ACTIVITY C02FFICI3YT AND COKDüGTI'TITY MYA3JÆ1-SNTS OF HIG-H-CH.ARG-E FLEGTYOLYTES IN AQUEOUS SOLUTION AT TWENTY-FIVE DZOYEES GENTIOPLIOE 3y Ri chard A . Wy nve en A TNESIS Suhinitt-ed to the School for Ad,vanced Q-raduate Studies of Michigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of DOCTOR OF PUIL030FHY Department of Chemistry 1959 ProQuest Number: 10008636 All rights reserved INFORM ATION TO ALL USERS The quality o f this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a com plete m anuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. uest ProQuest 10008636 Published by ProQ uest LLC (2016). Copyright of the Dissertation is held by the Author. All rights reserved. This w ork is protected against unauthorized copying under Title 17, United States Code M icroform Edition © ProQ uest LLC. ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 4 8 1 0 6 -1 3 4 6 AG Kl^OW LEDaMENT The author would like to express his sincere appreciation to his major px^ofessor. Dr. C, H* Brubaker, Jr., for ABSTRACT Mean activity and osmotic coefficients have been deter­ mined at 25^ for aqueous solutions of C o (en)^(NO^ Go(pn)^ (ClO^)^, K^Co(CIT)^, and [co(e n 2( comparison with potassium chloride solutions. , by isopiestlc The salts do not appear to be “ strong*' 3“1 and 3-2 types and required S values of 3 .2 3 , 3 »8 3 , 4.01, and 3 .43, respectively, to repre­ sent the data by means of the Debye-Hueke1 equation. The results obtained for the 3 -I electrolytes were similar to Co(en)^Cl^. The solubilities of the G o (e n ( N O ^ a n d K^Co(CN)g were determined to be 0.2749 and I.3II m, respectively. Meas­ urements were taken over the concentration range from about 0*05 m to the saturated or near saturated solutions. Conductivity measurements were also made on solutions of the same four electrol^/tes to afcout 0.1 N. A decided deviation from the 0nsager limiting law was observed. The limiting values obtained were found to be very similar to those obtained by previous workers. The extrapolations were made by the method of Shed.lovsky and of Ovren. procedure gave the higher limiting values, Jwq. The Shedlovsky The values of the constants A and B of the extended Onsager equation 'irere determined. A definite cause of the deviations observed, must await extension of the present theories to permit treatment of the hiah-charme salts studied. TABLE OF CONTENTS I. II. Page INTRODUCTION'............................................. 1 H I S T O R I C A L .................... A, E, 5 Isopiestlc Method........... 5 C o n d u c t i v i t y ..................................... 10 III. THEORETICAL.............................................. 22 IV. E X P E R I M E N T A L ............................................ 4l A, B, C, Raw Materials...................... 4l Preparation of Gonpounds ................. 41 43 Apparatus and Procedure........... 1, 2. V. Isopiestic measurements. . . . . . . . . Conductance measurements , 43 44 RESULTS AND D I S C U S S I O N ................................. 48 A. B. Isopiestic . . . . . . Conductivity . . ........................ 48 58 V I . SUMAURY................................................... 71 VII. B I B L I O G R A P H Y ............................................ 72 LIST OF TABLES TABLE I. Page Values of the Constant A of Equation 60 . . . , 4? II* Isopiestic Molalities and Osmotic Coefficients, of Electrolytes at 25®* ,49-50 III. Mean Activity Coefficients and Smoothed Osmotic Coefficients of Electrolytes at 2 5 ^ ............ 51-52 IV. V. VI. VII. VIII. IX* X. XI, Values of the Parameters § and B used In the Smith Method. ............................... 53 Isopiestlc Molalities, Observed and Calculated Osmotic Coefficients of Co(pn)^(C10/j_)^. . . . . 54 Values for S Determined by the Method of Randall and W h i t e ............... 55 Equivalent Conductances of Electrolytes at 25^.61-62 Limiting equivalent Conductances Obtained by the Shedlovsky M e t h o d ............................. 63 Parameters of the Semi-empirically Extended Onsager Equation at 2 5 ^ .................... .. Limiting Equivalent Conductivities at 25^ . . . . 64 65 Dissociation Constants of Complex Ions in Water Estimated from Conductance Data at 25*^........... 68 LIST OF FIGURES FIGURE 1. Pare Log ^ versus u ........................... 59 I. INTRODUCTION The present work is part of a program involved with a general study of the properties of high-charge type salts in aqueous solution. charge, such as The main objective is to find salts of h i g h — 3-2, 4-1, etc., which (l) e:clilbit little or no tendency to form ion pairs in dilute solution, negligible, (2) undergo if a n y , hydrolytic action, and (3 ) are sufficiently soluble so that any theories at higher concentration might be applied* By means of the preparation of very stable complex salts it should be possible to prepare compounds which actually give ions of Charge 3 or 4 in solution. If the cation or anion is large, due to the size and number of coordinated groups, it should be better able to carry this large charge without ad­ ditional complexation. This means that solvation effects would be smaller owing to the low charge density on these large ion surfaces* Also, if they are sufficiently stable or ’’inert", hydrolysis would be at a minimum* The salts studied in this part of the general program are of the 3 -1 , 3 -2 , and 1-3 charge types. Measurement of activity coefficients was suggested by the lack of data on activity coefficients and the effectiveness of measuring them by the isopiestic method. 2 In addition, it was hoped to be able to determine the distance of closest approach, 8 , from conductivity measurements such as was done by Dye and Spedding (l) for the alkaline-earth and rare-earth salts* In previous tests of this procedure the 8 values obtained from e.m.f* measurements of mean activity co­ efficients also gave conductances agreeing with experiment up to 0*008 N. Thus the chance of comparing calculated mean ac- tii/ity coefficients with those obtained experimentally and the availability of the c o n d u c t i v i t a p p a r a t u s dictated measuring a second property, conductivity, of the high-charge salts* To give a clearer picture of the activity and conductivity theory and calculations, the two properties will be covered separately. For example, the historical treatment of activity coefficients is given first, followed by that for the conduc­ tivity; the calculations for mean activity coefficients followed by those for the conductivity, etc. This separation of each section into two parts is adhered to except in cases where a clearer understanding results by considering both properties simultaneously• The concept of activity in chemical thermodynamics was introduced by G. N. Lewis (2 ). It was through the substitution of activities for concentrations that the mathematical form of the ideal law was preserved and could be extended to real sys­ tems, The activity of a chemical species can be ex'pressed as the uroduct of its concentration and. an activity coefficient which measures the deviation of the species from ideal behav­ ior# The numerical value of activity and activity coefficient depends upon the units of concentration employed* For elec­ trolytes the mean activity and mean activity coefficient are used because the activity and activity coefficient of a single ionic species cannot be determined* Values of activity coefficients can be d.etennined from boiling point elevations, freezing point depressions, e,m*f* measurements using cells with or without liquid junctions, from osmotic coefficients, and vapor pressures. The activity coefficient is a property determined by measurement of systems in equilibrium* The electrical con- tance, however, is a property determined by measurements of systems in disturbed states. When an ionizing electrolyte is dissolved in water, the solute consists of electrically charged atoms or groups of atoms, called ions* When an electrical potential is applied between a pair of electrodes in the sol­ ution the ions of the electrolyte migrate and a flow of elec­ tricity occurs* The specific conductance, L, of a solution is defined as the reciprocal of the solution's specific resistance. The s’oecific resistance is the resistance of 1 cm.^ of a sol­ ution 'oetween electrodes 1 cm* apart* The soecific conductance is a function, therefore, of the same variables as the specific resistance, namely, the nature of the electrolyte, the concen­ tration of the solution, temperature, etc* The equivalent conductance, is of more theoretical significance than the specific conductance* It is defined as the conductance of a solution irhich contains 1 equivalent weight of electrolyte between electrodes 1 cm. apart. The equivalent conductance at infinite dilution,-/^, is also an important function in theoretical considerations. It can be defined as the equivalent conductance of a solution which is dilute enough so that further addition of solvent does not affect the conductivity. Its value cannot be measured directly because the concentrations of these dilute solutions are so low that the physical measurements have too high a degree of u n ­ certainty. Its value is obtained by extrapolation of a suit­ able function of the equivalent conductances and normalities. Tills study was undertaken with the purpose of studying the mean activity coefficients and conductivities of four high-charge, complex salts. The salts studied were tris- (ethylenediamine )cobalt(III) nitrate, Go(en)^(NO^)^, tris(propylenediamine)cobalt(ill) perchlorate, Oo(pn)^(CIO^)^, potassium hexacyanocobaltate(lII), K^Go(CN)^, and tris(ethylenediamine )cobalt (III ) sulfate, [Go(en)^] ^ (SO^^)^. II. HISTORICAL A. Isooleatlc Method The Isopiestic method was introduced in 1918 by W, R. Bousfield (3 )# He adapted the term “isopiestic" to represent the equilibrium condition resulting after several solutions in a closed container had gained or lost water in order to arrive at the same vapor pressure*. The method was not made practical for accurate determinations of vapor pressures until the work by Sinclair (4) in 1933. At that time the most accurate determinations of vapor pressure were carried out by a method devised by Lovelace, Fraser, and Bahlke (5). Their method involved careful removal of a i r , a sensitive manometer and attained an accuracy of less than 0.001 ram. The method wo,3 , however, much too elaborate for general appli­ cation. Sinclair (4), intrigued by the simplicity of the iso­ piestic method, set out to test its experimental possibilities and found the attainment of equilibrium using the method of Bousfield