T H E
J O U R N A L
O F
PHYSICAL CHEMISTRY Registered in U . S. Patent Ofice
@ Copyright, 1964, by the Am,erican Chemical Society
VOLUME 68, NUMBER 11 KOVEMBER 16, 1964
Thermodynamic Properties of the Vapor Phase of Sodium Tetrachloroferrate(111)
by R. Ronald Richards and N. W. Gregory Department of Chemistry, University of Washington, Seattle, Washington 98106
(Received J u l y 16, 1964)
Thermodynamic properties of NaFeC14(g) relative to values for ferric chloride vapor and solid sodium chloride have been determined by study of the equilibrium between these substances, using a transpiration method. Bond energies and structural characteristics of the molecules are considered.
Studies of the system sodium chloride-ferric chloride have been published b,y Johnstone, et aZ.,l Morozov and Toptygin,2 and Cook and D ~ n n .It~ was observed by the earlier workers that the vapor pressure of ferric chloride above its liquid, particularly in the vicinity of 40-50 mole % sodium chloride, falls rapidly as sodium chloride is added; the decrease is much greater than expected from simple mixing effects. Cook and Dunri demonstrated the existence of sodium tetrachloroferrate as a solid phase by analysis of cooling curves and X-ray powder patterns. Their phase study indicates a congruent melting point a t 163'. The vapor pressure of NaFeCL above the melt has been reported by Cook and Dunn3 and by Korshunov, et aL4 Whereas, together with heat of solution, heal, of fusion, and heat capacity data also provided by Cook and Dunn, one can use the liquid phase vaporization data to calcula,te thermodynamic properties of the vapor, a considerable uncertainty arises from the combination of uncertainties in the numerous thermo-.
chemical equations required and lack of knowledge of activities in the liquid solution with ferric chloride. Morozov and Toptygin,2in a phase study, found that virtually pure sodium chloride exists in equilibrium with the melt on the sodium chloride-rich side of the phase diagram. In view of this we have undertaken an experimental study of the reaction NaCl(s)
+ FeC13(g) = NaFeC14(g)
(1) as a direct means of determining the thermodynamic properties of the addition compound. With the activity of sodium chloride at unity and its thermo(1) H. F. Johnstone and R. W. Darbyshire, I n d . Eng. Chem., 34, 280 (1942);. H. F. Johnstone, H. C. Weingartner, +nd W. E. Winsche, J . Am. Chem. S O L . 64, 241 (1942). (2) I. S. Morozov and D. Y . Toptygin, Z h . Neorgan. Khim., 2 , 2129 (1957). (3) C. M. Cook and W. E. Dunn, J . Phys. Chem., 6 5 , 1506 (1961). (4) B. G. Korshunov, I. S. Morozov, V. I. Ionov, and M. A. Zorina, Izv. Vysshikh Uchebn. Zavedenii, Tsvetn. Met., 3, 5, 67 (1960).
3089
R. RONALD RICHARDS AND Tu'. W. GREGORY
3090
dynamic properties well known, the properties of NaFeC1, relative to those of FeC13can be determined.
Experimental A transpiration method with argon as the principal carrier gas was used. The apparatus, Fig. 1, and procedure were similar to that described previously.6
v u Figure 1. Transpiration apparatus.
