ponent (urea, sucrose, etc.,) is larger than the water molecules and considered to be composed of "rigid, uncharged spheres of radius, a, it is clear that the center of any of these molecules will not he able to come closer than a distance, a, t o the 'surface' of the sedimenting particle. This results in a region of thickness, Za, surrounding the macromolecules in which the density varies from that of water to that of the solution. According to Kauzmann, this region of varying density can be approximated by assigning a water layer of thick-
[CONTRIBUTION FROM
THE
ness, a, to the macromolecules and assuming that the liquid more distant than a, from the surface of the macromolecule has the density of the bulk l i q ~ i d . ' ~ "In such cases as these, it is still possible to use the equations developed in the theoretical section of this communication. The 01) will r e f e l to the number of water molecules in the region from which salt is excluded, and the binding afFinities. k', for such regions will be equal to zero. (13) W . IC. Schachman, "Ultracentrifugation in 13iwliemi\try:" Academic Press, Inc , S e w York, N . Y . , 105'3, p. X R .
DEPARTMENT O F CHEMISTRY, CORNELL UNIVERSITY,
ITHACA, KE\V
YORK]
A Raman Study of the Bromide Solutions of Zinc and Cadmium'" BY WILBURYELL IN'^
AND
ROBERTA. PLANE
RECEIVEDNOVEMBER 14, 1960 Raman intensity measurements were made of zinc bromide solutions containing various ratios of total zinc t o total broinide. These results led t o the following as the most probable assignments for the three polarized lines: V I , ? cm. ( p = 0.06), ZnBrc'; Y I S B crn.-' ( p = 0.09), ZnBr?; uZoj cm.-l ( p = 0.13), ZnBr ?. Comparison with ZnBrp in nun-aqueous solvents indicated t h a t t h e aqueous ZnBra molecule is different from t h a t in other solvents and may be tetrahedral Zti(HnO)?Brr. Stepwise formation constants for the three complexes were found in concentrated solution t o be: (ZnBr +) /i%n+ + ) ( B r - ) = 0.3, (ZnBr2)!(ZnBr+)(Br-) = 1, (ZnBrl')!(ZnBr*)(Br-)a = 0.2. If ZnBra- were present, its principal Kainan band \vas coincident with t h a t of one of the other species. I n cadmium bromide solution of various ratios of total B r - t o total C d only one polarized line was found. Coincident with t h a t line, a t 166 cm.-l ( p = 0.08) which was due t o CdBrc-, was the principal line of one (or more) lower species. The lower species appeared t o be of less importance than in the zinc systein, while the tetrabromo species was of greater importance: (CdBrc=),'(Cd'+)(Br-)4> 1. ?,
Of the methods used for studying complex ions Aqueous solutions of Znti- and Br- had been in aqueous solution, none is more direct than the found to show Raman lines a t 172, 1S-l and 20s measurement of Raman spectra of solutions. This c m - I , while non-aqueous solutions of ZnBr2 method is direct in that each different complex showed a line a t (or near) 208 cm. and in some species present should exhibit its characteristic solvents a second line a t 172 ern.-'. On this vibrational spectrum.2 Thus, the Raman method basis, the line a t 208 em.-' was assigned to the differs from most other methods which determine linear ZnBrY molecule, that a t 172 cm.-' to the some property characteristics of one species (often tetrahedral ZnBrr= (whose other frequencies were the activity of the completely dissociated species) found to be 61, 82 and 210 cm.-lj and the interand from variations of this property infer the mediate line (184 cm. -') found only in water was presence of additional species. Furthermore, the assigned to ZnBr3--. No Raman evidence was very existence of a Raman spectrum shows that the found for any other species such as ZnBr+, for complex species has kinetic identity (ie., exists for which non-Raman evidence Previous times long enough to allow vibrations) and is bound studies of aqueous cadmium bromide solutions together by something other than hard-sphere detected the existence of only the tetrahedral coulombic attractions (;,e., the mean molecular CdBr4'.5 Thus, a primary aim of the present