A040
LEONARD I. KATZINA N D
JOHN
R. FERRARO
VOI.
74
[CONTRIBUTION FROM THE CHEMISTRY DIVISION,ARGONNE NATIONAL LABORATORY ]
Heats of Solution of the Cobaltous Nitrate Hydrates in Water and in Certain Organic Solvents and Binding Energies of Molecular Ligands’” BY LEONARD I. KATZIN AND
JOHN
R. FERRARO
RECEIVED MAY2, 1952 Heats of solution have been measured for the hexahydrate, tetrahydrate, trihydrate and dihydrate of cobaltous nitrate in water and in a series of organic solvents, including isobutyl alcohol, diethyl and monoethyl ether of ethylene glycol, acetone, methyl ethyl ketone, tetrahydrofuran, tributyl phosphate and dimethylformamide. For some solvents, where the solubility of the salt or its reaction product was insufficient, measurements were made in admixture with acetone. Such solvents include diethyl ether, tetrahydrofurfuryl alcohol and pyridine. Measurements were also made with mixtures of the other solvents cited and acetone. In the cases of pyridine, water, tetrahydrofurfuryl alcohol and isobutyl alcohol, evidence is found for a transition from a probably tetrasolvated neutral molecule in solution to a hexasolvated entity, frequently of lowered solubility. The solvents can be arrayed in order of base strengths on the basis of the heat measurements, and it is possible to estimate energies of binding of solvent groups by the metal atom. As a check on these, some measurements uf the heats of solution of some cobaltous nitrate pyridinates are also presented.
With the accumulation of evidence that a number of inorganic salts may be as soluble in organic solvents of the types alcohols, ethers, ketones and e s t e r P as they are in water, the way is open to studying these systems to establish the nature of the interactions between solute and solvent in essentially non-ionizing media. In special cases i t has been possible to obtain information on molecular and ionic interactions from spectrophotometric i n ~ e s t i g a t i o n . ~ -A~ start toward obtaining data on the energetics of the interactions has been made by measurements of the heats of solution for the uranyl nitrate hydrates in a series of solvents*; this is being continued by similar measurements with the hydrates of cobdtous nitrate, to be reported in this paper. Experimental The procedures used in the heat of solution determinations were those used in the prior work on uranyl nitrate? a weighed portion of salt was dissolved in 200 ml. of solvent contained in a dewar flask. Temperatures were followed with a calibrated Beckmann thermometer. Heat capacities were determined through electrical heating with a calibrated nichrome heater. Salt-to-solvent mole ratio in water was 1:180, and in the organic solvents about 1:80. The cobaltous nitrate hydrates were prepared from commercial chemically pure salt by recrystallization of the hexahydrate, and dehydration of the hexahydrate to the lower hydrates. The crystals of hexahydrate were analyzed, ground in a ball mill and reanalyzed, and then maintained in a closed vessel. In some cases, lower hydrates were prepared by desiccation of the hexahydrate over sulfuric acid; in others, tetrahydrate and trihydrate were prepared by melting the higher hydrates and removing water under xicuum a t temperatures below the melting point of the desired hydrate. Composition of final products was nlw:tys checked by analysis a t time of heat measurements. Water contents of the salts and of the solvents were checked by Karl Fischer titration. The commercial pure solvents were desiccated before use. Cobalt analyses were performed by a standard electrodeposition procedure. With agreement between duplicate cobalt analyses of 0.8-0.9 part in 100, and in water analyses of 0.5-1 part per 100, it is esti( l a ) Presented in part at Cleveland Meeting, American Chemical Society. April 9-12, 1951. (1) L. I. Katzin and J. C. Sullivan, J . Phys. Colloid C h c m . , 65, 346
(1951). ( 2 ) L. I. Katzin and J. R . Ferraro, THISJOURNAL, 72, 5461 (19.50).
(3) L. I. Katzin and J. R. Ferraro, ibid.. 74, 2752 (1952). (-1) I,. I . Katzin and E. Gebert, i b i d . . 72, 5455 (1960).