Argon (Matheson 99.99%) condensed in tuba A, which was then immersed in boiling liquid oxygen, served as a source of gas a t a pressure of ca. 100 cm. The flow rate was controlled with a capillary restriction F beyond which argon was condensed in tube G, or J, cooled with liquid nitrogen. The argon first passed through tube B containing CuClz heated to the vicinity of 410-440' to introduce (by decomposition to CuC1) a partial pressure of 0.5 to 3.6 mm. of chlorine to prevent subsequent decomposition of ferric chloride. This gas mixture then passed over a sample of FeC13(s) at C, held at various temperatures around 175' to introduce the desired partial pressure of ferric chloride, adjacent to the main reactor D containing NaC1. The temperature of the sodium chloride in D was held at various values ranging from 350 to 530' for the equilibrium study. The equilibrium mixture of gases left the reaction chamber via the small removable exit tube E in the center; the NaFeC14condensed near the junction of the furnace surrounding D and the separate furnace surrounding C; the ferric chloride condensed a t the outer end of furnace C ; the argon and chlorine continued on through the capillary orifice and into the liquid nitrogen-cooled trap G. Temperatures were held to within &1.5' of the desired value during the 1 to The Journal of Physical Chemistry
16-hr. runs. During the period the samples were brought to reaction temperatures, argon flow was reversed by means of stopcocks H and I so as to enter the reaction bone through the exit tube; the argon during this warm-up period was collected in the alternate trap J. When steady flow conditions, pressures, and temperatures were established, the stopcocks were quickly reversed to begin the run. Eastman practical anhydrous FeC13, or, in many experiments, material prepared by reaction of analytical grade iron wire with chlorine, was used. Samples were sublimed into place under vacuum from a side arm which was subsequently sealed off, Analytical grade sodium chloride, degassed before a run, was used. In general a given set of starting materials served for four or five runs; results from many independent samples were compared. Traces of ferric oxide were observed in the system after a run. A number of experiments were conducted in which the argon was initially bubbled through liquid potassium to ensure removal of water. Results, when this precaution was taken, did not differ from those when argon was taken directly from a fresh sample condensed from the commercial cylinder; hence most of the experiments were conducted without additional purification precautions. The reactor was always thoroughly evacuated and baked out before a run. No dependence of results on the presence of oxide could be detected. It was found that results were more consistent, and independent of flow rate, varying from 3 to 30 ml. min.-' (calculated a t 0' and 1 atm. (STP)), when ferric chloride pressures were high enough to cause some condensation of yellow liquid complex in the forepart of the reaction vessel D ; the sodium chloride a t the end of the reactor remained white with no trace of complex visible. Most of the experiments were oonducted with some complex mixed with the sodium chloride. I n some cases, to approach equilibrium in the opposite direction, argon and chlorine, without added ferric chloride, were allowed to flow over a mixture of previously formed complex and solid sodium chloride. From the exit stream, the ferric chloride condensed as platelets; NaFeCll condensed as liquid droplets which solidified as the furnaces were removed at the end of a run. I n some cases the two deposits were separated and analyzed separately; in others they were dissolved in the same solution, and total iron and total sodium were determined. At the conclusion of a run, the vessel was left filled with argon, the (5)
L.E.Wilson and N. W. Gregory, J. Phys.
Chem., 62,433 (1958).
THERMODYNAMIC PROPERTIES
OF
SODIGN TETRACHLOEOFERRA4TE(III)
inner collector tube E removed quickly, and the apparatus resealed. The condensates were washed out of the exit tube with water. An aliquot was acidified with a few drops of concentrated hydrochloric acid and the ferric ion reduced to ferrous with hydroxylamine hydrochloride. The acid seemed to ensure complete reduction. The ferrous ion was then complexed with 1,10phenanthroline and determined colorimetrically by the standard procedure.6 The sodium content in another aliquot was determined using a Becknian DU flame photometer with photomultiplier attachment,. Ferric chloride in the concentration present does not interfere.7 The aqueous solutions varied in sodium content from 2.5 to 28 p.p.in.; care was taken to avoid contamination. Chlorine pressures were calculated from the number of moles of chlorine transported, determined by solution of the condensed sample in aqueous potassium iodide and titration of the liberated iodine by an amperometric dead-st,op method.* Amounts of argon were determined by expansion of the collected sample into a calibrated volume K, Fig. 1, and measurement of the gas pressure. The equations of Merten predict that error caused by diffusion will be negligible in our a p p a r a t u ~ . ~This was verified experimentally in a zero flow rate “run” a t 530’ under normal reaction conditions; the amount of iron which diffused into the collector tube was found to be only 0.5% of that collected in a regular low flow rate experiment.