polarizability must change during vibration3). investigation was to determine which lower comThus, in principle, observation of Raman spectra is plexes are formed in aqueous solutions of the a general method for both defining and detecting bromides of zinc and cadmium. Quantitative illcomplex ions in aqueous solutions. tensity measurements were made both for this The present work was undertaken in order to purpose and t o determine the concentrations of the study as quantitatively as possibly Raman spectra various species as a function of solution composiof concentrated aqueous solutions containing rela- tion. tively simple complex ions. For the investigation, Experimental the bromides of zinc and cadmium were chosen. Measurements were made with a Cary Model 81 Ranian Both had previously been studied q ~ a l i t a t i v e l y . ~spectrophotometer. ~~ This instrument was altered 0 1 1 1 ~i i i (1) (a) This work was supported by t h e United States ilir Force through t h e Air Force Office of Scientific Research of t h e Air Research and Development Command, under Contract N o . A F 49(635)279. Reproduction in whole or in p a r t is permitted for any purpose of t h e United States Government. Some of t h e results were reported a t t h e 136th National Meeting of t h e American Chemical Society, .4tlantic City, New Jersey, September, 1959. (b) Based on work performed for partial fulfillment of t h e degree of Doctor of Philosophy. 12) G. W. Chantry and R. A. Plane, J . Chem. Phys., 33, 736 (1960). (3) Cf. D . A . Long, Proc. Roy. Sac. (London), B a l l , 203 (1963). I. -4. \%'oorlward and D. A. I,ong, Trans. F a r a d a y SOC.,45, 1131 i lW9).
t h a t the filter solution was replaced by pure isopropyl alcohol and sample tubes were used which were specially (4) M , L. Delwaulle, Conipl. v e n d . , 240, 2132 (1%5);
B d . Soc.
Chim.,France, 1966, 1294 (1955). (3) J. A. Rolfe, D. E. Sheppard and I.. A . Woodward, Trans. F a r a d a y Soc., 50, 1275 (1954).
(6) E. Ferrell, J. 51. Ridgion and H. I,. Riley, J . Chduz. .Soc., 1121 (193G). (7) (a) L. G. Sillen and B . Tiljequist, S v e n s k k e w . T i d s k r . , 56, 8: (1944); (b) S. A. Shchukarev, I.. S . 1,ilich a n d V. A . Latysheva, Z / I I O , . i i m v g . K h i w . , 1, 2 2 3 (19,X),
RAMAN STUDY OF ZINC AND CADMIUM BROMIDES
June 3 , 1961
2449 I
I
9
85.
8 i L
\;
Fig. 1.-Raman
I,
F '-
r
, -. :
",. -
~LI- . .
:b'
spectrum of zinc bromide solution showing the three polarized hands.
constructed with Liebig-type water jackets so that 25' water could be circulated around the tube t o provide thermostating. The sample volume was increased from 4.5 ml. to 12 ml. In order to relate observed Raman intensities t o concentrations of scattering species, internal standards were used which corrected for changes of refractive index and all geometric variations. The standard was in every case the AI line of C l o d - (dissolved in the solution being studied) whose absolute intensity is known.8 Each measurement copsisted of several alternately obtained traces of C104and the species in question. T h e relative intensity was obtained by comparing the area of the line in question with that of the standard run just before and just after. All such comparisons (usually five or more) for a single solution mere then averaged. T h e precision thus obtained and the accuracy found for solutions of known composition indicated that the final measurements contained a probable error less than =k 5y0 of the concentration of the species in question. Depolarization ratios were determined by the method Dreviouslv described.2 The solutions &died were prepared from two or more of the following solutes: ZnBrz, Zn(C!04)2, KaBr, LiBr, HC101, CdBrg, Cd(ClOJ2. All bromides and the HClOa were the purest grades commercially available, used without further purification. Zinc and cadmium perchlorates were prepared in solution by the exact neutralization of standardized HC1O4 with ZnO and CdC03, respectively. Stoichiometric concentrations were checked by analysis of zinc and cadmium by electrodeposition.