too slow to be practical. Sinclair (6) and Robinson Isotonic Is often used synonymously with iso­ piestic. It was introduced by Hugo de Tries, who first used an isotonic method in 1882, to define solutions in equilibrium with respect to transfer of the solvent. Tlie terra isopiestic, however, seems to have gained, the wider acceptance. and. later Scatclia.rd, Hamer, a,nd Wood (7 ) further Improved the method so that vapor pressure measurements would yield activity data with an accuracy comparable with that achieved in the e.m.f, and freezing point methods. The modifications incor­ porated into the apparatus and procedure to facilitate attain­ ment of equilibrium are as follows. By having good meta.llic conduction between solutions the retardation of distillation due to thermal resistance between solutions was reduced to a small value. TI10 solutions were held in silver-plated copper dishes, which were then placed in holes bored into a brass block. To prevent fluctuations of temperature, the block was only in contact with its container over a small circular area 5 cm. in diameter, which then acted as an effective thermal buffer. By placing some solution in the crevices between the sample holders (dishes) and the brass block, the distillation rate was greatly increased (due to the reduction of the temper­ ature gradients by substitution of solution for vapor in the gaps). The factors then limiting the rate of attainment of equilibrium were conduction of heat and diffusion of solute through the solution. These factors were minimized by making the solutions shallow and stirring (though not so much as to set up minute heating effects). The solutions were stirred by means of a rocking device situated, in the bath. Quantities of the solution were also kept to a minimum, but within weigh­ ing accuracy to decrease the amount of water which had to 7 distill. Tlie container was evacuated to remove air which int erf erred v/lth the distillo.tion. Six drops of water irere placed at the bottom to sweep out the air during evacuation and cut down evaporation from the dishes. To control the evaporation and prevent splattering, the air was drawn out very slowly into a bulb of approximately the size of the container, which in turn was connected to the vacuum line. W h e n the pressure reached that of the vapor pressure of water, the vessel was evacuated ten more times to ensure complete removal of air. drawback. The isopiestic proced^ure had one serious With solutions below 0,1 m, the time required to reach equilibrium was between one and two weeks. librium never seemed to be attained. Often equi­ Hence, as a rule the values obtained at low concentrations tended to be somewhat erratic. In 1943 R. A. Gorden (8) ran a series of measurements on the system KGl-NaOl over the concentration range from O.O3 to 0.10 m and at 25^» He reports that the most serious exper­ imental difficult]/ is the removal of air from the system. Evidence was adduced that the extreme slovniess with which equilibrium is attained in dilute solutions is primarily due to the rate of transportation of solvent in the vapor phase. The procedure adopted to reduce this was to pump the vessel initially down only to 60 mm. pressure and then allow it to rock for 6 hours; it vras then rumped to 38 mm. and left 8 overnight; in the morning, a further pumping reduced the pressure to the vapor pressure of water. It was then allowed to rock for 3 periods of 24 hours, at the end of each period the vapor above the solutions was pumped off. In this way he found he could effect a fairly complete degassing of the solutions and. thus eliminate the erratic results at low con­ centrations* In 193^ Robinson and Jones (9 ) me assured the activity coefficients of some bivalent metal sulfates. Tlie 2-2 charge type was examined since the symmetry was retained and hence rendered the theoretical treatment less complicated. They first calculated, the osmotic coefficients, 0, of KOI by**^ 0 = 55.51 In Eq 2m p from molar vapor pressure 1owerings reported by Robinson (lO). Since P q /p is the same for two isopiestic solutions, the osmotic coefficient of the sulfates could be calculated. The activity coefficients were then calculated* by the method of Randall and White (11). Mason and Ernst (12) used the isopiestic method for the measurement of the vapor pressure of aqueous solutions of lanthanum chloride and hence showed that it was also applicable to 3 -I electrolytes. * The theory involved in obtaining and using this equation will be postponed until the Theoretical Section, Due to the uncertainty in the experimental results when the Isopiestic method was used below 0.1 m some form of extrapd a t i o n was necessary to obtain results from 0.1*m'^zero con­ centration. Robinson and Jones (9) accomplished this by calculating the activity coefficients for concentrations less than 0.1 m from the literature data using the freezing point and e.m.f, me s.sûrement s. Mason and Ernst (12) overcame the difficulty by using the Debye-Hückel equation (page 29). In 1938 Mason (I3 ), with revised, techniques, extended the method to the determination of the vapor pressures of 6 more 3 -I electrolytes and extended his LaCl^ data to higher concentrations and obtained more accurate data below 0.4 m. The main features included the use of platinum gauze in the solutions to ensure more rapid thermal and distillation equi­ librium and a good thermal contact secured by pressing the dishes firmly against the bottom of the brass block while the dishes themselves fit tightly in the holes provided for them in the brass block. The activity coefficients of a large number of compounds have been determined by the isopiestic method. Of special interest is the application of the isopiestic procedure to complex salts similar to the ones considered in the present study. Robinson (l4) applied the procedure to Kj^Fe(CN)g and Brubaker (15,16) reported his findings on four additional cornulex salts of the 4-1, 1-4, and 3 -I charge type. There 10 still rema.lns, however, a definite lack of inforn:.tion on the mean activity coefficients at high concentrations for other similar salts. B, Conductivity The study of the phenomena exhibited, by chemical sub­ stances when they are subjected to the action of electrical forces began in 1776 with Cavendish# He measured the con­ ductivities of aqueous solutions of chemical compounds (1 7 )* In his apparatus the solution whose resistance was to be com­ pared was contained in a long tube with movable wire electrodes inserted at each end. One set of electrodes from two such tubes were connected with the outside of a N a i m e battery of Leyden jars, while the other electrodes were connected each to a separately insulated piece of tinfoil. Cavendish charged all the jars of the battery together to a known degree of electrification and shorted, first one of the pieces of tin­ foil through his body, then the other. By adjusting the lengths of the liquid columns, he was able to judge when he received a shock of the same intensity from each, end thus was able to compare the resistances of the two electrolytes. The branch of chemistry which deals with the electrical conductivity of solutions can actually be said to have origin­ ated when a distinction was drawn between metallic conduction and electrolytic conduction. 11 One of the most noteworthy of the early investigators is Kohlrau8ch. He ma,de an extensive study of the variation of the conductivity of electrically conducting solutions with concentration and temperature, and discovered that the specific conductivity, L, changed, with concentration. By expressing the concentration, N, in terms of gram-equivalents per 1,000 cm? he was able to measure the equivalent conductance of the solu­ tion, which is defined as . _ 1000 L 2 N Kohlrausch (l8) then proceeded to shovr that in dilute solu­ tions, the conductivities of strong electrolytes could be expressed empirically by the equation known as the square root law. It is also due to Kohlrausch that we have the law of independent ionic mobilities (l9), = x ° - x° Here " 4 and A + represent the contributions to the limiting value of the equivalent conductivity due, respectively, to the anion and. cation of the electrolyte. In 1923, Debye and. Hueke1 (20,21 ), gave an analysis of the specific distribution principle which enabled them to calculate 12 the conductivity of 'solutions. The resistance of an electrolytic solution is most freq­ uently determined by means of some form of Wheahstone bridge circuit, one arm of which is a conductivity cell containing the solution. In the earliest measurements direct current was employed, but this caused the results to be erratic because of the so-ca.lled "polarisation" due to gases liberated at the electrodes. Following the suggestion of F. Kohlrausch (22), a rapidly alternating current is now generally used. The direc­ tion of the current is reversed about a thousand times per second, so that the "polarizations" produced by successive pulses counteract one another. Kohlrausch did his experiments on the conductivity of electrolytes using a simple slide-v/ire bridge, an induction coil as a source of current to minimize the polarization, and a telephone to find the point of balance. The telephone replaced the galvanometer originally used as the detector. Since the initial development of the a.c. conductivity bridge, many technical advances have been made in bridge design, and in the source of and method of detection of the a.c. signal. To give a complete review of the subject would require a lengthy treatise. However, certain points in the development v;ill be considered, especially those in a series of papers by G. Jones and. co-workers. In 1928 Jones (2 3 ) published the first paper of the series. 13 It consisted of o,n experimental and theoretical study of tlie principles of design of the Wheatstone "bridge for use with alternating current* It was pointed out in this paper that the use of water as a thermostat liquid for electrical con­ ductivity gave erroneous results, since the presence of a conductor (i.e.