K O G C>.~ BATES
11:3ci
Vol. 64
l c ( J N I R r B T t l I O h P R O V 1 N1> I k P A K T V I ? T OF ( h i UI5l'KT, k'ALh L:NIVERSITI']
The Thermodynamics of Bi-univalent Electrolytes. VII. The Activity Coefficients of Lead Bromide from 5 to 40' RY ROGERG. BATES' Among the bivalent metal halides are found salts differing widely in behavior. In earlier papers of this series thermodynamic quantities were reported2J14 for aqueous solutions of zinc iodide, a typical strong electrolyte, and of cadmium bromide and cadmium iodide, salts which display properties characteristic of weak electrolytes. It was shown that the stoichiometrical activity coefficients of zinc iodide could be represented by the HUckeP equation with an ion-size parameter, a;, of 6.0 A. With cadmium bromide, however, both the Hiickel equation and the extended terms equation for unsymmetrical electrolytes of La Mer, Gronwall and Greiff" failed to represent the data above 0.001 -11. The formation of stable ion pairs, CdBrT, the dissociation of which could be expressed by an equilibrium constant. was postulated. With the use of the Debye-Hiickel limiting law and the actual ion concentrations, the activity coeficient could be reproduced satisfactorily up to a concentration limit of about 0.01 M. With cadmium iodide this device was unsuccessful, and no function yielding an unambiguous extrapolation was found. Lead bromide was chosen as an example of an electrolyte intermediate in behavior between the zinc and cadmium halides. Electromotive force measurements of the cell Pb-Hg
i
PbBr.:;ni) I AgBr-Ag
(1)
were made a t 5' intervals from 5 to -10' with molalities of lead bromide varying from 0.0015 to 0.018. The standard potentials of the cell and activity coefficients of the solute have been determined. The extended terms equation with a constant ai parameter of 1.55 A. and an added term linear in molality was found to give an adequate representation of the activity cneficient from 5 to 40' in this range of solute concentration. Experimental Procedure Lead bromide was prepared metathetically by the dropwise addition of a 13.5 .V solution of rvagent grade polas-..___I_
(1) Sterling Fellow, Y a l e CTniversity, 1 9 : 3 i - - l ~ ~ ~ p 9 r, e w i t a d ilress: National Bureau o[ Standards, Xyashington, 1J. C r1!198> ( 2 ) paper 111, ZnIn, 'THIS J O C R N A L , 60, "'38? ( 3 ) Paper I V , CdBrz. i b i d . , 61, 305 (1939). ( 4 ) Paper VI, Cdlp, ibid., 63, 399 (194l:I. ( 5 ) Hiirkel. Ph?-iir. Z..26 (6) La XIer. ( ~ ~ O I I ~:ind V ~ ~ : ~ hi..,. Chvm , 35, 22-b: lU.{ll
siuni bromide to a vigorously stirred 0.2 iM solution of lead nitrate, previously acidified with nitric acid and heated to 00'. The salt was recrystallized from hot water to which a few drops of hydrobromic acid solution had been added to inhibit hydrolysis. The cell solutions were made by the weight dilution of three stock solutions with conductivity water. The stock solutions were prepared by shaking lead bromide in two liters of conductivity water containing a little hydrobromic acid. In recognition of thc possibility of an acidity effect on the lead amalgam, an excess of acid was carefully avoided. The recrystallized salt contained some basic lead bromide; the amount of acid used in preparing the three stock solutions was sufficient to yield bromide/lead atomic ratios of 1.97, 1.99 and 3.04. Each stock solution was analyzed by gravimetric rnethods for both lead and bromide. The lead was converted to sulfate and the bromide to silver bromide. -4correction for the solubility of lead sulfate was applied. It is beiieved that the molality of lead in each stock solution was established with an accuracy of 0.1% and that the bromide molality was accurate to 0.05%. The lead amalgam used in all of the cells contained 10 to 12% by weight of lead. Phase investigations of the lead--mercury system' indicated the advisability of employing an amalgam inore rich in lead than the 5y0 amalgam often used heretofore. The preparation of the electrotlcs, the method of filling the cells in the absence of air, arid other experimental procedures were as described iii detail in other communications.*-' 'Three cells were made a t each molality. During the period of measurement, usually about twenty-four hours, no irreversible changes were noticed. Reproducibility of the cells a t molalities in excess of 0.005 was of the order of O.CI8 mv. Fklow that molality, triplicate cells usually agrwd rvithiti 0.15 tnv.