Results Solutions containing separately varied concentrations of Zn++ and Br- showed a total of three relatively intense Raman lines a t A v = 172, 186 and 205 cm.-l. In most solutions two of the strong lines were found, but a t certain compositions, all three were present to limited extents. Such a spectrum, by its nature one of the poorest obtained, is given as Fig. 1. The strong lines were in addition to the weak, depolarized lines observed a t 63, 81 and 213 cm.-I which, with the 172 cm.-l line, comprise the Raman spectrum of Z I I B ~ ~ ' . ~The intensities of the strong lines changed markedly one to another as the ratio of total dissolved Br- to total dissolved Zn++ was changed. It, therefore, was apparent that the three lines arose from separate chemical species. Each of the lines showed a small depolarization ratio (p172 = 0.06, p186 = 0.09, ~ 2 0 5 = 0.13) as would be expected for symmetrical stretching ( 8 ) G W. Chantry and R. A Plane, J . Chem. Phys., 32, 319 (1960).
0
2
5
6
8
Moles/liter bromide. Fig. 2.--Raman intensities (relative t o molar clod-) of the three polarized bands for 1.50 X zinc solutions with various concentrations of bromide. Circles refer to 172 cm-1 band; squares, t o 186 cm.-'; triangles, t o 205 cm.-'.
modes of nearly symmetrical species. The three lines were relatively sharp but varied in width somewhat (average deviation of the three 4110%) with solution composition. The average values for the width a t half height were 13.6 cm.-l for 172 cm.-', 12.3 for 186 cm.-l, 15.1 for 205 crn.-l. All observations made confirmed the previous assignment of the 172 cm.-' band as the A1 frequency of tetrahedral ZnBrd ion. The bands a t 186 and 205 cm.-' apparently arose from species containing other than four Br atoms per Zn. Any depolarized bands (asymmetric stretches or bending modes) from these species were either coincident with those of ZnBr4= or were too weak to be observed under the conditions and composition range studied. The spectra of solutions containing C d + + and Br- were markedly different from the zinc solutions in that a t all ratios of Br-/Cd++ only a single polarized line (p = 0.08) a t 166 cm.-' was found. In addition, weak depolarized bands were observed a t ca. 56 cm.-l (broad and probably v 2 and v4 unresolved) and a t 187 cm.-l ( v Q ) . This single spectrum had previously been assigned to tetrahedral CdBrd.4,5 Unlike Zn++, Cd++ either formed only CdBr4- or if other complexes were formed, the frequencies were nearly identical with those of the tetrabromo complex. In order to identify chemical species with the lines a t 186 and 205 observed in Zn++-Br- solutions, a number of experiments a t a variety of solution compositions were performed. In each experiment, the intensity, relative to dissolved C104-, of each of the three main lines was determined. In doing so, two difficulties were encountered. As Fig. 1 shows, the lines were close enough to the
WILBURUFLLINAND R O T ~ F R *I. T PIANE
Vol. 83
2
4 6 8 10 Ratio Br/Zn++, Fig. 4.- Raman intensities (relative t o molar Clod-) of the three polarized bands for solutions iri which the total concentration of zinc plus the total concentration of bromide equals 6.0 M . Circles refer to 172 cm. - 1 band ; squares, to 186 crn. - l ; triangles, to 205 cm. -1.