^water) near the cell caused an error in the value of the resistance being measured. Although the reasons for the errors were not all known, use of oil as the thermo­ stat liquid gave results independent of grounding, value of resistance being measured, specific conductivity of the bath liquid, and frequency. In 1929, Jones and co-worker (24) reported, on some im­ provements in the oscillator and detector. Their studies included the variation of resistance and. polarization with voltages, amplification, and bridge pickup. Their modifi­ cations made use of lower voltages to reduce heating effects of the current in the cell which, however, reduced the sen­ sitivity. To correct this they improved the step-up ratio of the amplifier. bances, This in turn resulted in increased distur­ such as tube noise, electric circuit hum, e t c . To counteract these disturbances they used wave filters, whi ch consisted of a variable inductor and a variable condenser in parallel with the telephone detector. In 1923, Parker (25 ) stated that he had, experimental proof that " cell constants" were not really constant but vary 14 wit h the resistance being measured. In 1930, Shedlovsky (26) undertook to design, build, and test a new form of cell whi ch could be used, to check the variation in "cell constant" when the nature or concentration of the measured, solution was varied- (i.e., variation in magnitude of resistance). His cell consisted of four electrodes which i;ere free from errors due to effects at the electrode which caused changes in the " cell constant". Thus cells with two electrodes could be compared with the four electrode cell. In 1931, Jones o.nd Bollinger (2 7 ) also undertook the study of cell design to investigate the variation of cell constant with resistance, Jones termed this phenomenon the "Parker Effect" to dis­ tinguish if irom polarisation. The fact that the "Parker Effect" , a function of bridge design generally l^eing used at that time, was unobserved or oro least unreported caused Jones to state that suspicion was thrown on all previous conductivity measurements of electrolytes in which the Kohlrausch bridge method had been used. Hannied. and Ovien (2 8 ) summarized the bellavi or so mewhat as foil ow s : "The capacitance of the cell is ordinarily com­ pensated by variable condenser in the opposite bridge arm, but Jones and Bollinger showed, that if the leads to t.ne electrodes are not widely separ­ ated from certain parts of the cell which contain solution, there is produced a capacitance by-pahh of such a nature that compensation is not practic­ able ." It was shown th.-'^t this fault in cell design would produce an 15 error which must vary irith the specific resistance of the solution. This offered a ready explanation for the obser­ vation that the cell constants of certain cells show a slight variation with the conductivity of the solution. To ascer­ tain this point Jones and Bollinger went through a. proof which is much too elaborate to begiven indetail, but in­ volved a variation of phase angle,frequency, resistance, degree of p latinisation and size of electrodes. It was in this study th"t the m o d e m day bridge design had its founda­ tion. Ohm's Lavr is defined as E - IR 5 where S is the potential applied across the ends of a con­ ductor, I the current, and R the resistance of the conductor. The unit of the resistance is thus determined by choice of the units of potential and current. If E is measured in volts and I in coulombs per second, i.e., amperes, then R is in absolute ohms. Olim found that R is directly proportional to . the length, 1, of a uniform, homogeneous conductor and in­ versely proportional to the cross section. A, so that, ^ A The proportionality factor o" is defined as the specific ^ 16 resistance of the given conductor in olun cm. (and represents the resistance of a conductor of 1 cm, length and 1 cm,^ cross section). The reciprocal l/r* = L is termed the specific conductance of the conductor; its dimensions are o:im“^ c m . ( a n d its numerical value is equal to the length in cm. of a conductor of unit cross section vrhicli has a resistance of one olun}. These relations are valid for electronic conductors if It is assumed that constant conditions exist, particularly wit h regard to temperature. In examining the applicahility of Ohjn* s X>aw to electrolytes, it was found that the current which passes thru an electrolyte solution is directly propor­ tional to the applied e.m.f., and thus Olim* s Law is obeyed.. The validity of Oliin* s Law for electrolytes Indicates that the mobility and charge of ions are Independent of the strength of the applied electric field. Two sets of conditions are known^ however, when devio-tions from Ohm's Lavr occur. Debye and Falkeniiagen, (29) showed that if the frequency of the alternating current used in meas­ uring resistances is so high that the period of oscillation of the ion is comparable with the time required for the for­ mation of the ion-atinosphere, the "period of relaxation" effect will begin to dimi.aish and the mobility of the ion increases with increasing frequency. The second set of conditions under which O h m ’s Law fails 17 to hold was investigated 'by Wien (^O). Wien showed experi­ mentally that at a sufficiently'' high field strength C$,000 to 300,000 v / c m . ) the conductivity was also observed to increase* The explanation is that the velocities of the ions bocom® so high, with these large fields, that the ionic atmospheres are left behind entirely/, and the ions move independently * In 1931» Jones and Bollinger (3I) published their fourth paper on the measurement of the conductance of electrolytes, wit h emphasis on the validity of Olira's Lair for electrolytes* They demonstrated that if adequate experimental precautions are taken to a,void errors due to heating, to polarization, and to secondary effects of inductance and capacitance, thero was no measurable variation of the real resistance of elec­ trolytes with variation of the applied voltage tiiroughout the range of voltage and frequency suitable for use in the Kohlrausch method of measuring electrical conductivity and, he n e e , Ohm *s Law applies. The relation betvreeii the measured resistance across the terminals of a conductivity cell and the specific conductivity of the solution depends upon the geometry of the cell. To avoid the necessity of constructing cells of uniform and accu­ rately known dimensions, a cell constant, k, was Incorporated and is calculated by the oouation L - k/R 7 18 from the measured value of R i/hen the cell contains a standard solution of Icnoirn specific conductivity, L. After Kohlrausch developed his method of measuring conductance of solutions by an a#c. bridge, he (3 2 ) determined the specific conductance of standard KGl solutions by mechanico.lly determining the cross sectional area, a, and length, 1, of two cells (k = l/a in cm ^ ). There w.as, however, some ambiguity in the manner in which Kohlrausch described the composition of his stondard solutions* Parker and Parker (3 3 ) in order to eliminate an inconsistency in units, proposed a. new concentration unit, the demal* A demal, (vrritten ID), solution was defined as one containing a gram molecule of salt dissolved in one cubic ~' o diameter of solution at 0 * Jones and Bradshaw (3^), using the latest principles in bridge and cell design, made new absolute measurements of the specific conductivity of standard KGl solutions and these are the standards generally accepted today* An analysis of the errors due to polarization and the factors upon irhich polarization depends was renorted in a paper on the galvo-nic polarization by alternating current pub­ lished in 1935 by Jones and Christian (3 3 ). With the use of a conductivity cell having a movable electrode and micrometer caliper to control and measure the sepo.ro.tlon, they came to the folloi/ing conclusions. First, polarization resistance is inversely proportional to the square root of the frequency; 19 2) polarization causes a capacitance in series with the re­ sistance which decreases with increasing frequency; 3 ) both polarization resistance and polarization capacitance are greatly dependent on the metal used for the electrodes and dependent to a lesser extent on the electrolyte and temiDera­ ture , but independent of the current density and separation of the electrodes and uninfluenced by another superimposed current of a different frequency* Although Kohlrausch (l8 ) discovered that errors due to polarization can be minimized by platinizing the electrodes, Jones and. Bollinger developed a convenient and reliable quantitative test for the quality and sufficiency of the platinization. During this study they gave proof of Warburg's law, that polarization resistance is inversely proportional to the square root of the frequency within the audio range. A test of the effectiveness of the plo.tinization could be based on this law, R3 where and R^+ K/(co)2 8 is the measured or apparent resistance of the cell is the true resistance of the electrolyte solution with errors due to polarization eliminated. Therefore, if the measured resistance, R ^ , is plotted against the reciprocal of the square root of the frequency, (co)T^, a straight line should be obtained, provided the other causes for variation of 20 resistance with frequency nave been eliminated. The intercept of this line on the axis of the resistance should give the true resistance. The difference between the -apparent resis­ tance and. the true resistance as thus determined, gives the error due to polarization. This depends upon the frequency, quality of the platinization and possibly on other factors. If the error as thus determined is insignificant the platin­ ization is adequate and no correction needs to be applied to the measured resistance to give the true resistance. The platinizing; solution used by Jones and Bollinger was composed of 0,025 N HOI containing 0.3^ by weight PtClq and 0.025^ of lead acetate. The lead acetate was found to improve the quality of the platinization. A great number of conductance studies have been reported. Of special interest are those on salts similar to the ones in the present series. James and Monli (3 7 ) reported on the conductivities of several 1-3 and 3-3 hexacyano complex salts. In 1 9 5 1 » they (3 8 ) reported, on the conductivities of some complex cobalt chlorides and sulfates. Since the limiting values of the chloride and sulfate were knoini to a high degree of accuracy, this permitted, the evaluation of the limiting values for the complex ions. In both cases the results were obtained over a narrow concentration range, thus limiting their usefulness. The Oi/en (39) method, of extrapolation waas used, to obtain the limiting values and. dissociation constants were 21 calculated, to explain the results obtained* In the present study some of the same salts were studied, but to much higher concentrs-.tions, and adlitlono.l salts were also examined* Ill* THEORETICAL In their general treatment of electrolytic solutions H a m e d and Oi/en (40) present a detailed discussion of the fundamental theories and basic experimental methods involved in studying