Standard Potentials The observed electromotive forces for cell (1) a t the eight temperatures are given in Table I. The constants a and b of the equation E, =
0'26
+
l7(t
- 25)
+ b(t - 25)'
(2)
are also included in the ta.ble, and AE is the mean deviation of the observed electromotive forces from the calculated values. The molality, m*, was calculated from the compositions of the cell solutions by the expression t i i * = ( m p b + + mip14)"' (3,) 'The relation between the molality, the stoichiometrical activity coefficient of lead bromide, 7, 2nd E , the electromotive force of cell (1) is given . ( 7 ) I'uschin, 2.n n o ~ p C'hrrn ( . ' h e w . 60. X W f I W 7 '
,
36,21.1 (1903); Taneckr. Z . p h r s i k
ACTIVITYCOEFFICIENTS OF LEADBROMIDE
May, 1942
ELECTROMOTIVE FORCES OF
TABLEI (1).
CELL
CONSTANTS O F
1137
EQUATION (2)
1
5 10 15 20 25 30 35 40
0.4187 .4222 .4256 .4297 .4334 ,4365 ,4400 .4431
0.39167 .39541 .39892 ,40221 ,40526 ,40824 ,41119 .41390
0.38112 .38456 .38787 ,39093 ,39392 .39662 ,39925 .40198
0.37138 .37466 ,37748 ,38069 ,38352 .38620 .38858 .39109
0.36651 .36960 .37264 .37550 ,37838 ,38069 ,38312 ,38546
0.36433 .36738 .37040 .37325 ,37578 ,37842 ,38077 ,38305
0.35723 ,36025 .36305 .36551 .36817 ,37059 .37287 ,37510
0.34841 .35117 ,35370 ,35602 .35841 ,36076 .36289 ,36493
m* x 103 a X 106
1.536
3.626 61.2 3.97 0.08
5.157 56.6 - 3.53 0.03
7.196 54.6 - 3.20 0.14
8.799 52.2 - 3.13 0.11
9.551 51.1 - 2.90 0.08
12.736 50.2 - 2.70 0.08
18.200 46.4 - 2.37 0.06
-
b X 108 AE mv.
a t each temperature by the equation (E/3k)
+ log m* + (log 4)/3 = (Eo/%) - log y
(4)
where E o is the standard potential of the cell and k is 2.3026RT/2F. The standard potential was derived a t each temperature from the measured electromotive forces by extrapolation to infinite dilution with the aid of the extended terms equation of La Mer, Gronwall and Greiff6 for electrolytes of the unsymmetrical valence type. Substitution of the extended equation for log y in eq. (4) yields an expression for E o in terms of ai, the ion-size parameter, natural constants and complex functions of the molality, the numerical values of which are tabulated in the papers of Gronwall, La Mer.and Sandveds and of La Mer, Gronwall and GreiiT:
+ +
+
(EO/3k) = ( E / 3 k ) log m* (log 4)/3 - - I x / ( a i nix) B ( I O ~ # ~ / U ;c(1034~)/~,! ~ ( 1 0 3 + ~ ) / (~5;) where x = 10-1%zai(2.4~Nm*p)~/~ = 0.21316ai(m*p)1/2; A = p/2.3026; B = 2(10-2)p2/2.3026; C = 6(10-3)fi3/2.3026; D = 3C; p = 108e2/(DkT);
-
CONSTANTS OF A
5 10 15 20 25 30 35 40
3.02654 3.04299 3.06002 3.07782 3.09646 3.11587 3.13598 3.15660
TABLE I1 EXTENDED TERMS EQUATION E
c
D
0.42192 ,42643 .43122 ,43625 .44155 ,44710 ,45289 .45887
0.8822 .8964 .9115 ,9275 ,9445 ,9624 ,9811 1.0006
2.6466 2.6892 2.7345 2.7825 2.8335 2.8872 2.9433 3.0018
each of the lead bromide solutions for several ion sizes somewhat less than 1.75 A,, the value which gives the closest representation of the activity coefficient of lead chloride.1° Figure 1 shows the change of the "apparent standard potential" with change of molality, the intercept a t zero molality giving the true standard potential. It is evident 1.8 if.