Zn(Cl04)z, KaBr. The intensities found are plotted vs. the ratio Br-,/Zn++ in Fig. 4. t In none of the experiments described above was 0 5 10 15 20 ZnBr4' the only zinc-containing species present. Thus, Fig. 2, for example, shows the concentration Moles/liter bromide. Fig. 3-Raman intensities (relative to molar c104-)of of ZnBr4- rising even at the highest Br- concentrathe three polarized bands for ZnBrl solutions at various con- tion used. It was necessary to prepare a solution centrations with added 0 300 M HC1O4. Circles refer t o with all the Zn as ZnBr4' in order to determine the 172 c111.-~band; squares, to 186 ctu.-l; triangles, to 205 inherent molar Raman intensity of ZbBr4-. For this purpose NaBr could not be used since precipicm. -l. tation of NaC104 occurred before more than about Rayleigh line so that the base line was not horizon- 80% of the total zinc was converted to ZnBr4'. tal. Furthermore, the three peaks were sufficiently The desired solution was prepared by using LiBr broad and close together so as t o not be completely to make a solution of the stoichiometric concenresolved. T o assign intensities to each peak, a trations: 0.218 Ad Zn(C104)2and 12.38 M LiBr. base line was sketched in t o resemble that found The spectrum of this solution contained only the in the absence of complexes. Individual peaks Clod- peaks and the 172 cm.-I peak (Le., 185 and were assumed to be symmetrical and were graphi- 205 cm.-l were absent and no new peaks appeared). cally resolved for each spectral trace. Although Thus, from the total zinc concentration, the obthe precision was found to remain *5y0 of the served molar intensity of ZnBr4= was found to be peak intensity, the uncertainty most probably in- 1.35 times that for the AI line of C104-.'O The creased. reliability of the assumptions made in obtaining Three series of experiments were performed. this value was indicated by the fact that the inIn one, seven solutions were prepared, each con- tensity per unit concentration of total zinc for less taining a total zinc concentration of 1.50 Ai7 (ob- concentrated solution asymptotically approached tained from approximately equimolar Zn (C1o4)2 this value. and Z11Br2)with varying amounts of added NaBr so For comparison with the previous studyj4 that the total concentration of Br- covered the solutions of approximately molar ZnBrz in methanol range 1.6 to 8.5 ill. The intensities (relative t o and in acetone were measured. The first showed 1.00 Ai7 C104-) observed for each of the three a peak a t 211 cm.-l, with width a t half-height 13.8 Raman lines is plotted as function of total Br- cm.-' and a depolarization ratio of 0.03. The concentration in Fig. 2. acetone solution showed a peak a t 200 em.-', with A second series of experiments was performed width a t half-height of 15.6 cm.-l and a depolarizawith solutions each containing 0.300 M HClO4 (to tion ratio of 0.01. serve as the intensity standard) and varying In an attempt to learn m o r e abcut the cadmium concentrations of ZnBr2 without additional Zn++ bromide system, a series of sJuiions were prepared nor Br-. The intensities (relative to molar C104-) from Cd(C104)2and NaBr in which the total stoiobtaincd for these solutions are given in Fig. 3. Br- was 2.0 chiometric Concentration of C d + + Finally, a series of experiments was performed M . The results, plotted in Fig. 5 , exhibit a maxiwhich was designed according to the Job method mum near Br-/Cd++ = 4 and a marked shoulder of continuous ~ a r i a t i o n . ~In these, the total below 2. ildditional experiments were performed Brstoichiometric concentration of Z n f + (10) This value does not contain correction for instrument reequalled in every case 6.0 M. The twelve in- sponse as a function of frequency. A calibration curve utilizing the dividual solutions were prepared from the appro- absolute intensities of CHL% ID. A . Long, D. C. Milner and A. G . priate mixture of two of the solutes: ZnBr2, Thomas, PYOC.R o y . SOL.(l.ondorr),8437, 197 (1956) 1 showed that the
+
+
(9) P. Job, Ann. Chrm., (10) 9, 113 (1928).
absolute intensity can be obtained by multiplying this value, and those of the other complexes discussed here, by 1.16.
RAMAN STUDY
June 5, 1961
OF ZINC AND
on a variety of solutions prepared from CdBrz, NaBr and HClOa. The results of these are given in Table I.
l'O
TABLE I
2451
CADMIUM BROMIDES
1
RAMAN INTENSITIES OF Cd++-Br- SOLUTIONS Stoichiometric concentrations CdBrt NaBr HC104
.290 .304 .306
0 0.330 0.585 1.195 2.424 5.032
0.499 .499 .499 .499 .490 .499
.499 f499 .500 .500 .099
0 0.998 2.000 6.000 5.995
.249 .249 .249 .249 ,249
0.297 .285 .302
Intensity of 166 cm.-' relative to molar C104-
0.15
.25 .3T .58 ,i
9 .SO
.26 .68 1.14 1.33 0.26
Relative intensity per molar Cd total
0.60
0.88 1.22 2.00 2.60 2.61 0.52 1.36 2.28 2.66 2.63
From either of the two series of experiments recorded in the table, it can be noted that the intensity divided by total Cd concentration (last column) increases with excess Br- and eventually becomes constant. The final value, 2.G3lo thus represents the molar intensity of the complex CdBr4-.