(A) I,. I . Katzin and E. Gebert, ibid., 79, 5484 (19.50). ( 6 ) I.. I. Katzin and E;. Gebert, ibid., 72, 5669 (l9S0) (7) L. Kaplan, R. A. Hilriebrandt and M , M e r , Reports ANI.4520. 4521 (unclassified). (1950); 4 0 C I 1 Nos. 2920, 3015. (8) I-. I. Katzin, I.,. L f . Sini.‘ h i t s J O U X N A I . , 74, 1191 (1952).
mated that 5 mole % of another hydrate might be overlooked in one of the lower hydrates, and 2 mole % in the hexahydrate. These might produce an error of 0.03 kcal./ mole in a single heat determination with the hexahydrate, and 0.2 kcal./mole for one of the lower hydrates. Duplicate heat determinations generally checked a t least this well. Calculation of the heat for the transition CO(NOa)g+6HgO(c) CO(NOs)*.2H20(~) 4H20(1) from the heats of solution of hexahydrate and dihydrate (Table I ) and the values in the third column of Table I11 gave heats (with the exception of tetrahydrofuran) ranging from 0.72 kcal. greater than the 10.24 kcal. value of the heats of solution in water to 0.77 kcal. less than this value, with a mean of 0.55 kcal. This is perhaps a little greater variation than might be expected, even though three experimental heats (one multiplied by 4) are involved, and may indicate the intrusion of some relatively slow reaction (hydrolysis, or reaction between nitrate and the organic solvent) between salt and solvent. In the case of uranyl nitrate,* where the chances of reaction are more apparent (more ready hydrolysis, possible reduction of U( V I ) to U(IV)), the corresponding variation is larger, and in the case of cobaltous chloride (unpublished data), with smaller reaction possibility, somewhat smaller. The aberrant tetrahydrofuran value has no ready explanation. Heats of Solution.-The results of measurements with the solvents water, dimethyl formamide, mono- and diethyl ether of ethylene glycol, tetrahydrofuran, tributyl phosphate, acetone, methyl ethyl ketone and isobutyl alcohol are given in Table I. Tests were also made with methyl
+
TABLE I HEATSOF SOLUTION OF THE COBALTOUS NITRATEHYDRATES IN ~ ‘ A T E R A N D IN VARIWJSORGANIC SOLVENTS (KcAL.! MOLE)
Water hlonuethyl ether of ethylene glycol Isubutyl alcohul
-5.28
-0.98
- G -56 -1.28
-2.52 4.85
-1.24 6.81
-4.89 -4.30 -1.65 0.30 -4.74 -17.76
0.94 -0.62 4.28 6 OR 0.99 -15.44
3.73 3.24 6.82 8.44 2.15 -12.76
3.50
4 !Ki”
0.2.5 8 77
Diethyl ether of ethylene glycol
Tetrahydrofiiran Acetone Methyl ethyl ketone Tributvl phusphate Dimethyl formamide
4.!i(lb
4.28 7.7V
10.12 5.16 -1Z.W
Thornsen, “Thermochemischen Untersuchungen,” also gives 4.96, according to reference 16. * Calculated from s o h t ion analysis; solid incompletely dissolved. a
isobutyl ketone, tetrahydrofurfuryl alcohol, diethyl ether and ethyl propionate, but the solubilities in the pure solvetits were too limited for satisfactory measurement. In a few cases, heats of solution could be calculated, when solution of the salt sample was sufficiently complete, by analyzing the liquid phase. This procedure gave -9.S4 kcal./ rnule for the dihydrate in tetrahydrofurfuryl alcohol, anti
HEATSOF SOLUTION OF COBALTOUS NITRATE HYDRATES
Dec. 5, 1952
5.52 kcal. and -2.28 kcal., respectively, for the trihydrate and dihydrate in methyl isobutyl ketone. Though they seem reasonable as t o order of magnitude, these values must be regarded with caution since there is reason t o believe that the solid phase in contact with the solution was not of the same composition as that originally added. Previous experience with salt-water-organic solvent systems'-* suggested that insolubility in the solvents indicated was probably related t o hexasolvate formation, either with the solvent, water or both. Dilution of the solvent t o be tested with a weak base solvent in which water is highly soluble (c.g., acetone) might be expected to give better solubilities. The expectations were realized, and measurements were made with cobaltous nitrate dihydrate and a series of mixtures of other solvents with acetone. The results, in terms of volume %, are shown in Table 11, and in mole % are plotted in Fig. 1.
