MET ALL IC NITRATES

THE RAMAN SPECTRA OF METALLIC NITRATES AND THE STRUCTURE OF CONCENTRATED

SOLUTIONS OF ELECTROLYTES

BY JEAN-PAUL MATHIEU AND MACKENZIE LOUNSBURY

Received 3 ~ d July, 1950

A comprehensive study of the Raman spectra of solutions of metallic nitrates at various concentrations shows that the NOa- ions experience some deformation as the concentration increases and that in concentrated solutions of most of them an equilibrium takes place between two forms of NO,-. The facts can be inter- preted by assuming that the saturated solutions have a structure very similar t o that of the hydrated crystals which are deposited from them.

It has long been known that the formation of ions by electrolytic dissociation can be detected by the study of the Raman spectrum in solutions of acids such as HNO,l and H,SO,.* In these cases, there is a rearrangement of the molecular structure, in agreement with the views put forth by Hantzsch. As the concentration of the solutions increases, the molecular form, which is that of the pure substance, becomes more abundant than the dissociated form.

Quite different is the case where the electrolyte is a typically strong one, e.g. a neutral crystalline salt dissolved in an ionizing solvent. Certain authors have attempted, by means of the Raman effect, to in- vestigate the presence of undissociated molecules, and of intermediate ions such as CaNO,+, for polyvalent electrolytes. But the idea of the molecule is then without meaning, because the pure state of strong electro- lytes is the ionic crystal. I f one admits that the form cf the pure sub- stance becomes increasingly abundant in these solutions as the concentra- tion increases, then one would expect to find in concentrated solution, a structure analogous to that of the ionic crystal, or a t least fragments of such a structure. In the Raman spectrum, lines analogous to those arising from the “external” vibrations of the crystal would appear. Now, a phenomenon of this kind has never been observed. On the other hand, when the ions are complex, i.e. composed of several atoms (so that

1 Rao, Proc. Roy. Soc. A , 1930, 127, 279. 2 Woodward and Horner, ibid., 1934, 144, 129.

Publ

ishe

d on

01

Janu

ary

1950

. Dow

nloa

ded

by U

nive

rsity

of

Mic

higa

n L

ibra

ry o

n 30

/10/

2014

01:

17:4

7.

View Article Online / Journal Homepage / Table of Contents for this issue

JEAN-PAUL MATHIEU AND MACKENZIE LOUNSBURY 197

they possess characteristic vibrational frequencies), these frequencies must be alterable by the changes with concentration in the electric field created by the charges of the other ions and of the dipoles of the ionizing solvent.

Experimental and Results We have studied systematically the influence of concentration on the Raman

spectra of solutions of metallic nitrates. The complex ion NO,- has a plane structure in the form of a centred equilateral triangle, and possesses four funda- mental modes of vibration (Fig. I) . Only the totally symmetrical vibration Avl, and the doubly degenerate vibrations Av, and Ava are active in the Raman effect .

The Raman spectrograms were obtained using a Cojan spectrograph with a numerical aperture of FI1-9, and a dispersion of about 30 A per mm. Measure- ments were made of the frequency (A, in cm.-l) of the lines, of their relative intensity I, and their depolarization factor p by photographic photometry.

FIG. I.

Tables I and X summarize the results of these measurements. The following abbreviations have been used :

P, polarized line (0 < p < 6/7) ; D, depolarized line ( p = 6/7) ; s, strong intensity ; m, medium intensity ; w, feeble intensity ; b, broad line ; n, narrow line ; N, normality of the solution studied.

Unless otherwise stated, the temperature was 40' C. Analysis of Results.-The preceding results (and many others which do

not appear in the Tables) may be analyzed in the following manner. (i) Only for concentrations of normal or less does the Raman spectrum

contain no more than three lines corresponding to the three active fundamental frequencies. The frequency Av, always appears as a broad, diffuse band. Several of these results are presented in Table 11.

To the above facts, valid for all nitrates in aqueous solution, may be added another which has been observed by various authors : 3* 4* 5 * the frequency Av, of the totally symmetrical line tends towards the value 1048.0 f 0-2 cm.-1 as the concentration decreases. Thus, in dilute solution, the spectrum of the nitrate ion agrees with the form of a centred equilateral triangle. This structure appears as a limiting case, corresponding t o the ion surrounded in an isotropic manner by the water molecules of the solution.