0
1
2
3
4
5
6
7
Ratio Br-/Cd++. Fig. 5.-Raman intensities (relative to molar Clod-) of the 166 cm-1 band of solutions in which the total concentration of cadmium plus the total concentration of bromide equals
2.0 M.
The final expression consists of a leading term which is that for the case where but a single complex I t is apparent from Figs. 2 and 4, that of the species is present and a correction term which is several complexes formed by Zn++ and Br-, a weighted average of the other complexes present. ZnBr4- (172 cm.-l peak) represents the one of The correction term is such as to cause positive highest Br-/Zn++ ratio. The other two strong deviations for high j and negative deviations for small j . For intermediate j ' s , there should be some peaks must originate from species of lower Br' content. Thus, from Fig. 2, for example, these cancellation. Furthermore, the maximum deviatwo species are seen to reach their maximum con- tion should occur for high j since higher n values centrations a t lower [Br-] than does ZiiBr4-. are involved and near the corresponding maximum, T o formulate these species, the Job experiments Co will be nearly 0 which is not true for a low j . recorded in Fig. 4 are helpful. For simple systems Finite values of Co increase the denominator of the containing but one complex species, the maximum correction, without adding to the numerator concentration and hence the maximum Raman in- (since n = 0). Although it is difficult to access the tensity occurs (for solutions of constant concen- role of solution non-ideality, this treatment can be tration metal ion plus ligand) a t the ratio of ligand used to interpret Fig. 4. The known species Znto metal ion corresponding to the species f o r m ~ l a . ~Br4- shows its maximum just above the ratio of 4. However, in the present system, which contains Since this deviation should be greater than that for three complex species, the situation is more com- either lower species, the positions of the other two plicated." It can be shown that for ideal solutions maxima indicate that the 203 cm.-' band charactercontaining i complexes of the type AB,, a maxirnurri izes ZnBr+ and the 186 cm.-' band characterizes ZnBr2. is reached in. the plot of intensity US. [Bt,t,l]/ The assignment suggested by the experiments [Atotal] when summarized in Fig. 4 is in disagreement with the ( [ B ~ ] / [ A ~ ] ) s t m a x . = 1 $earlier a ~ s i g n m e n t . ~The present assignment is, l i however, supported by the concentration calcula tions to be described below which show that using n=o n=O the molar intensities indicated by the experiments and justified on theoretical grounds, there is insufficient bromide in the solutions to form species where Cn is the concentration of AB, and I , its containing more than 1 and 2 Br atoms, respccmolar intensity. For a resolvable peak due only tively. Furthermore, if the reasonable molar into the species ABj, all I,,except Ij vanish and the tensities were abandoned, i t would not be possiblc for the solutions to contain any ZnBr+ (independexpression reduces to i ent of whether or not it had a Raman spectrum). n ( j - %ICn Because this species is a priori more likely than ZnBrs-, for example, the present assignment seems further justified. It thus seems more likely that the following is the explanation for the correlation n-0 between experiments done in various solvents. (11) L. I. Katzin and E. Gebert. J . Am. Ckem. Soc., 71, 5455 The peak a t ca. 210 cm.-' in non-aqueous solvents is (1950).