electrolytic solutions. Robinson and. Stokes (41) also present a general treatment of this subject, but in less detail. The present section will give a brief resume of the theories and thermodynamic background required to study the two properties with which this thesis is concerned. Further amplifie.ation of this section can be found in the two preceed.ing references. The modern quantitative theory of electrolyte solutions is based on the concept of the forces anting on the ions due to the presence of the ions themselves and external forces. In its higher refinements the sizes of the ions and inter­ actions with solvent molecules are also considered* The theory was founded, bv^ Debye and. Huckel (20) in 1923. They developed a th.eory for quantitatively predicting the devio.tions from ideality of dilute electrolyte solutions by mahing use of the basic assumptions that : (a) all deviations of dilute electrolytic solutions result from the electrostatic interactions between ions; (b) strong electrolytes are com- Toletely dissoci'^.ted. into ions in dilute solution; (c) each 23 ion can bo treated as a point charge ; and (d) the dielectric constant of the solution is the same as that of the solvent. The fundamental idea, underlying the deductions, is that as a conseauence of the electrical attraction between ions of opposite charge, there a r e , on the average, more ions of un­ like sign than of like sign in the neighborhood of ony ion. Every ion may, therefore, be regarded as being surrounded by a. centrally symmetric ionic atmosphere having a resultant charge whose sign is opposite to that of the ion itself. The essential feature is the calculation of the electrical potential, at a point in the solution in terms of the concentration and. charges of the ions ?.nd the properties of the solvent. This was done by combining the Poisson equation (a general expression of Coulomb's law of force between charged bodies) of electrostatic theory whth a statistical distribution formula to formulate a "distribution function" which gives the probability of finding a particle in a given position relative to another particle. Using the Poisson equation erepressed in the special form for the spherically symmetrical case, the electrical poten­ tial "V at a distance r from a given spherical centro.l ion-j is given as 9 24 where D Is the dielectric constant of the solvent, is th he cha.rge density and the subscript j is attached to p and to point out that the moving j -ion is the center of the coordin­ ate system. Debye and Hüchel assumed the Boltzmann distribution lav:, according to idiich, since the electrical potential energy of an i-ion is Zj_éY^, the average local concentration n/ of the i-ions at the moint in ouest ion is n - 10 I where n^ is the number of ions of species i per era-;, Zj_ the charge on the i-ion, € the charge on the electron, li the Boltzmann consto.nt, and T the absolute temperature. ea,ch i-ion carries a cha.rge z Since , the net charge dens it]/ is, summing for all ionic species By expanding the right-hand side of equ.ation (11 ) into an exponential series and considering only solutions so dilute that ions v/ill rarely be very close together (i.e. , z ^ e Y ^ « k T ‘) all terms of higher order than the second con be omitted. The first term of the eiqianded form odso vanishes since the solution is electrically neutral, meaning L = 0 12 25 Thus only the term linear in "Y is left o.nd eque,tion (11 ) reduces to 2. 2 = 13 - I By substituting the expression just obtained for into equo.tion (9) one obtains the Poisson-Boltzmann eaua.tion dr \ = "'"a dr 14 where ^ Equation (l4) can be 15 solved by substituting u r N^r 3^ = ''''' giving 16 s o tha.t u = 17 or Y, = 18 r r A and B are constants and determined by applying the appro­ priate boundary conditions, namely that ( a ) Y j - 0 when r = oo ; 26 (b) both Yj and d'^/dr must be continuous at r = a, where a is the dista-nce of closest approach of the other ions to the central ion j . The solution of equation (l8) under these boundary conditions is 'Yj = ZAi.exp l K (.a Dr 1 + Ka g )J ^ This equation represents the De by e-Hu oke1 expression for the time average potential at a distance r from the j-ion of valence Zj and in absence of any external force# At r s a, the potential, given by equation (19) after expansion and negleciting higher terms, becomes = ' V . //, 20 Where 21 and Here Y © is singly the potential at a distance r = a due to the charge zjE in a medium of dielectric constant D and Y j * is the potential due to the ionic atmosphere# Knowing can calculo.te the work that must be expended 27 to charge the ions reversibly to the potential , and. this work will be the free energy due to electrostatic Interactions. The extra electric free energy is simply related to the ionic activity coefficient, since both are measures of the devia­ tion from ideality. Thus for a single given J-ion the extra ■ free energy is equal to the additional electrical work required to charge the j-ion, due to the presence of its i on-atmo sphere, to the required potential • Hence 23 A F = w = kT In fj =: JT ^ ^ ^ d ( Z j € ) Substituting equation (22) into equation (2 3 ) and Integrating yields -kT In f K Id oa 1 ^ Ka The quantity K was defined in equation (15 ) as H - DkT £ n^z^' i and has the dimensions of reciprocal length. 15 The relation­ ship between the concentration n^ (ions per cc.) and c^, the concentration of an ion in mois per liter of solution,^ is expressed by C4 = 1000 n ^ N ^ ^ 25 28 where N is Avogad.ro’s number. Consequently, by defining the "ional" concentration as r = I or In the Important special case of solutions containing only a single electrolyte, which d.issociates into only 2 kinds of ions 27 P = 0^ 0 then Although there is no way of measuring the individual activity coefficients, it is nevertheless convenient to have the expression for the activity coefficient of an electrolyte in terras of the ions into which it dissociates. general case of an electrolyte cations and For the dissociating into anions, the mean rational activity coefficient may be defined 5 with E (hUf-)V-o = 29 29 and the mean Ionic activity defined by = ( a b n y ■)h-^ = 3I and the mean Ionic concentration d.efined. by c* = (cHar-)W-û Thus by conbining equations - ciA (24), 32 (2 8 ), and (29) and Chang;lug into common logarithms the expression for calculating mean activity coefficients in dilute solutions is obtained. log n = - 1 + A^(c)é vfnere S(f) - 2.303( Z t>i Z j 2 )3 / 2 ^ 2 j^ ^ 1 j j auid is the Debye-Huckel limiting slope a.nd A' _ S k 107® - -T3Twhere S is the distance of closest approach expressed in ângstrora units* Earned and Owen (42) have calculated the numerical values of S(f) and A*/S for aqueous solutions at 25^ for different salt types. 30 So far, the funda.raental theory necessary for treatment of the ionic atmosphere has been considered and applied to the calculation of the limiting law for the variation of activity coefficients. By addition of further concepts, such as application of the general equation for continuity to irreversible processes, it is possible to formulate exact equations for computing the electrostatic contribution of Coulomb’s forces to conductance of dilute electrolyte solu­ tions. The development of the theory is due to Debye and Hückel (2 1 ), Falkenhagen (2 9 ), o.nd Onsager (43). It will be remembered that Kohlrausch showed that, in dilute solutions, the conductivities of strong electrolytes could be expressed empirically by the equation W = V\_o - k (N 3 This equation was also obtained, for dilute solutions from the ion atmosphere theory, by Debye and Hückel. The reason it applies only to the limiting case of very dilute solutions is apparent from the assumptions which must be made in de ­ ducing i t . - Debye and Hückel first showed that, as a con­ sequence of the ion atmosphere vrhich form around any ion, this ion is subject to tiro retarding influences when it moves in an electric field (21 ). First, whenever the ions of an electrolyte are subjected to an electrical field disturbance, the central ion moves relative to its ionic atmosphere and 31 hence the latter no longer possess a symraetric.al structure, i.e*, there is a change in the charge density. as the dissymmetry effect. This is knovna If the disturbing force is suddenly removed, the ionic atmosphere will tend to revert to its normal equilibrium condition with a certain velocity. The finite time required for change from the disturbed to the normal condition is called the "time of relaxation**. The second electrical action that lowers the mobility of the ions is called the electrophoretic effect. in the following manner; It arises the ions comprising the atmosphere around a given central ion are also under the influence of the applied field and hence are also moving and, on the average, in the opposite direction. Also, since they are sol va,ted, they tend to drag along with them their associated solvent molecules, which results in a net flow of solvent in the direction opposite to the motion of any given solvated central ion. The central ion is thus forced to move against this countercurrent, which accounts for its lower mobility. A limiting law has been calculated for conductance of^^ electrolytes using methods similar to those used in obtain­ ing the limiting law for activity coefficients. However, the conductivity limiting law is a result of the two effects which slow d.own ion mobilities, i.e., relaxation and electro­ phoretic effects. The limiting law for the relaxation effect was first 32 developed by Debye aixl. Hückel (21 ) but treated more succesofully by Onsager (43), using an incomplete expression for potentio,l and assuming point charges. workers Falkenhagen and co- (44) extended and modified the Vneo'srj in order to mcüce allowjonces for the finite sizes of the ions. The computation of the concentration-dependent electro­ phoretic effects Oulso requires the use of the distribution function, but in this case with a disturbed symmetry. Boltzna,nn distribution, assumed and Stokes* or a similar distribution, The is ogain law for the motion of a sphere in a vis­ cous fluid is then applied. Its apiplicatlon arises in the calculation of the velocity of the counter-current which the central ion experiences due to the electric force applied. It is assumed that the entire charge, ) of an ionic atmosphere is found at a distance 1/k from the central ion and is distributed on a spherical shell of the radius 1/ k * By combining the two effects, the final velocities caai be calculated. The velocity of the ion under a potential gradient of unity gives the ionic mobility, -fhich, when multi­ plied Faraday *s constant, F, gives the ionic conductance. Since i f + Athe limiting lav/ expression may be formuloded. 