(ii) In every case, the first effect of increasing the concentration is t o cause a splitting of the band Av, into two others. The band of lower frequency is polarized ( p N 0.6 t o 0.7) ; the other is depolarized. Results for several cases are presented in Table 111.

The splitting of the band Av, when the concentration increases may be interpreted by a cessation of the degeneracy of the fundamental vibration t o which it corresponds. One finds, as one should, a polarized band and a de- polarized band, which excludes the hypothesis of a Fermi resonance between the frequency Av, and the first harmonic of Ava. This modification of the

Gerlach, Ann. Physik, 1930. 5 , 196. Grassmann, 2. Physik. 1932, 77, 616. Grassmann, ibid., 1933, 82, 765.

The polarization of the lines is in accord with the theory.

6 Theimer, Acta Physica Austrzaca, 1948, I , 384.

Publ

ishe

d on

01

Janu

ary

1950

. Dow

nloa

ded

by U

nive

rsity

of

Mic

higa

n L

ibra

ry o

n 30

/10/

2014

01:

17:4

7.

View Article Online

198 METALLIC NITRATES spectrum reveals a lowering of the symmetry of the nitrate ion. It is probable that this phenomenon is due to the deformation of the electronic envelope of the ion by its surroundings. The ionic atmosphere is no longer isotropic when the concentration is increased : a cation can draw nearer to a particular nitrate

TABLE I

1'7 1048 714

I 380

N = I 3'2

N = 6-4

N = 71

N = 2-2 4'4 7'6

10.8 12.6 16

N = 1.2

5'4 7'9 9'9

I 1-5 I 4

N = 3-5 Sat. soh.

N = 1.3 3'5 6-3

14'3 I 6.3

I 0

0.6 I047 720 I370

(4 Cu(NO,),

- - 1048 (sP) - 1378 (mDb) - 717 (D) 716 (mD) - - 1050 (sP) 1344 (mb) 1406 (mDb) - 718 (mD) 756 (mP) 1024 (m) 1049 (sP) 1328 (mPb) 1414 (mDb) 1478 (wb) 719 (mD) 756 (mP) 1024 (mP) 1050 (sP) 1313 (mPb) 1412 (mDb) 1478 (mD6) 718 (mD) 759 (wP) 1024 (mP) 1050 (sP) 1313 (mPb) 1413 (mDb) 1458 (mDb) 719 (mD) 757 (mP) 1024 (mP*) 1048 (sP) 1315 (mPb) 1405 (mDb) 1481 (mDb)

(g) Th(N03)4

714 (mD) 749 (mD) - 1048 (sP) - 1360 (mD) 1528 (wPb) 714 (mo) 750 (mD) - 1051 (sP) - 1368 (mD) 1528 (mPb) 715 (mD) 751 (mD) 1034 (m) 1051 (sP) 1318 (wD) 1408 (wD) 1538 (mPb) 713 (mD) 750 (mD) 1034 (m) 1050 (sP) I323 (mD) 1408 (WID) 1538 (double) 715 (wD) 751 (mD) I034 (sP) 1050 (sP) I323 (UW) - 1540 (doubie) 716 (wD) 751 (mD) 1034 (sP) 1050 (mP) 1317 (uw) - 1500 1543

* Values deduced from the decomposition of the photometric curve (cf.

TABLE I1 Fig. 4).

Cation

N . Avl . Av4 . Av3 .

Li

i I La I - 1'5

1050 720 I383

cu

1'2 1048 (p = 0.25) 717 (p = 0.86) 1378 (p = 0.83)

ion than to the other anions and thus form an association by pairs. Although Bjerrum considered only Coulomb forces in the formation of ion pairs, the forces of induction and of dispersion are not excluded from playing a part in the interaction of ions when they come very close together.

Publ

ishe

d on

01

Janu

ary

1950

. Dow

nloa

ded

by U

nive

rsity

of

Mic

higa

n L

ibra

ry o

n 30

/10/

2014

01:

17:4

7.

View Article Online

JEAN-PAUL MATHIEU AND MACKENZIE LOUNSBURY 199 One may ask why there is not a similar splitting of the doubly degenerate

vibration Av,. This does not occur because this vibration should approach that of a pure deformation. Now, the study of crystals 7 as well as the theoret- ical calculations8 shows that vibrations of deformation are always much less sensitive to variations in the symmetry of the local field of force than are the vibrations of valency.

