Feb., 1951
MOVING BOUNDARY
517
STUDY OF CADMIUM IODIDE C O M P L E X E S
have been treated at the Same temperature. Mead for the limiting conductance and of 3.2 X for the dissociation constant were obtained. and Fuossereport a value of 0.4508 for the limiting Since the specific conductance of the solvent, which conductance-viscosity product of tetra-rs-butylwas subtracted, amounted to 5% of the total ammonium picrate in ethylene chloride (D10.23) a t conductance in the most dilute solution, these 2 5 O . numerical values may not be very accurate. HowThe data appear to indicate that tetra-n-butylever, the treatment did indicate that the salt ammonium picrate is a weak electrolyte when at was not completely dissociated in dilute solution. low concentrations in butyl alcohol but that it Furthermore, the product of limiting conductance becomes a strong electrolyte at high concentrations. and viscosity, 0.435, is substantially equal to the Extension of the experiments, with variation of conductance-viscosity product of the pure salt, both components, is planned. 0.452. Walden3 has shown that this agreement (6) D. J. Mead with R. M.Fuoss, THIS JOURNAL, 61, 2051 (1939). is quite general, but this is the lirst demonstration of it where the dilute solution and the fused salt STATE COLLEGE, PA. RECEIVED AUGUST21, 1950
[CONTRIBUTION FROM
THE
CHEMISTRYDEPARTMENT, UN~VEERSITY OF WISCONSIN]
Moving Boundary Systems Formed by Weak Electrolytes. Complexes1
Study of Cadmium Iodide
BY ROBERT A. ALBERTYAND EDWARD L. KING It has been shown that the moving boundary method may be used to study complex ion equilibria. The constituent mobility of cadmium has been determined at 0 O over a range of iodide concentrations from 0.003 to 0.4 N . The constituent mobility of iodide in a solution containing 0.010 mole/liter of iodide has been determined over a range of cadmium concentration of 0.03 to 0.07 mole/liter. The equilibrium constants for the formation of the complexes CdI +, CdIz, CdIa- and CdI,' have been calculated from these data.
Numerous types of experimental data indicate that cadmium iodide in aqueous solution is not a strong electrolyte. Studies of the transference number of cadmium in solutions of cadmium iodide carried out by both the Hittorf method2 and the differential moving boundary methodS indicate that the cation transference number of cadmium decreases with increasing concentration, becoming negative at a concentration of 0.25 mole/liter. The activity coefficient of this substance is very low, even in relatively dilute solution.4 The existence in solutions of cadmium iodide of species with some covalent bond character is demonstrated by the Raman lines which are observed? Various complex species of cadmium and iodide have been proposed to explain the observed phenomena; it appears likely that all of the species, Cd++, CdIf, CdL, CdIa- and CdIe-, are present in solutions containing cadmium ion and iodide ion.0 It appears worthwhile to study, by the moving boundary method, solutions containing cadmium and iodide ions. The data are mainly of interest in connection with recent studies of weak electrolyte moving boundary systems' and are also of value in the further elucidation of the complex ion equilibria which exist in solutions containing cadmium and iodide. Svensson, Benjaminsson (1) Presented a t the Chicago Meeting of the American Chemical Society, September, 1950. (2) Redltch and Bukschnewski, Z . 9 h y s i k . Chcm., 87, 673 (1901). JOURNAL, 66, 1755 (1943). (3) Longsworth, THIS (4) Robinson and Wilson, Trans. Faraday SOL., 88, 738 (1940); Bates and Vosburgh, THIS JOURNAL, 59, 1583 (1937). (5) Delwaulle, Francois and Wiemann, Comfit. rend., 308, 184 (1939). (6) Leden, Z . 9hyssk. Chcm., 188A, 160 (1941). (7) Svensson, A c f o Chcm S c a d , 9, 855 (1948): Alberty a n d Nichol, THISJOURNAL, 70,2297 (1948); Brattsten and Svensson,Aeta Chcm. S c a n d , 8, 359 (1949); Alberty, THISJOURNAL, TS, 2361 (1960); Nichol, ibid , '72, 2367 (1950).