Results and Discussion Results are shown in Table I, with values of the equilibrium constant calculated on the basis that all the sodium was transported as sodium tetrachloroferrate. Sodium chloride is n o t significantly volatile a t these temperatures.1° The number of moles of sodium was subtracted from the total number of moles of iron to obtain the total number of moles of iron transported as ferric chloride monomer and dimer. The partial pressure of ferrous chloride can be shown to be negligible.5p11 The partial pressures of the various gases were calculated from the number of moles determined analytically from the simple expression P , = X,Pt, where the total pressure, Pt, and total number of moles for the evaluation of the mole fraction X , were taken as those of argon, since n-ir >> nFeC13 nFetcie ~ N ~ F ~ .c The ~ ~ breakdown of the number of moles of iron into pa,rtial pressures of monomer and dimer, respectively, was carried out using the equation, == 6907T-1 9.391, based on log data of Kangro and Bernstorff .5,12
+
+..
+
+
3091
It may be seen (Table I) that in five of the seven experiments in which the NaFeCL and FeC13 deposits were analyzed separately, the atomic ratio of Na to Fe in the former corresponds very closely to 1 : l ; in the other two, the experimental result indicates the ratio is slightly larger. We have taken this as evidence that the principal sodium-containing species in the vapor phase is NaFeCL. Polymers in significant quantities are not believed to be present because of the relationship of the amount of complex and of FeCl,(g). The equilibrium constant based on (NaFeCW2, for example, requires the partial pressure of this species to be proportional to the square of the pressure of FeC13. Data in Table I show this dimeric species cannot be the dominant one. A similar argument may be given for higher polymers. Species such as NazFeC15and Na3FeClGcannot be ruled out on similar grounds; however, the composition of the condensed complex suggests that, if such species are present, their partial pressures must be very small. From the slope of a In K us. T-l plot, the enthalpy change for reaction 1 was found to be 3.7 f 1 kcal.; the corresponding entropy change is 6.5 f 1.5 cal. deg.-1, taken as representative of a temperature of 450’. The enthalpy change for (l), estimated by combination of thermochemical equations based on earlier data, indicated in the introduction, is 2.7 f 6 kcal., in good general agreement. Kelley has pointed out that a rather large uncertainty exists in the published thermodynamic properties of FeC13(g).13 Using his recommended values and data from ref. 12, 101 and 28.7 cal. deg.-l mole-’ have been taken as So of FeCl,(g) and NaCl(s), respectively, at 723OK. These, together with our experimental result, give 136 cal. deg.-l niole-’ for the standard entropy of NaFeC14(g) a t 723OK. Without information on the vibrational frequencies, meaningful values of the entropy cannot be calculated on a statistical basis because the vibrational contribution is so large. We (6) H. H. Willard, L. L. Meritt, and J. A. Dean, “Instrumental Methods of Analysis,” 3rd Ed., D. Van Nostrand Co., New York, N. Y., 1958, p. 58. (7) J. A. Dean, “Flame Photometry,” McGraw-Hill Book Co., New York, N. Y., 1960, pp. 110-122, 164, 165. (8) G. Wernimont and F. J. Hopkinson, Ind. Eng. Chem., A n a l . Ed.,
12, 308 (1940). (9) U. Merten, J. Phys. Chem., 63, 443 (1959). (10) E. F. Frock and W. H. Rodebush, J . A m . Chem. SOC.,48, 2522 (1926). (11) R. J. Sime and N. W. Gregory, J. Phys. Chem., 64, 86 (1960). (12) W. Kangro and H. Bernstorff, 2. anorg. allgem. Chem., 263, 316 (1950). (13) K. K. Kelley, “Contributions to the Data on Theoretical Metallurgy,” U. S. Bureau of Mines Bulletin 584 (1960) and 593 (1961), U. 9. Government Printing Office, Washington, D. C.
Volume 68, Number 11
November; 196.4
R. RONALD RICHARDS AND N. W. GREGORY
3092
Table I : Results of Equilibrium Study of Reaction 1
Flow rate,
Argon
Temp,,
cm.8 m h - 1
pressure,
OC.
at STP
om.