Thus the Raman effect brings its contribution to the study of a much debated question, that of changes in the polarizability of ions in solution. Measurements of refraction,@ of absorption 1 0 ~ 1 1 and of rotatory power l2 have been directed towards this question. In particular, Bottcher, from a detailed

TABLE I11

Cation Na Li Be Sr Zn I cu ------

N . 7'6 3'2 6.4 3'8 6.9 4'6

lI357 1362 I342 I353 I340 I347 Av3 11410 1438 1420 1423 1408 1418

A1

3'9 1315 1410

study of the internal electric field in fluid dielectrics, has attempted recently t o draw the conclusion that the polarizability of ions and of simple molecules is not influenced by their surroundings.13 Although calculations based on the numerical data of refraction show that the mean polarizability of the nitrate ion in fact does remain constant in solutions of alkaline nitrates,l0 our results scarcely permit us t o think that the same is true of all the terms of the tensor of polarizability and for the derived tensor. The study of the Rayleigh radi- ation from solutions of NaNO, l5 gives similar indications.

(iii) Above a certain concentration, which depends on the nature of the cation, more profound modifications appear in the spectra of the nitrates of certain polyvalent cations.

TABLE IV

Ca

10.8

1428

0.83

Cation cu Ce

I 3-0 Sat.

1481 I463

0.93 D

N .

AvQI . P .

La

8.8

1461

0.82

Th

(a) One or two new bands, as broad as the bands Avg, appear at frequencies AV;, which are a little higher than Av3 (Fig. 2 and 3) as shown in Tables I and IV.

(b ) There appears a new line, of frequency Avq' a little higher than Av, (see Table V), which several authors have already ~ b s e r v e d . ~ ~ l8 Its frequency de- pends on the cation, but not on the concentration. On this point, our measure- ments for Ca(NO,), agree with those of Grassmann' and of Nisi,17 but not of Bauer.16 We have not found the frequency claimed by Ollano and Frongia l8

for Ba, Mg and Al.

Couture, Ann. Physique, 1947, 2,94. 8 Bauer and Magat, J . Physique, 1938, 9, 319. @ Fajans, Trans. Faraday Soc., 1927, 23, 357.

1 0 von Halban and Eisenbrand, 2. physik. Chem., 1928, 132, 401. 11 Kortiim, Bas Optiscite Verhalten geloster ElektroZyte (Enke, Stuttgart, 1936). la Darmois, Progrds rbcents duns l'itude de la structure des solutions +4lectro-

l3 Bijttcher, Physica, 1942, 9, 937.

l6 Mathieu and Lelong, Compt. rend., 1943, 216, 800. 16 Bauer, Magat and Silveira, ibid., 1933, 197, 313. 1 7 Nisi, Proc. Phys. Math. SOC. Japan, 1933, 15, 114. 18 Ollano and Frongia, Nuova Cimento, 1933, 10, 306.

lytiques (A.S.I. No. 785) (Hermann, Paris. 1939).

Bijttcher, Rec. Trav. Chim., 1946, 65, 14.

Publ

ishe

d on

01

Janu

ary

1950

. Dow

nloa

ded

by U

nive

rsity

of

Mic

higa

n L

ibra

ry o

n 30

/10/

2014

01:

17:4

7.

View Article Online

2 00 METALLIC NITRATES (c) The line Av, broadens and its apparent half-width in some cases reaches

20 t o 30 cm.-1. This phenomenon is very probably due, in all cases, t o the appearance of a polarized line of frequency Av,’ close t o Av,, because we have been able to prove the existence of a new line, Av: = 1024 cm.-1, in the spectrum of copper nitrate (cf. Fig. 4 and 7) and Avl’ = 1034 cm.-l in the spectrum of thorium nitrate (cf. Fig. 8).

FIG. 2. FIG. 3.

The modifications of the spectrum indicated in the preceding section cannot be explained by the hypothesis of a cessation of the degeneracy of the vibrations of the nitrate ion for the following reasons : the simple frequency Av1 would never under any conditions split into two ; the lines AV, and Av,’ are almost always both depolarjzed ; the number of lines in the region of Av3 exceeds two (always three, sometimes four).