and Brattsted have shown that the ionization constants of amino acids may be determined from moving boundary experiments with solutions of different PH. As pointed out by Longsworth8it is doubtful if the direct moving boundary method could be applied to solutions of cadmium iodide owing to the difficulty of finding sufficiently slow indicator ions. In the present study the mobility of the cadmium and iodide constituents have been determined by means of moving bwndasy systems similar to those used in the electrophoresis of proteins, e. g., a cadmium salt is dissolved in an electrolyte which extends throughout the U-tube. This method has the advantage that it is unnecessary to find an indicator electrolyte and the ratio of iodide concentration to cadmium concentration may be varied over a wide range. It will be assumed provisionally that all of the species Cd++, CdI+, CdI2, CdIa-, C d I d exist. The equilibria which are established very rapidly in solution are C d + + n1CdIn+*-" tz = 1,2, 3, 4 (1) for which the corresponding concentration equilibrium constants are
+
K , = ;(CdIn+z-n)/(Cd++)(I-)n n = 1, 2, 3, 4 (23
The moving boundary experiments in which cadmium disappears across the boundary lead to a direct evaluation of the cadmium constituent mobility.' This is the average mobility of the cadmium in solution and is given by the equation GCd
=
+
+ (Cd1z)uz + (CdIa-)us + (CdI4')Ur
(Cd++)uo (CdI+)Ui (Cd++) (CdI+)
+
+ (CdIz) + (CdI3-) + (CdIr-)
(31 (8) Svensson, Benjaminsson and Brattsten, Acta Chem Scand., 8,
307 (1949).
ROBERT A. ALBERTY AND EDWARD L. KING
518
VOl. 73
ments made with a miaoacope comparator, and the thicknesses of the end-plates were determined with a micrometer. This end-plate correction amounted to 0.89% of the volume of the limb, and therefore is not negligible as has often been assumed. The average cross sectional area of the channel (0.7580 sq. cm.) was obtained by dividing the corrected volume of the limb by the outside length of the cell. A modified top section with attached electrode vessels was used.aJ* Gas formed by slow electrolysis of a dilute electrolyte in a vessel attaclied to the closed electrode vessel (4) was used to bring the initial boundaries into view.13 Due to It is seen that the constituent mobility depends the small volume (about 25 ml.) between the upper surface upon the mobilities of the several species, the of the concentrated salt and the top of the test-tube, this of apparatus is not adapted for the injection of any equilibrium constants for their formation and the type appreciable volume of solution into the closed side, as in concentration of iodide ion. The distribution counter-current electrolysis. The Ag-AgC1 electrodes were of cadmium among the various species is dependent mounted on 40/35 standard taper joints. It would have only on the concentration of iodide ion at a given been preferable to have used Ag-AgI electrodes as some conversion of the silver chloride to silver iodide must occur temperature if the activity coefficients of the as the electrode is introduced into the electrode vessel. It various complexes and iodide ion are assumed to be has been shown by the use of iodine tracer(Ilal) that this c~nstant.~ metathesis during the time that the electrode is being inThe moving boundary experiments in which io- serted into the test-tube introduces a negligible amount chloride into the solution. dide disappears across the boundary lead to a direct of The current through the cell was maintained constant evaluation of the iodide constituent mobility within 0.02% by a galvanometer-phot0tubed.c. amplifier arrangement constructed by the Rubicon C0mpany.1~ The lir = galvanometer is connected in series with a standard cell (I-)u1 (CdI+)ul 2(CdI2)~24-3(CdIj-)~i 4(CdId')ur across a standard resistance which is in series with the mov(CdI+) B(CdI1) 4-3(CdIj-) 4(CdI4") (I-) ing boundary cell. If the potential drop across the standard resistance decreases as the result of an increase in the (5) of the moving boundary cell, the light beam rewhere U I is the mobility of iodide ion. This equa- resistance flected from the galvanometer mirror is shifted so as to iltion becomes luminate a larger area of the phototube. As a result the output voltage of the d.c. ampliUI ulK1(Cdif) 2uaK2(Cd++)(I-) 3uaK$(I-)' 4u&(I-)3 fier which supplies current to the fir = moving boundary cell is increased. 1 Ki(Cd++) 2Ke(Cd++)(I-) 3%(Cd++)(I-)' 4K4(Cd++)(I-)a Since the photo-cell is partially when the appropriate substitutions are made. illuminated when the galvanometer is in its normal or zero the device is able to make either positive or negaEquation (6) lacks the simplicity of equation (4) position, tive corrections. The current was calculated from the since the concentrations of both cadmium ions and potential drop across a known resistance.% The specifi: iodide ions are involved. The iodide constituent conductances of the leading solutions were measured a t 0 mobility depends only upon the cadmium ion con- using a Jones conductivity bridge.'* The schlieren photographs were taken on Eastman Tri-X centration if the cadmium concentration is suf- Panchromatic plates using an exposure time of seconds. ficiently high so that CdI+ is the only complex ion The photographs were enlarged and traced by 10 hand. In of importance. the case of unsymmetrical peaks the velocity of the centroidal ordinate was used.