the EDAA complexes and the strain is gwater in the transDCd-4 complex than in the one dcriv-
.I-
(8) Honda, M., Schwarzenbach, G..'Helv. M(EDAA) > M(cis-DCAA) > Chim. Acta 40. 27 11957). M( ~TU~S-DCAA) (9) Irving, H., J+illia&s,-R. J. P., Kature (London) 162, 764 (1948); Analyst 77, 813 (1952); Chem. SOC.(London). Spec. On the other hand, the metal sequence Pub11 1953,'3192. for any of the three complexing agents (10) Schwarxenbach, G., Ezperientia 12, is : 162 (1956). (11) Schwarxenbach, G., Helv. Chim. Acta Pt(che1) > Pd(che1) > Cu(che1) >
Ni(che1) > Co(che1)
I
CHI
(6) Cotton, F. A., Harris. F. E.. J . Phus. Chem. 59, 1203 (1955). ( 7 ) Durham, E. J., Ryskiewich, D. P., J . A m . Chem. SOC. 80, 4812 (1958).
K i t h these two sequences in mind, it is understandable that cis-DCAA does not react any more with cobalt, whereas complexes still are formed with nickel, copper, palladium, and platinum. With trans-DCAA the complexes of nickel and copper are also no longer formed and this agent has therefore become specific for palladium and platinum (8). LITERATURE CITED
(1) Agren, rl., Schwarzenbach, G., Helv. Chim. Acta 38, 1920 (1955). (2) Anderegg, G., unpublished results. (3) Anderegg, G., Nageli, P., Muller, F., Schwarzenbach, G., Helv. Chim. Acta 42, 827 (1959). (4) Banks, C. V., Yerick, R. E., Anal. Chim. Acta 20. 301 119.59). (5) Charles, R. G , - > . Am. Chem. SOC. 76, 5854 (1954). \ - - - - ,
32. 839 11949'1. (12) '%id., 35,2344 (1952). (13) Ibid., 36, 23 (1953). (14) Schwarxenbach, G., Z. anorg. u. allgem. Chem. 282, 286 (1956). (15) Schmarxenbach, G., Ackermann, H., Helv.Chim. Acta 32. 1682 (1949). (16) Schwarxenbach, G., Anderegg, G., Sallmann, R., Ibid., 35, 1785 (1952). (17) Schwarzenbach, G., Gut, R., Zbid., 39, 1589 (1956). (18) Schwarzenbach, G., Gut, R., Anderegg, G., Ibid., 37, 937 (1954). (19) Schwarxenbach, G., Senn, H., Anderegg, G., Ibid., 40, 1886 (1957). (20) Smith, G. S., Hoard, J. L., J . Am. Chern. Soe. 81, 556 (1959). (21) Spike, C. G., Perry, R. W.,Ibid., 75, 2726, 3770 (1953). ( 2 2 ) Weakliem, H. .4.> Hoard, J. L., Ibid., 81,549 (1959). (23) Kesterback, S. J., Martell, A., A'ature (London) 178, 321 (1956).
RECEIVEDfor review October 6, 1959. Sccepted October 15, 1959. 12th Annual Summer Symposium Division of Analytical Chemistry, ACS, and ASALYTICAL C H E v I s T R Y , Urbana, Ill., June 1959.
Use of an Unbalanced Bridge Circuit in High-Frequency Titrimetry JOE M. WALKER,' JACK L. LAMBERT, and LOUIS D. ELLSWORTH Departments o f Chemisfry and Physics, Kansas Sfafe University, Manhaftan, Kan.
b The feasibility of using a modulated off-balance radio-frequency signal originating from the detector side of a high-frequency impedance bridge as a method for performing high-frequency titrations was investigated. The use of an unbalanced bridge circuit was found to b e applicable to the acid-base titrations studied. Several relationships were inferred relating admittance changes to specific conductivity changes. An equation was derived relating the unbalance of the bridge, as measured by a voltmeter, to that of the true admittance obtained under balanced conditions. Frequency, electrolyte concentration, and the dielectric constant of the solvent were found to affect the titration curves in a manner predicted by the equations for admittance values. A new titration cell utilizing magnetic stirring is de-
scribed. An off-balance bridge circuit instrument should prove useful for titrations within the electrolyte concentration conditions studied, and the mathematical relationships derived should contribute to the theoretical knowledge of the circuitry of highfrequency titrimetry.
T
principles of high-frequency titrimetry have been studied previously ( I , 2, 4). The purpose of this investigation n-as to study the feasibility of using a modulated off-balance radio-frequency signal originating from the detector side of a high-frequency impedance bridge as a method for performing high-frequency titration. A bridge-type circuit similar in principle to that described by Hall and Gibson HE
(3) was used with a magnetically-stirred titration cell. APPARATUS
The apparatus was selected to measure parallel Capacitance and highfrequency conductance independent of other circuit components (Figure 1). A General Radio Type 1001-A standard signal generator was used as the highfrequency source (oscillator and modulator in Figure 1). Independent measurements of high-frequency conductance and capacitance were made with the General Radio Type 821-A Twin-T impedance bridge. A National communications receiver Model-NC-98 was used to amplify the unbalanced modulated signal from the bridge. Present address, Department of Physical Science, Kansas State College, Pittsburg, Kan. VOL. 32, NO. 1, JANUARY 1960
0
9
The modulation envelope was observed on a n oscilloscope, and a n Eico hCiodel 221 vacuum tube voltmeter was used to measure the amplified and detected unbalanced signal for determination of the effective admittance. The complete system was mounted in a well shielded transmitter cabinet. All instrumental grounds were connected to a common bus bar consisting of a 6-foot length of 3/ls-inch copper tubing fastened electrically and securely to the rack. The high-frequency cell was connected by a 24-inch length of coaxial cable to the impedance bridge. The cell (Figure 2) was constructed by mounting a Berzelius borosilicate beaker with a surrounding copper band, A , directly over a magnetic stirring apparatus (Labline, Inc., RIagnestir). The copper band was inch m-ide and 18 mm. above the base and was held in position by a piece of 3/8-inch plywood, F , in which a hole had been cut for insertion of the beaker and band. The magnetic stirrer was secured in a rigid 3/s-inch plywood box. One-half inch Plexiglas, E, formed the top of the cell box in which a hole of proper diameter had been cut to hold the beaker securely. The copper band on the beaker was connected to a coaxial connector on the side of the box by size 16 solid copper itire, A second copper wire connected the outside or ground terminal of the coaxial connector to the magnetic stirrer. The top of the stirrer and the band served as the electrodes of the cell. The effect of the magnetic stirrer is constant, and no special efforts were made to regulate the stirring beyond keeping the rate approximately constant by observation.