TABLE V

In addition, the measurements of the relative intensity of the lines as a function of concentration do not agree with such an hypothesis. The intensity of the bands Av,‘, Av3/ and Av,’ increases relatively much more quickly as a function of the concentration than does that of the bands A,,, Av3 and Av,. This phenomenon occurs simultaneously for the three frequencies. Fig. z and 3 show this for CU and Th in the region Av, ; Fig. 5 and 6 do likewise for Ca and Th in the region Av4 (see later). When the line Av: is not clearly separ- ated from the line Au,, its appearance and its increase in intensity cause a dis- placement of the centre of gravity of the two lines, which varies continuously with the concentration. This renders doubtful the conclusions which have been drawn 6 from variations in the frequency of Av,.

Existence of Two States of the Nitrate Ion.-The preceding facts suggest that, in concentrated solutions of certain nitrates, a t least two states

Publ

ishe

d on

01

Janu

ary

1950

. Dow

nloa

ded

by U

nive

rsity

of

Mic

higa

n L

ibra

ry o

n 30

/10/

2014

01:

17:4

7.

View Article Online

JEAN-PAUL MATHIEU AND MACKENZIE LOUNSBUKY 201

of the nitrate ion exist. The passage from one state t o the other is discontinuous, as is shown by the constancy of the frequency of the lines, particularly Av4 and Avp'. (The diffuse bands Av, do not lend themselves so well t o a precise measurement .) A progressive variation of the dynamic parameters, due t o an increasing deformation of the nitrate ion, would involve a continuous modification of the frequency of the lines.*

Let us suppose then, that the intensities I and I' of the lines Ava and Av4' are pro- portional respectively t o the numbers n and n' of the two forms of the nitrate ion, as expressed by

u = I'/I = n'/n.

Fig. 5 and 6 show the variation of the ratio u = I'/I as a function of the concentra- tion, The relationship is linear, which gves

nln' = Kn,, . - (1)

where no = n + n'. . * (2)

We have investigated the influence of various factors on the proportions n and n' of the two forms of the nitrate ion.

(i) The addition of an electrolyte having one ion (either cation or anion) in common with the considered nitrate increases the ratio u just as a simple increase in con- centration does. This result (see Table VI) agrees with that of Bauer l6 and of Grass- mann.4

(ii) The addition of neutral salts (i.e. without a common ion) likewise increases the ratio u, but less than in the preceding case. Some results are given in Table VII.

AV J #

FIG. 4.

Upper curve : solution. Lower curve : crystal.

(iii) A rise in temperature increases the ratio o as does the addition of salts, as indicated in Table VIII.

FIG. 5.

* Let us recall that the hypothesis of two forms of the nitrate ion has been made in order to explain the absorption spectrum.10

c"

Publ

ishe

d on

01

Janu

ary

1950

. Dow

nloa

ded

by U

nive

rsity

of

Mic

higa

n L

ibra

ry o

n 30

/10/

2014

01:

17:4

7.

View Article Online

202

NJ7.00 A 7-00 A 8-34 A 6-35 A 8-77 A I - I ' 3 4 B - 2-42 C -

0 0 0.3 0.3 0.37 0-32

METALLIC NITRATES TABLE VI

5 '10A 9.66 A 4 .56D -

0.35 0'35

TABLE VII

u 0.56 0.67 0.82 1.04 I 1-0 1'2 1.6

(E = Ca(NO,),, G = CsC1, H = LiCl, K = Th(NO,),.)

TABLE VIII

Solution. P - / x T n

- - 40 70

0' 49 0.56

$To C 43- 65 95

FIG. 6.

These last results show that the energy U necessary to form the second state Applying these results to (n') of the nitrate ion from the first (n) is positive.

those expressed b y relations ( I ) and (2), one may write :

njn' = n,e-u/kT (U > 0). . . - (3)

Publ

ishe

d on

01

Janu

ary

1950

. Dow

nloa

ded

by U

nive

rsity

of

Mic

higa

n L

ibra

ry o

n 30

/10/

2014

01:

17:4

7.

View Article Online

[To face page 203

Publ

ishe

d on

01

Janu

ary

1950

. Dow

nloa

ded

by U

nive

rsity

of

Mic

higa

n L

ibra

ry o

n 30

/10/

2014

01:

17:4

7.