= The first photograph was taken Experimental as soon as the moving boundary had completely resolved The moving boundary experiments were carried out in a from the concentration boundary. The schlieren patterns standard Tiselius cell of 3 X 25 mm. cross section, and the were then recorded at 10-2O-minute intervals during the boundary velocities weredetermined with theaid of aschlieren experiment so that the boundary displacements reported camera utilizing a cylindrical lens.1° The vertical magnifi- are averages of 5-10 measurements. The boundary vecation factor of the camera was 0.9610 * 0.0004 over the locities were determined with respect to an index on the region of the cell actually used in measurements.ll Since plates produced by a fine wire stretched across the face of the refractive index change across the moving boundaries the limb of the cell. All of the solutions were prepared using freshly boiled was small (An -0.0002), a-diagonal knife edge angle of 40" was used. The magnification of the cylindrical lens system doubly distilled water. The final dilutions were made in a was such that the boundaries had areas of from one to two sq. cold room a t lo. The concentrations reported are for this in. after enlargement of the photographs by a factor of 6.68. temperature. Reagent grade sodium iodide and cadmium The exact cross sectional area of the cell was obtained by iodide were used without further purification. Cadmium perchlorate solutions were prepared by treating reagent weighing the cell with one limb filled with mercury or water. The same limb of the cell was then used in all mobility de- grade cadmium carbonate with an equivalent amount of terminations. In the water calibration it was necessary to perchloric acid. The concentrations of the solutions were grease the cell but the quantity of grease used was kept to a determined by standard analytical procedures, and the PH minimum. The volume determined with mercury was values were between 5.3 and 7. The lithium iodide and 0.09% higher than that determined with water, and the lithium perchlorate were recrystallized from water several average was used in calculating the cross sectional area. times, The mercury(I1) iodide was N.F. VI1 grade and I t was nece-ssary to correct the volume of the limb of the cell was used without further purification. for the fact that the a o s s sectional area of the rectangular holes in the end-plates was greater than the cross sectional Moving Boundary Systems area of the channel. The cross sectional areas of the holes LiI, LiC104(6) c LiI, LiC104(y) ::LiI, LiC104in the end-plates were calculated from a number of measure(p) + 0.0050 M Cd(ClO&, x N LiC104, y N
where the a n ' s are the mobilities of the species in which n iodide ions are associated with one cadmium ion and the concentrations are in gramformula-weights per liter. This may be converted to an equation
+
+
+
+
+
+
+
+
+
+
+
+
(9)This statement is not correct if species involving more than one cadmium are present at appreciable concentrations. Leden' has shown the cadmium iodide complexes to contain but one cadmium ion in the concentration range studied in the cadmium constituent boundary experiments. (lo) Longsworth, I n d . En& Chcnz., A i d Ed., 18, 219 (1946) (11) T h e authors are indebted t o R AX, Rock for the focuqing and testing of this optical system.
+
+
(12) Alberty, J . Phys. Colloid Chem., 63, 114 (1949); supplied by the Pyrocell Company, New York. (13) Johnson and Shooter, Science, 109, 39 (1949). (14) Bonn, Marvin and Alberty, forthcoming publication. (15) The authors are indebted to H. H. Marvin for the assembly current source and measuring circuits. (1G) Supplied b y Leeds and Northrup Company.
Feb., 1951
MOVINGBOUNDARY STUDY OF CADMIUM
LiI(a)."-This moving boundary system which is illustrated in Fig. l a was used to determine the positive cadmium constituent mobilities. The total salt concentration of the a solution ( x y 0.010) was 0.100 equiv./l. The ionic strength of these solutions is not constant but varies with the extent to which the reactions for complex formation occur. It is assumed that the variation in the mobilities and the equilibrium constants due to this variation in ionic strength is small. Lithium salts were used because i t was found that sharper a,fl boundaries were obtained by using lithium salts rather than sodium salts. The 6 solution was made up to contain the salts in about the same ratio as the a solution and a t 'about 40% of its concentration.
+
+
a P
IODIDE COMPLEXES
519
correction to be discussed later), I= is the specific conductance of the a solution, and fi&j is the average mobility of the cadmium constituent. A position sign is given to Y=@ if the boundary moves with the current and a negative sign if i t moves against the current. The data obtained with this moving boundary system are given in Table I and the constituent mobilities are plotted ve~sus the logarithm of the total iodide concentration in Fig. 3a. It was found that the composition of the 6 solution had no effect on the velocity of the a@ boundary over a wide range of values of the ratio (LiI)/(LiClOJ. The composition of the 6 solution would, however, be expected to exert an influence on the sharpness of the moving boundary. The shamness of the movine boundarv deoends upon the 'specific conductance-of the fl shutiin and upon the iodide ion concentration of the fl solution. If the iodide concentration in the B solution is quite low, cadmium diffusing into the region immediately behind the moving boundary will have a higher constituent mobility than ahead of
r N No1
IN LiC10. y N Lil
a
0.0050M
+
x + y - 0.09 y (0.034
0.04