36 In its final form the limiting law (for the conductance of electrolytes dissociating into two kinds of ions in fields of ].oi: frequency and magnitude) mny be written JV = JVo - S(j^)(Nr 37 = o< Ac +/? 36 where and represent the limiting slope. For aqueous solutions at 2 5 '^ the constants are defined as follows (45), .2289w *Q 39 60 .19w'" 40 and. The factors w*, w"^, and Q, are valence factors and defined, by w* = |zgZ2 l( 1Z1 Z2 I w* = ^taiL.t-.issLy Uisizgl 41 “ 42 and " 0.2929u'^+UatT^J ^3 The parameter q'**' which anpears in the definition of Q is given by (|zil * The Onsaaei' conductance equation is one means of comparing 34 theory with experimental results. Several extensions have been used for extending the range in which the Onsager equation can be used. One such extension considers the introduction of finite dissociation constants to interpret the conductance of electrolytes which fall below the limit­ ing law in dilute solution (46). The reciprocal of the ionization constant of the associated ion pair is given by Q(b) is an integral in terms of the function b, where b is given by b = é^/SDkT 46 Values of Q(b) have been computed by Bjerrurn and by Fuoss (47). However, it was pointed out by Kraus (48) that all negative deviations from Onsagers equation can not be ascribed to ion association. Another extension is based upon estimating the effects of the mathematical simplifications used in deriving the law and correcting by the addition of two terms of order higher than (c)^. Assuming complete dissociation, Onsager and Fuoss (49) and Fuoss (50) have shown that such terms appear as follows A_= x f - ( X c T + /e*)(N)^ + AN los N + BN 4% 35 where the constants A and B are cemi-enpirioal and only in the case of symmetrical valence types has much success been found for their theoretical e x p l a m t i o n (51 )• Rearrangement of equation (4-7) to read -A-°J =. A log N + B 48 shows that a plot of the bracketed terms against log N per­ mits evaluation of the constants A and this is knovm as an Owen (39) plot and B.A plot such as isused to obtain the value of -A? when ordinary extrapolation procedures do not yield sufficient precision. A preliminary value of JL? is selected from a rough extrapolation of This value is then versus (N)*^. used to calculate + (o(*AP + /3*)(N which remain constant while the selection of a-A? to best fit the Owen plot is found. This final value of-A? is then used to calculate more accurate values of _A.4- (oc^^A? 4 ^8^)(N)‘e and the procedure repeated until a value of -A? is obtained which will express the da,ta by equation (48) to the maximum concentration and yet within the limits of experimental error. The third possibility for extending the Onsager conduc­ tance equation is by purely empirical extensions. A summary of these and othei* conductance equations can be found in reference (52). The activity, a, of a pure chemical solute in a solution 36 îïiay be given a general definition by the equation 49 - Fj® = RT In aj, where refers to the increase in total free energy, F, when one mole of component 1 is added to an infinite amount of solution at fixed temperature, pressure, and v/ith the number of moles, n ^ , U g , . . • ^ { i - l ) > kept fixed. of all other components is the partial molal free energy in some arbitrary state. Before the activity can be given a definite numerical value the standard state must be clearly and unambiguously defined. For electrolyte solutions, the standard state of the solvent is the pure solvent at the same temperature and pressure as the solution. For electrolytes, however, the pure solute is not a very practical choice, since it is often a solid with properties very different from those of solutions. For electrolytes, the standard state is a hypothetical sol­ ution at unit concentration and at the temperature and pressure of the solution (i.e., 25^C. and one atmosphere), and has the property that the mean ionic activity coefficient approaches unity when the concentration is reduced to zero. To obtain a more sensitive measure of the non-ideality of solutions in terms of the solvent, Bjerrum (53) intro­ duced the concept of osmotic coefficients. He defined the practical osmotic coefficient, 0, for an electrolyte 37 dissociating into i) ions as = -(^RT^mMi/1000 50 where the subscript 1 refers to the solvent and Mq is the molecular weight of the solvent. Combining equations (49) and (5 0 ) yields In a j = 5I -i^'^mMj/1000 The activity of the solvent can be expressed as 3-X = Pl/Po where 52 is the vapor pressure of the solution and P q that for the pure solvent. Strictly speaking, the ratio Pi/p^ should be replaced by the ratio of fugacities, fi/fp. However, since the vapor pressure of electrolyte solutions and solvent are of simlliar magnitude , the deviation of p^ from f^ and P q from fo are equal to within an amount less than exi^erimental error in measuring pressures. After solutions of two different salts have been allowed to equilibrate through the vapor phase, an isopiestic condition exists in which ^l(m) = ^KmR) 53 where a^ is the solvent activity and m is the molality of the solution under investigation and mR is the molality of a ref­ erence solution in which the activity or osmotic coefficient 38 Is known as a fimction of concentration. Thus for isopiestic solutions one obtains -Om wh i c h perraits the calculation of osmotic coefficient of a solution in terms of the corresponding property of the ref­ erence solution. The method of graphical integration given by Lewis and R a n d a l l (5 4 ) or the following expression obtained by Randall and White (ll) log # - (l-r"' 2 , J. . - âTfe 55 permits evaluation of activity coefficient from osmotic co­ efficients. Since the lower concentration limit for which data can be obtained by the isopiestic method is around 0.1m, some form of the Debye-Huckel equation must be used to extend the (1 - 0)/(m)^ versus (m)^ plot to infinite dilution. One method, developed by Scat chard (55) involves calculating the osmotic coefficient from the expression (1 - ^)(3alc. ^ 0 .7676Sjj^(f )oj^(m)’^ 4 e-Bm - (^0)smoothed 56 where the (^i^ )smoothed f ^ obtained by the method of Sc at chard 39 and Prentiss (56), v/hich. was used in treating freezing point data, and represents a smoothing of the experimental date.# Here the 8 ^ ( f ) is defined by 57 where was given in equation (34) and d^ is the density of water. The constant is a function of A (equation 35 )> wit h the numerical values available in tabulated form (57)# The -gBm term is equal to the slope of a *^(^1 ^V(^)^obsd [^(l - 0 ) / ( m ) ^ calci^ against (m)^ plot and is used to represent the data at higher concentrations. Numerical values of B and (= A (d^ )'k^') are chosen so that the deviation, is I not.large at any concentration. A value of is selected by trial which permits the equation (1 - 0)/(m)* = 0.7676Sm(f)cr^i 58 to give the best fit of the expierimental data at the lowest cone entra,tions. So long as the osmotic coefficients can be calculated by equation (56) and the deviations e.re small, the activity coefficients can then be calculated by the method which Smith (5 8 ) used in treating solutions of sodium chloride at their boiling point, namely. In =_ 2.503Sp,|f)(ffih - Bm + 1 4 Cm}"^ r J 0 IQ + A(f> 40 The two terms containing the are evaluo^ted graphically. If term is not small or if it is applicable over too narrow a concentration range to warrant its use, the method of calculating the osmotic coefficients is not used. The activity coefficients are then calculated by graphical in­ tegration of equation (55) with the experimental plot extended to Infinite dilution by means of equation (58). IV. Raw Materials : EXPERiœNTAL Th.e following is a list of th.e reagents used in this work. Ammonium Carbonate, (NH4 )2C.0^, Fisclier Scientific, G*P* Reagent Ammonium Gbloride, NH4 CI, Merck Reagent Grade Ammonium Hydroxide, KH4OH, I'^allinckredt Analytical Reagent Barium Chloride, BaClg^RHgO, “Baker*s Analyzed" Reagent Gobaltous Chloride, CoCIg*ôHcO, Mallinckredt Analytical Reagent Cobaltous Nitrate, C o (N O ? )p *6H2O , Mallinckredt Analytical Reagent Calcium Chloride, GaClo, Mallinckradt Analytical Reagent p-Dioxane, Mallinckredt Analytical Reagent Potassium Chloride, KCl, Mallinckredt Analytical Reagent Potassium Cyanide, KGN, Mallinckredt Analytical Reagent Potassium Hydroxide, KOH, Fischer Scientific, C.P, Reagent Potassium Permanganate, E H 1O4 , Mallinckredt Analytical Reagent Propylenediamine, CH^CHNH2CH2NH2 Eastman Organic Chemicals Silver Nitrate, AgN O ? , "Baker's Anadyzed" Reagent Sodium Bisulfite, NaHSO^, Mallinckradt Analytical Reagent Sodium Hydroxide, NaOH. ikillinckral.t Analytical Reagent Sulfuric Acid, H 2SO21., 'Baker's Analyzed" Reagent In addition to the above, distilled (or conductivity) water and C.P. grade ethanol and acetone v:ere employed. C• Preparation of Compounds; Potassium hexacyanocobaltate(ill) was prepared according to the procedure as given in Inorganic Syntheses (59). Two methods of purification were used, and, conductivity results from each were found identical. One method was repeated 42 fractional precipitation with dioxaiie from conductivity water and the precipitate dried in a vacuum desiccator over R g O g . The second, was recrystall!zation three 1 1mes from conductivity water and then the precipitate was stored over anhydrous CaClg. The anhydrous form results with either method and was the form used in this work* T r i s (propylenediamine)cobalt(ill) perchlorate was pre­ pared by a quantitative metathesis reaction between Co(pn)^Cl^ and AgClO^ in aqueous solution* The Co(pn)^01^ was prepared by the method used by Jenlcins and lioiik (3 8 ). The anhydrous propylenedianine used was made from 70^ propy1enodiamine by the method of Rollinson and Bailar (6 0 ). The silver perchlor­ ate was prepared by reacting o/a excess of Ag2*^> nitrate free, wit h O.lM HClO^* The resulting AgClO^^ solution was separated from the excess ^^2^ by filtration, diluted, and analyzed by AgOl precipitation. An aqueous solution of the complex chloride was then quantitatively titrated with AgClO^, mailing sure no more than one or two drops excess were added. The AgGl was filtered off after digestion on a steam bath for one hour* The resulting G o ( p n ) ^ ( G l O ^ s o l u t i o n was then con­ centrated by evaporation and the Go(pn)^(GIO^)^*H20 precip­ itated by addition of ethyl alcohol* The salt was recrystal­ lized a minimum of three times from conductivity water and dried in a vacuum oven at 90° until the anliydrous form resulted. Tris(ethylenediamine)cobalt(lII) nitrate was prepared by 43 a quantitative metathesis reaction between Co(en)^Cl^ and AgNO^, The Co(en)^Gl^ was 23repared according to the pro ­ cedure found in Inorganic Syntheses (61). The metathesis reaction was carried out as above using AgNO^ in place of the AgGlO^j.