View Article Online

JEAN-PAUL MATHIEU AND MACKENZIE LOUNSBUKY 203

Discuss ion Nature of the Two States of the Nitrate Ion.-(i) The experimental

results do not agree with the hypothesis of an electrolytic dissociation following Ostwald’s law. This law leads, a t a given temperature, to the relation

I - u -- a2 - An,,

where a = n/no and I - a = n’/n, ; whereas relations (I) and (2) give the following :

I - u CC = Kn,. . (4)

Similarly, the influence of neutral salts does not occur in the direction predicted by the theory of dissociation. On this point our experiments confirm the conclusions of Bauer.ls

(ii) It could be admitted that, in concentrated solution, some cation- anion associations are formed which are closer than those whose existence Bjerrum has supposed, in that they would be formed without interposition of water molecules. They would differ, however, from undissociated molecules or from ionic molecules in that their formation would involve only electrostatic forces, account being taken of the polarization of the ions. Let us suppose that the frequencies Av’ (740, 1030, 1500 cm.-l) are characteristic of these associations and the frequencies Av (715, 1050, 1400 cm.-l) characteristic of the non-associated nitrate ions. If the associated form possesses only three frequencies, then it must retain to a high degree the ternary symmetry. This condition is satisfied if the cation M is placed on the axis of the nitrate ion and not in its plane. If the valence force system is used to calculate the nitrate frequencies, the direction, Av --f Av’, of the variation in frequencies can be explained by admitting a decrease in the force constant f of the valence bond and an increase in the deformation force constant d. But the previous hypothesis leads on the contrary to a decrease in f. The frequency Avl is expressed as follows :

where m = mass of an oxygen atom. Placed in the non-uniform field H of the cation M, each of these atoms, of negative charge e, is subjected to a force of attraction proportional to its elongation s with a coefficient equal to edH/ds and the frequency Avl undergoes a change :

Avl = dfF,

As dH/ds > o and e < 0, the frequency must increase. Thus it is evident that the elementary electrostatic considerations cannot account for the observed facts.

On the other hand, the hypothesis of a cation-anion association by contact does not easily explain the specific differences in the action of each cation. One would expect, for example, the electrostatic effects to increase with the polarizing power of the cation, as measured by the ratio q/r of its charge to its radius.

Now the order of increasing values of q/r in no way corresponds to that of the appearance of the second state of the nitrate ion in the solu- tions of these cations at comparable equivalent concentrations. In particular, the cations A1 and Be with great polarizing power, produce no important modifications of the nitrate spectrum. Neither can one understand by the hypothesis of association by contact, why the line Av4’, for example, is in most cases depolarized, but in other cases polar- ized as it is in the nitrate solutions of copper and of mercury.

Publ

ishe

d on

01

Janu

ary

1950

. Dow

nloa

ded

by U

nive

rsity

of

Mic

higa

n L

ibra

ry o

n 30

/10/

2014

01:

17:4

7.

View Article Online

204 h2ETALllIC NITRATES (iii) Several authors 3s 4, 17 have already compared the spectra of

nitrate solutions to those of crystallized nitrates. The comparison has rested solely on the line Av, and usually for the powdered crystals. On this subject, Gerlach has stated two facts. (a) In dilute solution, the frequency Av, tends towards the value which it has in the crystallized nitrates of large cations. (b) With the introduction of water of crystal- lization into a nitrate, the frequency Av1 approaches the value which it has in dilute solutions.

We have extended this comparison to much more complete spectra, obtained from single crystals. In general, there is no strict relationship between the spectra of the saturated solutions and those of the anhydrous nitrates, as shown in Table IX. For each cation, the first column gives the frequencies observed in the concentrated solution, the second in the anhydrous crystal. On the contrary, the spectra of nitrate solutions and of the hydrated nitrate crystals, which grow in them at ordinary. tem- peratures, are quite analogous. Rousset and his co-workers have already made a similar observation with copper sulphate. The analogy may be drawn from the results presented in Table X.

Consideration of the results given in Table X suggests that, as the concentration of the solutions increases, the disposition of the nitrate

TABLE IX

Rb Sr Ba Pb

ions tends towards that which is characteristic of the hydrated crystals which are deposited from the saturated solutions.

The Quasi-crystalline Structure of Concentrated Solutions .-Let us try to make more precise the preceding idea.