0.197
+
and 41 is ['lzxdx) - Y2(x)1, 42 is [l/~X,*(x)2Y,*(x)]and 43 is [1/zX,(x)-2Y3(x)] in the notation of the extended theory. Values of p a t 5' intervals from 5 to 40' were' recalculated from recent values of E , the electronic charge; k, the Boltzmann constant; and D, the dielectric constant of water.$ The constants A , B, C and D are given in Table 11. The best value of ai a t 25' was ascertained by computing E o from the electromotive forces of
THE
1.55 if. -
"
"
L
I
I
0.01 0.02 0.03 0.04 0.05 3 m. Fig. 1.-The apparent standard potential as a function of molality for three different values of al.
that the extended terms equation with a value of 1.55 A. for ai will reproduce Y p b B r l closely over the range of solute concentration studied. This value of ai was employed for the computations a t the other seven temperatures as well. It is known that the deviations in Eo caused by differences in postulated a, are linear in molality. Thus the ex-
(8) Gronwall, La Mer and Sandved, Physik. Z.,29, 358 (1928). (10) S Mary Consilia Hannan, Dissertation, T h e Catholic (9) D was taken from t h e paper of Wyman and Ingalls, THIS University of America, 1936 The data of Carmody [TEEJOURNAL, 60, 1182 (1938). Values of 6 , k and N , t h e Avogadro 61, 2905 (1929)l have also been fitted t o t h e extended equation at number, were from Wensel, J Research Not. Bur. Standards, 22, 376 25', with the use of an ion-size parameter value of 1.75 A. (ref. 6 ) . (1939) JOURNAL,
KOGERG. BATES
llYX
trapolation plots a t the other temperatures were substantially straight, although their slopes were not zero. The true value of the standard potential was obtained in each instance from the equation =q.PPPT.nt)
=
+ BmC
Vol. 64
The activity coefficients listed in Table I V and those calculated from eq. 9 are thought to be correct to about k0.003, corresponding to an error in E-Eo of about 0.3 mv. a t a molality of 0.01.
(6)
The Lead Amalgam Electrode
The numerical values of the constants E o and P were derived a t each temperature by the method of least squares and are given in Table 111. The
Subtraction of 0.0713, the standard potential of the silver-silver bromide electrode at 25',l1 from the standard potential of cell (1) gives 0.1229 for the potential of the 11% lead amalgam TABLEI11 electrode, a value considerably higher than 0.121 1 CONSTANISOF E Q U A ~ I O6.N STANDARD POTENTIALS Eo(eq. 7) B EO 1 found for the 5% lead amalgam electrode by the 6 0,051 0.19542 0. 19538 extrapolation of electromotive force measurements 19521 10 .055 .19520 of lead chloride solutions.10 15 .ox3 .19488 19393 The results of a recalculation of the potential 20 ,008 .19180 19453 of the electrode containing 5% of lead from litera2 ,004 . 19423 . 19408 1933 1 30 002 ,19345 ture data on the solubilities of the lead halides, 35 -0.019 19267 19267 together with the potentials of the lead halide40 -0 032 .19178 . 191%3 lead amalgam (5%) electrode, by means of the E o values may be calculated from the equation relation ti
E! = 0.19403 - 0 00113 (t - 2 5 ) - 0.00000227 i t - 2 5 1 ~ where (7
with a mean error at the eight temperatures of 0.08 mv.