* The Go(en)^ (NO^ was recovered by evaporation of the filtrate and was dried until the anliydrous form re­ sulted. T r i s (ethylenediamine)cobalt(ill) sulfate was prepared from Go(en)^Gl^ and H2S0^ using the method described by I'leyer and Grohler (62). Go(en)^Gl^ was dissolved with stir­ ring in ice-cold, concentrated H2SO/1.. The mixture vras then placed in a vacuum desiccator for 24 hours over concentrated H 2SO2J.. A beaker of KOH pellets was also present to remove the escaping HCl. Tlie solution was then cooled with ice and ice-cold ethyl alcohol was added. The precipitate which formed was filtered and dissolved, in 20^ ice-cold HgSO^ and ago-in precipitated with ice-cold ethyl alcohol. After fil­ trating, the precipitate was dissolved in v/ater. Addition of ethyl alcohol caused an oil to form which cnystallized after being rubbed with a glass stirring rod. The tetra- hydrate form resulted. C* Apioaratus and Procedure : 1. Isopiestic measurements: The apparatus and pro­ cedure used has been described by Brubaker (1 6 ,6 3 ). 44 Duplicate s.amp le s of two solutions were run together, one being the reference salt, KGl, and the other the salt under investigation. When duplicate samples agreed to within three parts per thousand in molality, the salts were considered at equilibrium. The constp.nt temperature bath iras controlled at 24.978 ± O.OOg^G. 2* Conductance Measurements: The resistance measurements were made with an A, G. bridge essentially of the design of Jones and Bollinger (24,28). The actuod bridge was designed by Thompson and Rogers (64). The oscillator used permitted resistance values to be taken at five frequencies over the range 400 cycles per sec. to 5,000 cycles per sec. An os­ cilloscope was used to determine the balance point. Before each run the value of a standard resistance was checked to ensure that the bridge was functioning properly. The cells were held at a constant temperature of 25.00 + 0.015°G. in an oil bath. constants of about A group of three cells, with cell 0.3 cm”^, 1.0 cm"^ and 30 cm"^, were used to cover the concentration range 1 x 10"4^ to 3 % 10“^N. For the higher concentrations a Leeds and. Northrup type B con­ ductance cell (cell constant about 30 om"^) was used. The other two cells were similar to the erlenmeyer type described by Daggrett, Bair, and Kraus (65). A conductance cell was sealed, to a A Leeds and. Northrup t\rpe 500 ml. erlenmeyer flask which had the add.ed. feature (introduced by Dye) of two 45 stopcocks. One stopcock was attached to the cap, a.nd the other to an added side-arm. This permitted the introduction of carbon dioxide free conductivity water directly from the distilling appo.ratus under a pressure of nitrogen. Also, a steady strea.m of nitrogen was permitted to flow through the cell whe n the top was removed for mailing additions to the solution. The cell constants were determined using aqueous potassium chloride solutions (66). The electrodes were lightly platinized, using a current of about 20 milliaraps. for 40 second.s, with the polarity re­ versed every 10 seconds. When the variation of resistance wit h frequency over the range 400-5000 c.p.s. (equation 8) wo,8 greater than approximately 8 ohms, the electrodes were re-cleaned with fuming nitric acid, reylatinized and the cell constant redetermined. The conductivity v;ater was prepared by the method des­ cribed by Vogel (67)* First, water in equilibrium with the carbon dioxide in the atmosphere was prepared by distillation from an adkaline potassium permanganate solution of demineral­ ized water. This was then redistilled in a distillation apparatus through which nitrogen was flowing. The water pre­ pared in this way had a specific conductivity of approxim­ ately 0.6 X 10“^ olim"^cm^^. For the dilute solutions the erlenmeyer type cells were used. The water was forced into the weighed empty cell b>^ 46 means of nitrogen pressure. After reweighing the cell and water, the exact weight of water was calculated. Tlie cell plus water then placed in the thermostat to permit d.eter— minatlon of solvent conductance. of a stock solution were added. Then successive portions The contents of the cell were then thoroughly/ mixed and the cell replaced in the hath. The attainment of temperature equilibrium was indicated when successive resistance readings checked to within 0.01^. resistance values were then recorded. from the bath and contents remixed. The The cell was removed The contents were again 8.1lowed to reach tempera.ture equilibrium and the resistance values rechecked. Remixing of the solution continued until the successive readings checked to within 0.01^. For the higher concentrations the stock solutions were added directly to the Leeds and Northrup type B conductance cell after the cell had been rinsed several times with the solution. The resistances were recorded after equilibrium was reached and the procedure repeated for new portions of the solution in order to check the rinsing procedure. Densities of solutions of the compounds were also meas­ ured in order to be able to transfer molality data to volume concentration. They were determined at 25^D. with a pycnom- eter and are represented by the equation d - Am + 0.99707 60 47 The values of A for the various electrolytes are found in Table I. TABLE I VALUES OF TIIE CONSTANT A OF EQUATION 60 Electrolyte A Co(or)^(KO^ .1945 C 0 (pn )-j(CIO^^ .2558 K,Co(CK)g .1862 ^o(en)p2^®°4b .3740 V. A. RESULTS AND DISCUSSION IsoTDlestlc The experimental results are given in Table II as molal­ ities of the isopiestic solutions and the corresponding osmotic coefficients, which were calculated from equation (54) using kno\m values of potassium chloride solutions. From the ex­ perimental results given in Table II the activity coefficients given in Table III were calculated using one of two methods. The first method tried in all oases was that employed by Smith (5 8 ) for treading sodium chloride solutions at their boiling points. In - Bm . 1 + AjTTmIt 4 Jo m The application of this method depends upon the calculation of osmotic coefficients using the expression (l - ^calc. “ 0«7676Sjjj,if )Gr^(m)~ - s'Bm - 0)smoothed 56 This renresents the Debye-Hückel expression for osmotic co­ efficients with a linear term of ^Bm to represent the data at higher concentration (55). In the actual solutions there exist interactions other than those considered by Debye and Hückel in deriving the 49 TABLE II ISOPIESTIC MOLALITIES AND OSMOTIC GOEFFIGIEl^TTS OF ELECTROLYTES AT 25^ C o ( e n ) ^ (N O j)^ C o ( p n ) j ( C l 0 4 )2 ^o'oad. ®av. ^ ob sd . 0 .0 3 0 5 5 0 .6 9 1 8 0 .0 5 7 4 7 0 .6 6 9 3 .0 5 2 6 7 .6 7 8 9 .0 6 8 9 8 .6 6 C 3 .0 8 2 7 6 . 6468 .0 9 0 5 6 .6 4 2 4 .1 2 6 6 .6 2 4 1 .1 1 1 7 .6 2 7 0 .1 3 4 9 .6 0 9 8 .1 3 3 6 .6 0 9 8 .1 5 7 4 .5 9 5 2 .1 5 4 8 .5 9 8 4 .1 8 5 3 .5 7 9 5 .1 6 5 9 .5 8 9 4 .2 5 8 7 .5 4 1 0 .2 0 2 7 .5 7 1 9 .2 6 1 2 .5 4 0 8 .2 2 4 3 .5 6 2 9 .2 7 4 9 .5 3 6 1 .2 5 0 2 .5 5 2 3 .2 5 7 8 .5 4 6 4 .2 6 1 2 .5 4 9 8 ^av. 50 II, continued KjCo(OW)g |po(en )j]2 (2^4)3 A ^obsd. O.26I3 0.03035 ^obad. 0.7479 0.07393 .7075 .1453 .2417 0,1508 .6926 .1489 .2379 0.2730 .6819 .2407 .2027 0.4571 .6768 .3504 .1705 0.5828 .6768 .4580 .1705 0.6775 .6804 .5004 .1681 0.7309 .6857 .6190 .1641 0.7667 .6876 .8993 .1862 O.8I72 .6918 1.003 .1993 0 .84-97 .6924 1.064 .2043 0.9507 .7007 1.252 .2259 1.026 .7063 1.298 .2310 1.082 .7116 1.429 .2499 1.217 .7258 1.536 .2622 1.223 .7305 1.800 .2979 1.235 .7331 1.844 .3050 1.306 .7421 1.311 .7425 ™av. O.08I6O TABLE III MEAN ACTIVITY COEFFICIENTS AND SMOOTHED OSMOTIC COEFFICIENTS OF ELECTROLYTES AT 25° Go(en),(NO ) m 0 GoCpn)^ (0104)3 y 0 0.01 0.505 0.7980 0.513 0.7967 .03 .357 .7185 .368 .7156 .05 .296 .6832 .305 .6787 .07 •258 .6592 .266 .6563 .10 .222 .6338 .228 .6351 .15 .184 .5995 .189 .6003 .20 .158 .5709 .163 .5740 .25 .140 .5465 .145 .5527 .141 .5498 .2612 .2T49( satd. ) .133 .5361 52 TABLE III, continued K^Go(CN)^ (co(en)3] 2 (S0 4 ). m 0 0.01 0.522 0.9126 .03 .385 .7487 .0654 .3418 .05 .323 .7116 .0440 .2943 .07 .293 .7089 .0339 .2761 .10 .260 .6968 ,0256 .2569 .15 .228 .6902 .0186 .2393 .20 .207 .6838 .0146 .2219 .25 .193 .6830 .0120 .2040 .30 .181 .6801 .0102 .1872 .50 .153 .6758 .00648 .1685 .75 .135 .6887 .00462 .1686 1.00 ,127 .7055 .OO 38I .2100 1.20 .123 .7284 .00337 .2291 1.30 .122 .7424 .00320 .2385 1.3ll(satd.) .122 .7425 1.50 .00294 .2625 1.75 .00272 .2962 1.844 .00265 .3047 0.152 0.4757 53 limiting expression, (e.g., short range interactions between ions and solvent molecules). Thus by includ.ing a term linear in concentration, a more theoretically significant result is obtained in which the parameter § is not forced to t'\ke some of the responsibilities of the linear term. By adjusting the values of â and B to fit the experimental curve, expressions could be obtained which would give a better fit over a smadler concentration range, or a poorer fit over a greater range* The values of ê and B which were found to fit best the experimental data over the widest concentration range and with reasonable accuracy, are given in Table IV. TABLE IV VALUES OF THE PARAMETERS â AldJ 3 USED IN THE SMITH I^IETHOD Electrolyte B S Co(en)^(NO^)^ (0.480) (3.45) 0.971 3.83 K^Go(GN)g (0 .1 3 1 ) (4 .1 3 ) [Co(en)^]2 (S0^)^ (0.792) (3 .6I) Co(pn)^(0l02^)^ The values for three salts are in parentheses to point out the fact that the method was not found to reproduce the experi­ mental data with sufficient accuracy over a concentration range large enough to warrant its use. A comparison of the observed osmotic coefficients for Co(pn)^(GIO^)^ and those 54 calculated from equation (56) are tabulated in Table V. TABIE V ISOPIESTIC MOLALITIES, OBSERVED AND CALCULATED OSMOTIC COEFFICIENTS OF Go(pn)^(CIO^)^ ®av. Aotasd. icalc. , 0.05747 0.6693 0.6778 .06898 .6603 .6633 .09656 .6424 .6418 .1117 .6270 .6259 .1556 .6098 .6099 .1548 .5984 .5973 .1659 .5894 .5910 .2027 .4719 .5718 .2243 .5629 .5616 .2503 .5523 .5498 .2578 .5464 .5466 .2612 .5498 .5450 When the Smith method was found unsuitable, the second method, that of Randall and White (ll), was applied* In this case the activity coefficients are determined by graphical Integration of the equation In = -(l - ^) - 2 ^ ^ ^ 1 £ ^ d m ^ 55 The extension of the function (l - 0 ) vs* mb' to