Ar
10.1 10.0 10.0 15.8 17.7 21,3 30.1 10.3 16.8 18.0 3.36 10.0 10.9 15.7 17.0 26.0 9.69 10.2 10.6 16.6 22.9
103.6 103.0 98.9 99.8 96.4 93.G 95.2 100.5 97.2 95.1 102.0 99.3 102.5 95.2 97.1 85.4 100.4 100.5 103.8 96.8 91.8
364 436 241 254 284 399 362 111 135 104 71.9 121 127 105 137 75.5 25.9 136 157 111 61.2
3508 350 400 400 400 400 400 450 450 450 500 500 500 500 500 500 530" 530 530 530 530a a
mmoles trmsported N a as Fe as Fe a8 NaFeClr, FeCla, NaFeCla, x 10' x 10' x 102
2.96 3.87 7.70 13.1 11.5 9.66 19.4 19.5 25.0 17.1 ,4.35 7.56 9.90 32.6 14.3 9.21 30.6 6.61 3.95 3.95 87.0
Total Fe,
x 10'
,..
...
6.76
4.98
3.85
8 83
...
... ...
... 9.71 8.06 ...
... 15.0 10.4
11.5 8.78 ... ... 25.1 17.0
...
...
4.2
6.76
...
...
21.4 ...
32.G
...
... ...
... ... ...
,..
... ...
...
...
...
...
13.6 24.0 21.2 17.84 36.6 31.7 40.1 27 4 6.19 10.96 9.90 54.0 21.3 13.5 44.5 9 14 5.38 5.38 126
Calcd. pressures, ,---mm. X loa-FeCla NaFeCL
6.54 6.95 18.9 29.7 24.2 13.9 30.9 88.4 90.4 76.8 25.6 27.4 23.7 144 48.0 47.0 47 1 18.6 16.7 12.5 503
Equilibrium constant K =
'(NaFeCla) P(FeC1a)
8.43 8.89 31.6 51.5 39.0 22.6 51.0 177 180 156 61.8 62.0 55.8 331 101 104 1190 48.9 41.6 34.4 1300
1.29" 1.28 1.67 1.73 1.62 1.63 1.65 2.00 1.99 2.04 2.41 2.26 2.36 2.30 2.11 2.21 2 , 52a 2.63 2.49 2.75 2 . 5ga
Points determined without prior introduction of ferric chloride into carrier gas.
have made some estimates, however, which suggest that our value is reasonable, The combined translational and rotational contribution is expected to be of the order of 77 cal. deg.-l mole-l. The rotational contribution of ea. 30 was based on a model in which the four chlorine atoms are arranged tetrahedrally about the iron atom (at the same distance found in the solid in a crystal structure determination to be reported from this laboratory) with the sodium atom near the center of o9e of the faces of the tetrahedron at a distance of 2.5 A. from Bach of the neighboring chlorine atoms. If one assumes an electronic contribution of about 5 , associated with the unpaired electrons of iron(III), this leaves 54 cal. deg.-' mole-1 to be contributed by the vibrational partition functions, an average of 4.5 for each degree of freedom. This average corresponds to a frequency of the order of 140 cm.-l. Woodward and Taylor14 have observed the Raman spectra of an ethereal extract of an aqueous solution of FeCla.HCl ; they have assigned frequencies for the solvated tetrachloroferrate ion of 106(2), 133(3), 330, and 385(3) cm.-'. If these values are used to estimate the contribution of nine of the degrees of freedom for the vapor molecule NaFeCI4,the remaining contribution to the entropy from the additional three degrees of freedom (associated with the presence of the The Journal of Physical Chemistry
sodium atom) would have to be ca. 20, which would require three frequencies of the order of 50 cm.-'. One would certainly expect some change in the Woodward-Taylor frequencies for NaFeC14; however, even frequencies of the order of 50 cm.-' appear not unreasonable when compared with values for bending frequencies in some of the transition metal halides. l5 Using an estimate mean value of AC, for (1) of - 1 cal. deg.-l, the enthalpy change at 298.2OK. is found to be 4.1 kcal. This, together with data from ref. 5 and NBS Circular 500,l6 leads to a value of -392 kcal. for A H ' z ~for ~ reaction 2. Ya(g)
+ 4Cl(g) + Fe(g)
=
NaFeCldg)
(2)
If the sodium-chlorine bond energy in the complex is assumed to be roughly the same as that in sodium chloride, an average value of 73.4 kcal. is obtained for the Fe-C1 bonds. The value of the latter in FeCls(g) is 81 kcal. and in FezC16(g)an average of 65 kcal. It is (14) J. A. Woodward and
M .J. Taylor, .I. Chem. SOC.,4473 (1960). (15) L. Brewer, G. R. Somayajulu, and E. Brackett, Chem. Rev., 6 3 , 111 (1963). (16) D. D. Wagman, W. H . Evans, S. Levine, and I. Jaffe, "Selected Values of Chemical Thermodynamic Properties," National Bureau of Standards Circular 500, U. S. Government Printing Office, Washington, D. C., 1952.