(i) By X-ray diffraction, Prins 2 2 ~ and then Beck 24 have detected some regularities in the arrangement of ions in aqueous solutions of electro- lytes. Prins obtained the most definite results with thorium nitrate. These may be interpreted by assuming that the Th ions, surrounded by the other constituents of the solution, form close packings, whose dis- tribution is statistically regular and homogeneous. These experiments give information on the distribution of heavy cations. Ours, based on the diffusion of light by anions, complete them and allow more precise conclusions. If the interpretation which we propose is accurate, then the structure given as possible by Prins must be replaced by that of the hydrated crystal.

as Rousset, Lochet and Magne, Compt. rend., 1947. 224, 270. 2o Magat, Tables annuelles de constantes-Effet Raman (Hermann, Paris, 1937). 21 Couture and Mathieu, Ann. Physique, 1948, 3, 521. 22 Prins, J . Ckem. Physics, 1395, 3, 72. 23 Prins and Fonteyne, Physica, 1935, 2, 570. 24 Beck, Physik Z. , 1939, 40, 479.

Publ

ishe

d on

01

Janu

ary

1950

. Dow

nloa

ded

by U

nive

rsity

of

Mic

higa

n L

ibra

ry o

n 30

/10/

2014

01:

17:4

7.

View Article Online

JEAN-PAUL MATHIEU AND MACKENZIE LOUNSBURY 205

(ii) The specific action of the various cations may be probably ac- counted for by the differences between the crysta.1 structures of the salts which we have studied. It is likely that none of them are isomorphous. Unfortunately, the crystal data on the hydrated nitrates are yet incomplete and the structure of none of them is known.

At least their Raman spectra provide some information. The existence of two lines of the same type in the neighbourhood of the symmetrical frequency Avl in the spectra of the nitrates of aluminium, copper and

TABLE X

LITHIUM NITRATE, LiNO, . 3H,O 7 N soln. . . 720 - - 1051 Crystal . . 717 - - I054 Fused crystal . 722 - - I055

CALCIUM NITRATE, Ca(NO,), .4H,O 16 N soln. . 716 746 - 1050 Crystal . . 721 746 - 1052

ZINC NITRATE, Zn(NO,), . 6H,O 7 N soln. . . 719 - - 1050 Crystal . . 710 to 720 I053

(double ?)

COPPER NITRATE, Cu(NO,), . gH,O 13 N and 14 N

Crystal . . 720 755 1020 1047

ALUMINIUM NITRATE, Al(NO,), . gH,O 4 N soh. . . 719 - - 1050

Fused crystal . 721 - - 1050

CEROUS NITRATE, Ce(NO,), . 6H,O Sat. soln. . . 714 741 1047 (double)

THORIUM NITRATE, Th(NO,), . 4H,O

Crystal . . 714 748 1036 -

soln. . - 719 757 1024 1048

Crystal . * 730 - 1046 I057

Crystal . * 716 738 I044 I054

16 N soh. - (716) 751 I034 (1050)

1422 - - 1416 -

I440 -

- I

- 1428 - I424 - -

- 1408 - I370 - -

I405 - I 480 1381 1440 1498

- 1468 - I444 - -

ZINC NEODYMIUM NITRATE, Zn,Nd,(NO,),, . 2 4 H,O * 2-5 N soh. . 716 746 - 1048 - - Crystal . * 719 749 1041 I045 - - - - -

* In this case, the selective absorption of the Nd+++ ions does not permit the determination of the frequency of the bands situated in the region 1300-1400 cm.-l for the solution.

cerium allows the conclusion, for example, that the crystal lattice con- tains at least two families of nitrate ions, whose surroundings do not possess the same symmetry. These structural details are found in the saturated solutions, certainly for the copper salt and probably for that of cerium. On the other hand, the line Avl which is still present, though feeble, in the concentrated solutions of Th(NO,),, has disappeared in the spectrum of the crystal.

Naturally, the regular surroundings which we assume for the nitrate ions has a statistical character ; there are important instantaneous fluctu- ations about the mean distribution of the ions and molecules. This ex- plains the fact that the Raman lines always have a much greater width

Publ

ishe

d on

01

Janu

ary

1950

. Dow

nloa

ded

by U

nive

rsity

of

Mic

higa

n L

ibra

ry o

n 30

/10/

2014

01:

17:4

7.