infinite dilution was carried out by means of the Debye-Hückel equation and required that the parameter S have the values recorded in Table VI. TABLE VI VALUES FOR 8 DETERI^UNED BY THE METHOD OF RANDALL AND WHITE Electrolyte § Go(en)^(NO^)^ Go(pn)^(C 10 ^)^ 3.23 (3 .1 6 ) K^Go(CN)^ 4.01 [Co(en)^]g(804)^ 3.43 The value for the Co(pn)^(GlO^i^is in parenthesis to show that it would be the value required if the Randall and White method had been applied. It was found, in both the present study and in that by Brubaker (16) that the activity coefficients calculated by either method, differed by only about one per cent. A comparison of the § values obtained by the two different methods shows that the method of Randall and White yields the lower values. This is to be expected, since the linear term was obtained from the deviation between experimental and cal­ culated data. The 8 was then increased to permit the &Bm term to be added and have the resulting expression still fit 56 the experimental data. The linear term alone appears to be insufficient to account for the deviations from the Debye-Hückel expression and a better reproduction of the data could possibly have been obtained by introducing further arbitrary terms in higher powers of concentration so that the would remain small at the higher concentrations. The limiting value for (l - is given by the Debye- Hückel theory a,s 2*868 for 1—3 and 3“*T valence type elec­ trolytes and 9*069 for the 3-2 type. Since the objections to the theory in finite concentrations vanish as m approaches zero, these limiting values of (l - ^)/m^ should not be sub­ ject to errors greater than those found, in the experimental techniques used to evaluate the various constants found in the limiting expression, such as the dielectric constant of water, etc. A fundamental equation of the Debye-Hückel theory was shoivn to be /Oj = exp 11 The higher order terms neglected by the approximation exp 1 - ej^^/kT 62 are functions of the valences of the ions, and while nearly negligible for 1-1 electrolytes, increase markedly in magnitude 57 w he n the charge on the ions increases. The exact determina­ tion of the effect of extended terns of equation (ll) is very difficult, since it is obscured by other factors present (68). On the oasis of a complicated ma the mat i cad treatment presented by Gronwall, LaMer, and Sandved (69) and the simpler ionassociation theory of Bjerrum, large deviations from the Dobye-Hùckel first approximation are to be expected for poly­ valent electrolytes. By considering the electrolytes in view of Bjerrum's theory we see that if r, the minimum distance of approach of two ions of opposite sign, is greater than o b — 6“ |z^Zp|/2DkT, then the probability of ionic association is negligible. and 21 For 3-1 and 3-2 electrolytes, b equals 10.5 respectively. Since these values are much greater than â for the electrolytes studied (Tables IV and VI) considera-ble ionic association of the Bjerrum type could be said to exist. In any case, the 8 values are small and do not approach the values to be expected from crystallographic radii. The concentrations of the saturated solutions of the Co( en)-^ (NO^ )^*HpO and K^Go(GN )^v/ere found to be 0.2749 and 1.311 m, respectively. The conversion of the undissolved Co(pn)^(G10^)^ to the monohydrate in equilibrium with the sat­ urated solution was slow and its solubility was not determined, but is estimated to be .27 m. The highest concentration em­ ployed for the [ C o ( e n ) ^ 2 (S02|.)^ was limited by amount which could be weighed conveniently into the dishes. 58 The logarithms of the •activity coefficients given in Table III are plotted in Figure 1, along with the values ob­ tained by Bnubaker (16) for Co(en)^Gl^. By definition, is unity at infinite dilution for all electrolytes. c a s e ,^ In any decreases rapidly with increasing molality at low values of m. The steepness of this initial drop, however, varies with the valence type of the electrolyte as is exem­ plified by the 3-2 salt behavior. The activity coefficients of the Go(en)^(NO^ )^, Cb(pn)^(GlOj^)^ and Go(en)^Cl^ are all within about 2.% of each other and are represented by one curve until approximately .09 m. Although the activity coefficient data does not show the present 3-i salts to be very "strong" electrolytes, they are very similiar to the values obtained for the Go(en)^Gl^, Data such as this would seem to Indicate the possibility of estimating the activity coefficients of similiar size and charge type com­ plexes. With the Q]o(en)^^^ the extrapolation is some­ what uncertain, but the results are of the right order of magnitude with other 3 —2 electrolytes, such as Al-gC^^O/j.)^ and In2 (S0 ^)^ (?0). B. Conductivity In (addition to the Isopiestic measurements of activity coefficients it seemed desirable to try to determine the 1.00 0.50 Go(pn)^(010/j.)^ Vo (@ n )-7(NO -2) 0,10 |Co(en)Jp(30. ) 0.05 FIGURE 1 60 distance of closest approach, parameter, 8, from conductivity measurements, as uas done by Dye and Spedding (l) for the alkaline earth and rare earth salts. This would have enabled one to substantiate the values of 8 by a second and independent method. From the experimental results given in Table VII, the values of JLq were cadculated by the method of Shedlovsk^^ (71 )• -Ao’= A - S(^)N* The extrapolation to infinite dilution of the 63 values as a function of the square root of the normality, can then be used as an indication of the applicability of the Ons.ager limiting law since the theory is being followed when the slope of the curve is zero. It was found, however, that for all the salts studied the slope was not zero, bLit had a decided u p ­ swing. The upswing, from the curve minimum to the limiting value, was observed to vary from a maximum of about 42.2 con­ ductance units with the |[Go(en)^!^^ ^ ^ 4 to a minimum of 1.24 for the K C o (CN)^. Although the technique of Dye and Spedding 3 D can handle a slight upswing, the magnitude of the deviations found with the present salts did not permit the 8 po.rameter to be calculated by this method. The observed voulues of the limiting equivalent conductance obtained by the Shedlovsky method are given in Table VIII. The value for the sulfate is in parentheses to show that the 61 TABLE VII EQUIVALENT CONDUCTANCES OF ELECTROLYTES AT 25° Co(en)^(NO^ NxlO^ JL NxlO^ 0.17248 141.87 1.3817 133.80 3.2964 127.49 .32775 140.23 1.6524 132.61 5.3353 123.15 .50322 138.78 1.8254 132.01 6.2610 121.65 .55665 138.36 1.8907 131.79 9.9483 117.20 .79662 136.99 2.2708 130.28 29.627 1.0990 135.18 2.6028 129.42 78.432 1.2053 134.60 3.1044 128.05 211.58 74.213 1.2057 134.60 3.2343 127.66 288.89 69.812 Nx 1o 3 _A_ 102 .19 88.285 Co(pn>^3 ^^104 )^ Hx 1o 3 _A_ HxlO^ JS_ NxlO^ _A_ 0.098169 129.05 0.84051 122.78 4.3566 112.77 .18140 127.88 0.86718 122.69 5.5635 110.79 .29019 126.61 0.98445 122.32 7.0419 108.49 .30363 126.44 2.1662 117.86 8.8596 106.18 31845 126.40 3.3393 114.75 19.289 98.637 .43830 125.26 3.3528 114.78 27.267 94.587 .51138 124.74 • 62 TABLE VII, continued KjCo(ON)g NxlO^ N x 103 -A- N x 103 JL 0.51600 164.81 1.7722 158.17 0,66384 163.76 1.8225 158.10 12.663 141.93 0.67491 163.58 2.1315 157.09 19.294 135.38 0,86460 162.55 3.1473 154.06 28.882 130.24 0,97386 161.79 3.2655 153.55 119.36 113.30 1.0824 161.37 3.7839 152.79 210.09 107.40 1.1288 161.01 4.3572 151.36 299.27 103.91 1,4242 159.73 NxlO^ JL [Oo( en )^32 ^®°4 1 MxlO^ _/L 6.4080 N x 103 148.34 -A. 0,23889 136.05 5.6155 67.467 26.707 44.161 0,81565 108.82 .6,0890 65.566 44.457 38.577 6.6255 64.628 153.10 27.920 51.560 337.91 23.130 1,4727 94.901 2,3912 84.133 3.8719 74.356 14.898 63 value was selected by adding the limiting values for the two ions rather than by extrapolation, TABLE VIII LIMITING EQUIVALENT CONDUCTANCES OBTAINED BY THE SHEDLOVSKY METHOD Electrolyte ^ Co(en)^(NO^)^ 146.24 ± 0.07 Co(pn)^(GlO^)^ 132,4 7 + 0.06 K^Go(CN)g 172,59 t 0.09 n0o(en)^2(S0^)^ (154.80) This was considered more accurate in view of the steep slope observed and characteristic of 3-2 salts in general. The 0\'7en method of extrapolation was then applied with the hope that this extrapolation procedure would give a more accurate limiting value. The use of this method was also suggested by the fact that the values of the limiting ionic conductivities of the complex cobaltic ions reported in the literature had been calculated by means of the Owen method. The values of JL^ and the constants A and B obtained, when this procedure was used, are found in Table IX, No value for the sulfate is given since the method is not sufficiently sensitive to warrant its use. From the limiting conductivities of the nitrate, per­ chlorate, potassium and sulfate ions, the limiting ionic 64 TABIE IX PAEIAMETERS OF THE SEKL-EMPIRICALLY EXTENDED ONSAGSR EQUATION AT 25° Electrolyte A B ^ Oo(en)^(MO^)^ 1,586 3,248 146.12 t 0.07 0 o(pn)^(010^)^ 4,679 12,400 132.40 ± 0.06 E^0 o(0N)g 1,293 2,914 172.52 t 0.09 conductivities of the complex cobaltic Ions may beobtained w i t h a high degree of accuracy. The results have been tab­ ulated In Table X In order to permit a comparison of the limiting Ionic conductivities obtained In the present study w i t h the Shedlovsky and Owen methods, as well as the values previously reported by other workers* From the table it can be seen that higher limiting values are obtained when the Shedlovsky method is used. In either case, the two methods give results within the experimental error of 0 ,05^ for all Iona, From the data in Table X It can be seen that the varia­ tion In the limiting conductivities of the complex cobaltic ions Is that which would be expected, i.e., as the size in­ creases,, the mobl 111y'lcecomes less (74). The larger mobility of the Oo(GN)^^ and GoCen)^*^^ Ions (approximately 100 and 75 units, respectively) compared with those of the rare earth trivaient ions (close to 7 0 ), would seem to indicate that In 65 TABLE X LIMITING EQUIVALENT CONDUCTIVITIES AT 25° Present Literature Ion Shedlovsky Owen Value Ref. Co(en)^*^ 74.80 t 0.07 74.68 ± 0,07 74.7* (38) Oo(pn)^'*‘^ 65.11 t 0,06 65.06 t 0.06 65.06* (38) Co(CN)^'^^ 99.07 1 0.09 99.00 t 0.09 98,9* (37) NO^"^ Literature value was used 71.44 (72) 0104-1 Literature value was used 67.36 (73) Literature value was used ^ 8Oy0O (72) Literature value was used #3.