Activity Coefficients Large-scale graphs of EE., a and b against m" were constructed and values a t round molalities were obtained by interpolation. These constants are given in Table IV, along with the activity coefficient of lead bromide at 25' calculated from eq. 4.
&,-E&
= fiibX2
+ k log
i%p
(101
K s p is the activity solubility product constant, are given in Table V. The activity coefficients were calculated from the extended terms equation. An estimated ai value of 1.4 A, for lead iodide was employed. It is evident that measurements of the electromotive forces of the saturated lead halide electrodes likewise indicate a lower potential for the 5% amalgam electrode than was found for the electrode formed of 11% amalgam.
TABLE V TABLE 11' CALCULATION OF THE POTENTIAL OF THE 5% LEADAMALAT 25' FROM E. M. F. AND SOLUBILITY THE ACTIVITY COEFFICIENT OF LEADBROMIDE. CON- GAM ELECTRODE DATA STANTS OF EQUATION 9 nt
*
E,,
0.002 0.42467 .004 .40215 ,005 ,39483 .OO7 ,38430 .01 .37458 .015 .36365 ,018 ,35865
6I
X 105
59.9 57.9 64.8 51.5 47.9 46 2
b X 106
-3.84 -3.58 -3.21 -2.86 -2.51 -2.38
-log
Y~~
0.148i .1631
.l905 ,2368 .2887 ,3116
7%'
0.794 ,710 ,687 .645 ,581
,515 ,488
For the other temperatures between 5 and 40' -log Y, is expressed in terms of -log Y26, the change of 3k with temperature (3k)t = 0.08871 4- 0.000299(t - 25) (81 and the constants of eqs. 2 and 7 by the relation -log ut = -log 72s f
0.08871
(t - 25) + 0.000299(t - 25) [0.000767 - 0.00337& + a + ( b + 0.00000227)(t - 2511 (9)
X
C1 Rr
mPbX2
(satd. s o h )
ai
0 . 0393712v13 1.75 .02666'* I .55 .0016512 1.4
-log Knp
4.801 5.241 I 8.020 ,001ti4117 8.026 Ag-AgCI, C1-; E o 0.2224 Hg-HgtCls, CI-; E o = ,2679 Ag-AgBr, Br-; E@= .Oil3
$bX2
'%b-Hg
0 .262014*150.1200 .275314 ,1203 .358016 .1208 ,1206
Summary Electromotive force measurements of the cell Pb-Hg (11%) PbBrz (m) AgBr-Ag have
I
1
(11) Owen and Foering, THIS JOURNAL, 68, I575 (1936). (12) Burrage, J . Chem. Soc., 129, 1703 (1426). (13) Herz a n d Hellebrant, 2.a?rorg. allgem. Chem., 190,188 (1923). (14) Jahn-Held a n d Jellinek, Z . Elektrochem., 4P, 401 (1936). (15) Priepke and Vosburgh, THIS JOURNAL, 62, 4831 (1930). (16) Bates and Voshurgh, ibid.. 59, 1188 (1937). (17) Lnnford a n d Kiehl, ibid., 63, G67 (1941).
May, 1942
STRUCTURE OF POTASSIUM OXYHEXAFLUOCOLUMBATE
been made a t intervals of 5' over the temperature range, 5 to 40'. The molality of lead bromide was varied from 0.0015 to 0.018. The standard potentials of the cell were evaluated
[CONTRIBUTION FROM THE
1139
with the use of the La Mer, Gronwall and Greiff extension of the Debye-Hiickel equation. Activity coefficients were calculated. WASHINGTON,
BAKERLABORATORY OF
D.
c .