i
OSCILLATOR
c4
OSCILLOSCOPE
TWIN-T
IMPEDANCE BRIDGE
RECEIVER
Figure 1. Blockdiagram arrangement of complete apparatus
1 ~~
MODULATOR
VOLTMETER
-%-
FUNDAMENTAL
c2
SIMPLIFIED
qw CP
Figure 3. Fundamental and simplified equivalent circuits I
I‘ !
e Figure 2.
THEORY
t
1
Titration cell assembly
A.
The analysis of the fundamental and simplified equivalent circuits of the cell and solution (Figure 3) has been developed by Reilley and McCurdy (4) with the follorving results:
Copper band Magnetic stirrer C. Stirring b a r D. Coaxial cable connection E. Plastic plate F and G. Plywood
E.
the extreme values of ( A Y p ) m s xis: J
admittance,
Figure 4.
Twin-T bridge circuit
I I
B, = w C , =
Y , = Gp
+ jBp
(3)
where C1 is the capacita,nce due to the walls of the container, and Cz is that due to the solution. K O ,the reciprocal of the resistance of the solution ( R in Figure 3) , is the low-frequency conductance of the solution. An extension of this analysis yields the equation for Y,:
-
From this the limits of magnitude of Y , as K O+ 0 and as K O+ are w(C,C2/Cl CZ)and w C 1 , respectively. Therefore the difference between the magnitudes of
+
10
ANALYTICAL CHEMISTRY
This equation permits the prediction. all other factors being held constant. of the magnitude of ( A Y p ) m a xin ternis of frequency and in terms of Cl and C2. One may use as a measure of the variation of admittance, AY,, the offbalance signal, AEpJof a Twin-T bridge, as the low-frequency specific conductivity is varied with the bridge initially a t balance. The bridge consists of tn-o T networks, 1 and 2, connected in parallel between the generator, E , and detector of impedance, 2 (Figure 4’1. The Thevinen equivalent circuit is shown in Figure 5. At balance, ITa, is zero and there is no signal in the detector. I n the unbalanced condition. the Thevinen equivalent admittance changes by AYac:
Figure 5. Thevinen equivalent circuit
17Lb)
- J ( C a + c4y
n-here Yt, and Yta are the values of Y1 a t balance and unbalance, respectively. The titration cell is in parallel with a bridge admittance, Y,, and the two together make up Y t . If one writes the folloning relationship: Yta
=
Y,,
+ y,
,
(7)
80
t
80
180
I-
70
70
160
60
60
I40 n
50
2
50 n
I20
W
40
*
a
0
40
W
roo
a
0
30
W
a
30
20
IO
80
20
60
10
40
0 0
0
2
I
20 0
I
2
3
3
4
5
K, x l o 3
5
4
KO X IO3
0
Figure 6. Results obtained by plotting unbalance of bridge in volts at 30 Mc. on addition of 0.15N potassium chloride solution to distilled water against low-frequency specific conductivity in mhos
0
0.4
0.2
0.6
K,X
0.8
1.0
lo3
Figure 7. Curves demonstrating effect of solvent on unbalance of bridge at 10 Mc. plotted against low-frequency specific conductivity AYac =
where Y,, and Yp6are the v:tlues of the cell admittance Y, a t balance and unbalance, respectively, then is given by:
ysz
+
+
ypb)
+
~’pa~’pb+jW(C3
+
50
40
Figure 8. Correlation of experimentally determined and calculated unbalance of bridge
30 0
>
a
Admittonce a t 10 Mc. on a d dition of 0.15N potassium chloride solution to distilled woter; both plotted against low-frequency specific conductivity in mhos
a
z 4
p.
4 20
Admittance a t 30 Mc. on addition of 0.15N potassium chloride solution to distilled water; both plotted against low-frequency specific conductivity in mhos
This may be written in the form: W*C3C4[AYP]
Ya(ypa
Figure 9. Correlation of experimentally determined and calculated unbalance of bridge
where P, R, and S can be evaluated from Equation 9 As the only part of the circuit that changes during titration is Y,, then P, R, and S, which are only functions of w and the bridge values, are constant during a given titration. If the term S in the denominator of Equation 10 is large compared to the term Y,& then AY, is approximately directly proportional to AY,,. I n the Thevinen equivalent circuit above, the unbalanced detector signal, AE,, is given by: AE, =
IZ
=
EZ
(11)
1 -A + z Yo0
which is equal approximately to A E , ZZ ( E Z ) A Y , , E k A Y ,
(12)
if 2