Conclusions
2452
WILBURYELLINAND ROBERT -1.PLANE
Vol. 83
due to the linear molecule but is absent from aque- I , = KM(vo - vp)4 45(b?ilbQ,)2[ 6 / ( 6 - T p ) ] / ous solutions (as supported by the fact t h a t only vD[l - e x p ( - h v , , / k T ) ] in non-aqueous media is the line completely described in ref. 8 ) be proportional t o the number polarized). The line in aqueous solution at 186 of Zn-Br bonds in the complex. With the corcm.-' assigned t o a species of formula ZnBrz is, in fact, due to a hydrated, perhaps tetrahedral, mole- rections, the calculated molar intensitieslO are 0.62 cule such as Zn(HzO)zBrz,with VI frequency thus for ZnBrz and 0.27 for ZnBr+. From the values of the relative molar intensities, quite similar t o tetrahedral ZnBr4". On this basis, the data of Figs. 2, 3 and 4 can be directly conthe similarity of the frequencies of ZnBr+ and the other two species can be understood in terms of a verted t o solution concentrations. Furthermore, approximate values of molarity equilibrium conhydrated ion such as tetrahedral Zn(H20)3Br+. Although i t was possible to obtain the relative stants can be determined. These are molar intensity of ZnBre', i t was not possible to Zn+' f Br- = ZnBr' K = 0.3 prepare solutions in which all the zinc, or all the ZnBr+ + Br- = ZnBr2 K = l bromide, was converted only to ZnBrz or only to ZnBrz + 2Br- = ZnRr4K = 0.2 ZnBr+ (cf. Fig. 2). However, in certain solutions (of relatively high Br-T "Zn++T) ZnBr+ was ab- Considering the wide range of solution composition sent. If i t is assumed that Zn++ was also absent, (ionic strength varied from 3.5 to S.5) these conthe relative molar intensity of ZnBrz can be deter- stants are remarkably constant. n'ithin a random mined. On this basis, it was found to be 0.6. At scatter (average deviation of all reliable values slightly lower ratios of Br-T/Zn++T i t seems reason- as%), the constants showed no detectable trend able to assume t h a t a negligible fraction of the with ionic strength. The values themselves are in ~ Zn-++T is uncomplexed. Thus, from these s o h - fair agreement with those found p r e v i ~ u s l y ,extions, in which the concentrations of ZnBr4= and cept that the second (formation of ZnBrz) is larger ZnBrz are determined, the concentration of ZnBr + and ZnBra- is not detected in the present work. is found by difference and its molar intensity turns These facts could be taken as evidence that the peak a t 186 cm.-l is due t o both ZnBrz and ZnBr3-. out to be ca. 0.25. The values of molar intensities for ZnBrz and If true, however, the coincidence must be nearly ZnBr+ based on solution stoichiometry are not perfect since this peak is even sharper than the especially precise. There is, however, an alternate other two. From Fig. 5 it is apparent that although species method for obtaining these values which indicates that the above values cannot be far from correct. with less than 4 Br-,'Cd*+ are formed, they are of The Wolkenstein theory, l 2 for which strong sup- less importance than in the zinc system. If they port has recently been found,13 states t h a t the are assumed to be of negligible importance, an estiquantity ba!bQ (the change of mean molecular mate can be made, using the relative molar intenpolarizability during vibration, which is responsible sity of CdBr4= found t o be 2.63, for the molar for Raman intensity) is a bond property Thus, i t equilibrium constant (CdBr4=),' (Cd + +) (Br -) . is reasonable that the quantity is directly trans- The values found are far from constant particularly ferrable from ZnBr4' to the lower complexes. a t low (Br-r)!(Cd++T) where the neglected lower This would mean t h a t the molar intensity would species are most important. If, however, these (with correction made for differences of frequency solutions are ignored, the constant is found to be and degree of depolarization by using the equation greater than unity, as compared with 6 X lo-? for the corresponding zinc constant. Thus for (12) hI. Wolkenstein, Compl. m u d . acad. Sci. V.R.S.S., 32, 186 Cd++ as compared t o Zn++, the lower Br- com(1941). plexes are of less importance while the tetrabronio (13) G. W C h a n t r y and L . A. Woodward, Trans. F a r a d a y Soc., 56, complex shows greater tendency to form. 1110 (19GO).