RECEIVED FEBRUARY 6, 1942
CHEMISTRY, CORNELL UNIVERSITY ]
Structures of Complex Fluorides.' Potassium Oxyhexafluocolumbate,K,CbOF, BY M. B. WILLIAMSAND J. L. HOARD Hampson and Pauling2 have reported X-ray data which indicate that Z r F F ions with the point group symmetry of C3,-3m exist within cubic crystals of potassium and ammonium heptafluozirconates. Cubic crystals of potassium oxyfluocolumbate, KCbOF6, might be expected to have a structure like that of potassium heptafluozirconate and to contain CbOF6' ions of symmetry CJV. The fact that two compounds of similar formulas both crystallize in the cubic system is, however, by no means conclusive evidence that they belong to the same structural type (compare, for example, potassium and cesium chlorides). It has seemed of particular interest t o investigate the structure of K3CbOF6 in detail since monoclinic crystals of potassium heptafluocolumbate, Kd2bF.1, have been shownlb to contain discrete CbF,= ions with the point-group symmetry of Czv-mm, entirely different from that found for ZrF7=. There are, moreover, certain features of the structure proposed by Hampson and Pauling2 for the heptafluozirconates of potassium and ammonium which make it desirable to iivestigate other compounds that are presumably of a similar type. We find actually that crystals of KsCbOFs and K3ZrFr give rise to closely similar X-ray diffraction data. Crystalline potassium oxyfluocolumbate, K3CbOF6, has been prepared in the form of small shining cubes by several investigator^.^ Marig n a reported ~ ~ ~ that his crystals were doubly refracting; Balke and Smith3bobserved only a faint double refraction along the edges of their specimens, and Baker3cconcluded that his preparation (1) For earlier papers in this series see (a), THISJOURNAL, 67, 1985 (1935); (b), ibid., 61, 1252 (1939); (c), 61, 2849 (1939); (d), 62, 3126 (1940);(e), 68, 11 (1941); (f), 64, 633 (1942). (2) G.C. Hampson and L. Pauling, ibid., 60, 2702 (1938). (3) See (a) Ch. de Marignac, Bibl. unio., Arch. sc. phys. nul. Gcnloc, 98, 259 (1865); (b) C. W. Balke and E. F. Smith, THIS JOURNAL, SO, 1637 (1908); (c) H. Raker, J . Chem. Soc., 86, 760 ( 1879).
was perfectly inactive in polarized light. The specimens of KSCbOFs used in our work were small brilliant cubes which seemed to be perfectly isotropic under the polarizing microscope and entirely stable in air. They resulted from the isothermal evaporation of an aqueous solution prepared from freshly recrystallized K2CbOFb-HZO and K F taken in the mole ratio one to four. It may be noted by way of comparison that crystals of Ks2rF.r commonly assume an octahedral habit. Accurately oriented Laue and oscillation photographs from KaCbOF6 show no deviation from the point-group symmetry of O h - m 3 m ; the probable space-group of the crystal is thus limited to o h , 0, or Td. The lattice constant a is.8.87 A. as given by back reflection data, and the corresponding unit cell contains four stoichiometric molecules. The absence of reflections from planes with mixed indices points to a face-centered lattice. Excepting that a = 8.95 A.(instead of 8.87 A,) all statements of the preceding paragraph apply equally well to K3ZrF7.2 Indeed a further detailed comparison between the observed intensities of X-ray powder lines for K3CbOF6 (Table I) and the data reported2 for K3ZrF7makes it quite certain that the two substances crystallize with similar structures. Except for a few lines a t large angles of scattering, the description of the intensity patterns is nearly identical for the two compounds. Such minor differences as appear are readily understood in terms of the small difference in lattice constant, the substitution of columbium for zirconium and of oxygen for fluorine, and possible variations in the effects of thermal vibrations on the scattering of X-rays by the crystals. To establish the exact character of the structural type in which K&bOFC and KsZrF, (also