^— (72) SO4-2 estimated by the 0\\ren method. these ions the first layer of water molecules is replaced by the cyanide and ethylenediamine groups, respectively, and hence water molecules do not appear to attach themselves to these foreign groups as readily as to other water molecules. W i t h large spherical ions one would ex%:ect solution effects to be much smaller owing to the lower charge densities on their surfaces, a condition more favorable to a higher mobility. The deviations of the observed conductivities is shown In Figure 2. It is a plot of A qQ * q versus (N)s^ where — A -^O ^ ( N 1 Aq* Is the value obtained from equation (63 ) and A q is the limiting value obtained by extrapolation in the Shedlovsky 66 - '4 U ©©O o LO 67 method* When the Shedlovsky values are replaced hy those obtained from the Owen method, the curves do not pass thru zero, but the general shape is the same. The value for ^Go(en)Tj^2 (S02|,)^ has such a large deviation that when It is plotted the axis requires conç^ressing to such an extent that all sensitivity is lost. For this reason, only the beginning of the sulfate curve is shown* An explanation of the differences between experimental conductivities and the theoretical Onsager equation has been discussed by numerous workers in terms of incorrplete disso­ ciation. For example, James, Jenkins, and Monk (57*50) have calculated dissociation constants for the dissociation of ions of; (a) the type (b) the type into ions of the type and X “^, into ions of the type M*? and (c) the type ZM**^ into ions of the of the values obtained for the dissociation constants, K, are given in Table XI, type and and Several Two of the values given are for salts that were also studied in the present w o r k , while the others are vex»y similar to the remaining salts. It has been common practice, especially for spectrophotoraetric work, to regard the perchlorate of polyvalent cations as exempt from the diffi­ culties which arise when other salts, more susceptible to ionpalr* formation, are used. However, it should be noted that spectrophot ornetrie evidence has been found, by Herdt and Bereatecki (75), for ions in Ce(ClO^)^ solutions. 68 TABLE XI DISSOCIATION CONSTAITTS OF COÎ-IPLSX IONS IN WATER I'lATED FROM CONDUCTANCE DATA AT 25 lon-pair KxlO^ Ref. Go(NH^)^C1‘»‘2 35.4 (38) Co(en)^Gl'*‘^ 18.6 (38) Co(pn)^Gl^^ 25.0 (38) Co (NH^)^S04^^ 27.7 (38) Co(en)^(SO^)^^ KGo(GN)^‘^ 3.55 59.0 (38) (37) Thus, although the K values given in Table XI are for the chlorides, the perchlorate and nitrate of the appropriate cation might be expected to yield values within the same order of magnitude. From the magnitude of K for these salts, it \rould appear that dissociation is far from complete in solutions of this type of high valence electrolyte, Hoivever, the evaluation of K can be done in one of several waps. One method, is the arbitrary selection of some conductance curve to represent a hypothetical completely dissociated electrolyte (4 5 ,7 6 ). All d.eviations of the electrolyte under consider­ ation from the hypothetical salt a.re then considered, as re­ sulting from incomplete dissociation. However, the difficulty of selecting an experimental curve as a stand.ard is greatly magnified in the case of high-charge salts. 69 Another approach Is that of Fuoss (7 7 ) and Shedlovsky (7 8 ), where K and are simultaneously evaluated by a suitable extrapolation to Infinite dilution. Both methods have the ooimnon dis sad vantage, however, that some knowledge of the activity coefficient of the electrolyte as a function of the concentration is required. The would be known for the salts under investigation, but the values of the activity coefficients for the ion-pairs would have to be estimated. The two largest approximations, however, are ; (a) the selec­ tion of a mobility for the ion-pair with the aid of assumptions of uncertain validity, e.g., that the ion-pair and the tri­ vale nt ion are similar in size, shape, and solvation, and (b) the selection of a standard curve to represent the com­ pletely dissociated electrolyte. It is interesting to note that H a m e d and Hudson (79) found these assunptions to be inadequate to escplain the mo­ bilities calculated from their diffusion studies of the ionpairs formed in zinc and magnesium sulfate solution. It might also be added that large differences in the values of the dissociation constants are often found when different methods are used to evaluate them. A case in point is the |oo(NH^ ) for which Bale, Davies, and Monk (80 ) found K = 11.3x10*"^ by spectronhotometric means, whereas Jenkins and Monic (Table XI.) obtained X % 2.77x10"^ from conductivity measurements. At the present time it is impossible to state definitely 70 whether the observed values approach the limiting slope from below due to the presence of an incompletely dissociated electrolyte or whether the theoretical calculation of the limiting slope is presently inadequate to handle the highcharge type salts studied. Part of the failure of the Onsager equation comes from the mathematical simplifications used in deriving the limiting law. Bjerrum's method of ion-association represents one way to reduce the magnitude of error in the limiting law. Although the O^fen method is based upon the assumption of complete dissociation, it is difficult to dis­ tinguish between the effects of ion-pairs, postulated in the estimation of K, and the higher electrostatic terms represented ty A N log N and BN. Until A and B are evaluated theoretically and/or the selection of a standard conductivity curve is made less arbitrary in the calculation of K, there seems to be no ideal method available to explain the deviations found with high-charge type salts. Empirical extensions of various theoretical equations can be found to represent the experi­ mental data, but are dangerous when applied as extrapolation procedures due to the weight given to the empirical parameters. The main problem seems to be to distinguish, at concen­ trations beyond the Onsager range, between effects of inter­ ionic forces, viscosity, and incomplete dissociation, bearing in mind that further disturbing influences may eventually demand consideration. VI. SUMMARY The activity coefficients and conductivities of aqueous solutions of four high-charge electrolytes have been determined. The electrolytes studied were Oo(en)^(NO^ )^, Co(pn)^(0lO2j^)^, K^Go(GN.)g, and [Co(en)^] 2 (S0^)^. The activity coefficient data does not show the salts to be " strong". The highest values observed for the activity coefficients were for the K^Go(GN)g, The values obtained for the 3-1 salts were very similar to those previously obtained for Go(en)TjGl^. Data such as this would indicate thé possi­ bility of estimating the activity coefficients of similar size and charge type complexes. The values obtained for the 3-2 sulfate were lower than other 3-2 salts. The conductivities do not follow Onsager’s limiting equation as expected. Shedlovdlcy Whether the upswing observed in the * plot is a result of ion-pair formation or in­ adequacy of the present theories to cope with unsymmetrical high-charge types is still unknovm. The values of the limiting conductivities obtained for the conç)lex cobaltic ions are 74.80, 65*11* and 99.07 ohm"*^ cm“^, for the GoCen)^"*"^, Go(pn)^’*'^, and Go(GN)^"^ ions, re­ spectively. These values correspond with those obtained for the limiting values by other workers. 3I3LI0C~RAPHY T. Speddlng, F. H., J. Am. Chen. Soc. 7 6 , 888 (1954). 2. Lewi8 , G. N., Proc. An. Acad. Sci., 259 (l907). 3. Bousfleld, W. R . , Trans. Far. Soc., I3 , 401 (19I8 ). 4. Sinclair, D. A., J. Phjs. Giiem., 5. Lovelace, B . , Frazer. J., Soc., 4 5 , 2930 (1923). and Sease, V., J. 6. Robinson, R. A,, and Sinclair, D. A., ibid., 7. Soatcliard, G . , Hamer, W, J . , and Wood, S. E . , ibid, 60, 3061 (1 9 3 8 ). 8. Gordon, R. A., ibid., 6^, 221 (1943). 9. Robinson, R. A., and Jones, R. S., ibid., H61, 495 (1933). An. Ghem. I83O (1939). 959 10. Robinson, R. A., ibid., 11. Randall, M , , and W h i t e , A., ibid., 4B, 2514 (1926). (1936). II65 (1935). 12. l'îason, G. M. ,and Ernest, G. L . , ibid., 13. Mason, G. M . ,ibid., 60, I638 (1938). 14. Robinson, R. A., ibid., 5 9 . 84 (1937). 15. Brubaker, Jr., G. H . , %8, 2036 (1936). 5762 (1956). t 16. Brubaker, Jr., G. H . , ibid., J2.» 4274 (1957). 17. Cavendish, H. ,"Scientific Papers of the Hon. Henry Gavendish," Vol. 1, Cambridge (l92l), p. 24,311. 18. Kohlrausch, F .W., W i e d . Ann., 19. Kohlrausch, F. 1 2 3 , 161 (1885). 315 (1897 )- W ., ibid., 6 , 145(1879), ibid.,,26, 73 20. Debye, P . ,and Hüokel, E . , Physik. Z . , 24, 185 (1923 ). 21. Debye, P., and Huckel, E . , ibid., §4, 305 (1923 ). 22. Kohlrausch, F. W , , and Ninnaldt, F . , Gott. Nach., 415, (1868), Ami. Physik., 280, 370 (1869), Kohlrausch, F. W . , Physik. 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C . , and Monk, C. B . , Trans. Far.^ Soc., 46, 1041 (1950 ). 38 . Jenkins, I. L . , and Monlc, C. 3., J. Chem. Soc., 68 (l95l) 39 . Oifen, B. B . , J. Am. Chem. Soc., 61, 1393 (1939). 2407 (1929). 18 06 (1930 ). G . , and Bollinger, G. M . , ibid., 21» 4ll (1931 ). I 78 O (1933). 74 40# Harnedi H. S, , and Owen, B, B « , *^lie Physical Chemistry of Electrolytic Solutions," , Reinhold Publishing Corp., New York, N. Y. (1958 ;. 41. Robinson, R. A., and Stokes, R. H., "Electrolytic Solutions," Buttenforth Scientific Publications, London, (1955). 42. Reference 40, 43 . Onsager, L. , Physik. Z. , 28, 277 (1927). 44# Falkenhagen, H . , Leist, M . , and Kelbg, G . , Ann. Phys., Lpz., 6 11, 51 11952). 45 . Reference 40, p. 179, Table (5-3-1). 46. Bjerrum, N. , Kgl. Danske Vidensk. Selskab., %, No. 9 (1926). 47 . Reference 40, p. I 7 I, Table (5 -2 -3 ). 48. Kraus, C. A. , J. Phys. Chem., 49. Onsager, L. , and Fuoss, R. M . , ibid., 36 , 2689 Tl932). 50 . Fuoss, R. M . , Physik Z., 25» 59 (1934). 51 * Fuoss. R. M . , (1957). 52 . Reference 40, p. 211 . 53» Bjerrum, N . , Z, Elecktrochem, 24, 259 (1907); Proc. Internat. Congr. Appl. Chem., Sect. x, London, (l909). 54 . Lewis, G. N . , and Randall, M . , "Thermodynamics and the Free Energy .of Chemical Substances," McGraw-Hill Book Co., New York, N.Y., (1923 ) p. 273. 55 . Scatchard,. G . , Chem. Rev., 8 , 321 (l93l). 56. p. 165, Table (5 - 2-1 ). 673 (1954). and Onsager, L . , J. Phys. Chen.,61^ 668 Scatchard. G . , and Prentiss, S. S , , J . Am. Chem. Soc., 2 6 , 1486 (1934 ). 57 . Reference 40, p . 176, Table (5-2-6). , 58 . Smith, H. R . , J. Am. Chem. Soc., 61, 500 (1939). 59. Bigolow, J. H . , "Inorganic Syntheses," McGraw-Hill Book C o . , Inc., New York, N . Y . , 2, 225 (1946). 75 60. Rollinson, G. L . , and Bailôr, J. C . , ibid., 2, 197 (1946). 61. Work, J. B., ibid., 2, 221 (1946). 62 . ^1926) Groliler, K , , Zeit. anorg. Chem., 155. 91 63 . Brubaker, Jr., G, H., Jolinson, C. 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Ghem. Soc., 72, 3781, 5800 (1951 ). 80. Baie, W. D. , Davies. G. W. , and Monlc, G. 3., Trans. Far. Soc . , 22, 816 (1956).