LOGARITHMIC DISTRIBUTION FUNCTIONS FOR COLLOIDAL PARTICLES
interesting to note that if a structure in which the sodium is bridged to the iron in FeC14- through interaction with two chlorines is considered, the average energy for the six bonds in the same as the average of the eight Fe-Cl bonds in Fe2Clfi. The standard heat of formation of NaFeC14(g) at 298°K.) calculated using -60 f 3 kcal. as AN’
3093
for FeC13(g)5t12and -98.2 kcal. for NaC1,’G is - 154 4 kcal. mole-’.
f
Acknowledgment. This work was supported in part by grants from the National Science Foundation and from the U. S. Army Research Office (Durham), which we acknowledge with thanks.
Logarithmic Distribution Functions for Colloidal Particles’&
by W. F. Espenscheid,IbM. Kerker, and E. MatijeviC Chemistry Department, Clarkson College of Technology, Potsdam, N e w York
(Received J u l y I S , 1964)
The distribution function used in earlier light-scattering studies had been erroneously termed a logarithmic normal distribution when, in fact, this was a new distribution function with different parameters and properties. This new function, called a zeroth-order logarithmic distribution, is described herein. Since one of the parameters is the modal value of the variable, this new function permits exploration of the effect of changing the breadth of the distribution while keeping the mode invariant. A generalized logarithmic function is described which permits selection of other moments of the distribution as the size parameter appearing explicitly in the distribution function.
In a recent series of papers from this laboratory, the particle size distribution of a variety of colloids has been determined by comparison of the polarization of the scattered light with theoretical calculations. These calculations assumed that the particle sizes could be represented by a two-parameter distribution function which we had called a logarithmic normal distribution. 2-4 For each particular system, a “solution” consisted in determining the values of the distribution parameters which gave theoretical light-scattering functions in agreement with the experimental data. This approach has also been followed1 by Heller and his collaborators with different experiments and a different distribution function than utilized lby us.6 It has become apparent to us that the distribution function which we had used is actually a new distribution function, rather than the logarithmic normal distribution, and that the parameters in question stand
for physical quantities different from those stated. We would like to clarify the matter in this paper by describing in detail some of the properties of this new distribution and by comparing it with the logarithmic normal distribution. We will then write the expression for a generalized logarithmic distribution function which may be reduced to the logarithmic normal distribution or to the one used by us. For reasons which (1) (a) Supported in part by research grant AP-0048 from the Division of Air Pollution of the Public Health Service: (b) SoconyMobil Fellow: part of a P h . D . Thesis by W. F. Espenscheid. (2) (a) 34. Kerker, E . Daby, G. L.Cohen, J. P. Kratohvil, and E . Matijevib, J. Phys. Chem., 67, 2105 (1963); (b) M. Kerker, E. Matijevi6, W. F. Espenscheid, W. A. Farone, and S.Kitani, J. Colloid Sci., 19, 213 (1964). (3) E. Matijevi’, S. Kitani, and M. Kerker, ibid., 19, 223 (1964). (4) W. F. Espenscheid, E. Matijevii., and M. Kerker, J . Phys. Chem., 68, 2831 (1964).
(5) W. Heller and M. L. Wallach, ibid., 67, 2577 (1963); H. Bhatnagor and W. Heller, J . Chem. Phys., 40, 480 (1964).
Volume 68, Number 1 1
L.
November, 1964