View Article Online

206 METALLIC NITRATES for the solutions than for the crystals (Fig. 4). In particular, the width of the high frequency bands in the copper nitrate solutions (cf. Fig. 2) can mask the splitting into lines which one observes in the crystal.

(iii) Prins 22 emphasizes that his conception of the state of solutions is quite opposed to that which envisages microscopic nitrate crystals dispersed in a disordered medium.as From our experiments, it is not possible to draw such definite conclusions : where quantitative measure- ments are available, it is found that the ratio of the intensities of the lines is not always the same in the crystal as in the saturated solutions. For instance, the ratio 0 has the following values * :

Ca(NO,), : Solution (16N) 1.8 ; Crystal (16.1N) 2.2. Th(NO,), : Solution (16-3N) 2-5 ; Crystal (2oN) - 5.

It is hardly possible to tell whether such differences are due to the in- fluence of the fluctuations in the liquid state or to the superposition of the spectrum characteristic of the crystal on that of the solution.

(iv) In addition to the lines characteristic of the complex ions or molecules, there appear in the diffusion spectra of ionic or molecular crystals, " external " lines corresponding to oscillations of the lattice, in the course of which the ions or molecules execute translational or rotatonal vibrations.261 27 The spectra of hydrated nitrates are rich in such whose frequency varies from 40 to zoo cm.-l (13 lines for aluminium nitrate, 12 for the double nitrate of zinc and neodymium), see also Fig. 7. These external lines are not found in the spectra of any of the solutions. Doubtless the reason is that because these vibrations bring forces or couples of interionic or intermolecular attraction into play, their frequencies are sensitive to fluctuations in density; and as these lines are numerous, their increase in width is sufficient to obscure them in a continuous spectrum.

Interpretation of the Influence of the Various Factors.-(i) The effect of the elevation of temperature on the Raman spectrum of the solutions studied shows that the modification of the nitrate ions by the increase in concentration is accompanied by an absorption of energy AU. The change in heat content

may be calculated from the data of Table VIII, by means of the van't Hoff equation :

A?€ = AU - T A S

A H = R J ' T 2 -?&- - T, ' (loge K1 - loge K2)

where For Th(NO,),,

In principle, one might attempt to evaluate AH theoretically for a given solution from the difference between the heat content of the quasi- crystalline state and of the disordered state. But certain of the necessary data, such as the lattice energy and the heat of fusion are unknown; others, such as the mutual potential energy of the ions in solution, are difficult to calculate correctly; only the energies and entropies can be estimated. Theimer,6 who has attempted some calculations of this type in the hypothesis of an incomplete dissociation, recognizes that they are too uncertain to justify their use.

K = n'/n = I'/I. AH = - 1200 cal./mole.

* These values are only approximate, because they refer to a single crystal

25 Mathieu, Spectres de vibration (Hermann, Paris, 1945). 26 Stewart, J . Chem. Physics, 1934. 2, 147. 27 Rousset, La diffusion de la lumiBre (Gauthier-Villars, Paris, 1947). 28 Mathieu, Compt. rend., 1949, 229, 1068. z9 Bernal and Fowler, J . Ckem. Physics, 1933, I , 515.

in a given orientation and may vary with the orientation.

Publ

ishe

d on

01

Janu

ary

1950

. Dow

nloa

ded

by U

nive

rsity

of

Mic

higa

n L

ibra

ry o

n 30

/10/

2014

01:

17:4

7.

View Article Online

JEAN-PAUL MATHIEU AND MACKENZIE LOUNSBURY 207

(ii) The action of electrolytes having an ion in common with the nitrate studied (Table VI) may. be interpreted as that of an increase in concentration. As for the influence of foreign electrolytes (Table VTI), which is contrary to the hypothesis of an incomplete dissociation,ls it acts in an indirect manner, and one can think that it favours the approach of a nitrate ion to a cation by. dehydrating them. We have observed, in fact, that this influence is stronger for LiCl (small cation, strongly hydrated) than for CsCl (voluminous cation, weakly hydrated).

Laboratoire des Recherches Physiques, Sorbonne,

Paris.

Publ

ishe

d on

01

Janu

ary

1950

. Dow

nloa

ded

by U

nive

rsity

of

Mic

higa

n L

ibra

ry o

n 30

/10/

2014

01:

17:4

7.

View Article Online