6041
Molal Heats o f Solution of C o ( N O 3 I 2 2 H,O i n Mixtures of Various Liquids with Acetone
20-30
E
TABLE I1 HEATSOF SOLUTION OF COBALTOUS NITRATEDIHYDRATE IN MIXTURESOF ACETONEWITH OTHERSOLVENTS ( KCAL./ MOLE) Second solvent Water
VOl.
%
Isobutyl alcohol
Tributyl phosphate
Tetrahydrofuran Ethylene glycol diethyl ether
0.3 1.3 2.9 5.6 13.1 20.5 25 50 75 87.5 25 50 75 95 5
5o 87.5 25 50 75
Second solvent Pyridine"
AH
-1.65 -4.42 -8.54 -11.42 -13.46 -11.57 -4.20 -3.90 -3.70
Dimethyl formsmide
-3.04
-1.79 -2.00 -3.31 -4.26 2.19 -3.75 -4.23 -2.40 -8.07 -3.48
-
Ethylene glycol monoethyl ether Tetrahydrofurfuryl alcohol Diethyl ether
Vol.
%
2" 2 12.5 25 30 37.5 25 50 75 25 50 75 25 50 75 25 50
AH
- 9.51 -14.39 -16.31 -17.61 -17.73 n "
-9.35 -12.92 -15.54 -4.14 -5.60 -6.00 -6.18 -8.19 -8.91 -2.10 a
Sa1t:solvent = 1:200 instead of 1:M. bSa1t:solvent Co(NOa)*.6Py precipitates. Incomplete solubility or precipitate formed. 0
= 1:100.
It had been shown, in earlier experiments with uranyl nitrate,' that the heat of reaction of water with a lower hydrate (e+, the dihydrate) in an organic solvent afforded a measure of the order of base strengths of the solvents so tested. The results of a similar series of measurements for solutions of cobalt nitrate dihydrate in organic solvents are shown in Table 111. TABLE I11 HEATOF REACTION OF WATERWITH COBALTOUS NITRATE DIHYDRATE IN VARIOUS SOLVENTS AH.
water'to pure
Solvent
solvent (kcal / mole water)
AH,
water to dihydrate soh.
(kcal./ mole water)
-0.96 Dimethyl formamide -0.74 .14 - .26 Tributyl phosphate .51 - . I O Tetrahydrofuran .00 .70 Isobutyl alcohol Diethyl ether of ethylene glycol .08 -80 Monoethyl ether of - .23 - .94 ethylene glycol Acetone .79 - .06 .07 1.09 Methyl ethyl ketone
Mole ratio, water/ salt
Hut
effect
(kcal.) mole salt)
4.0 4.3
0.87
4.0
2.44
4.0
2.75
4.0
2.89
4.3 4.1 4.0
3.04 3.57 4.04
1.7
Apparent Heat Capacities of Solutes.-As in the case of the uranyl nitrate experiments, approximate heat capacity
I
I 0 75
I
I
0.5
0.25
0
mole f r a c t i o n Aceione
Fig. 1.-Heats of solution of cobaltous nitrate dihydrate in mixtures of various solvents with water: I , pyridine: 11, water; 111, dimethyl formamide; IV, tetrahydrofurfuryl alcohol; V, ethylene glycol monoethyl ether; VI, isobutyl alcohol; VII, tetrahydrofuran; VIII, tributyl phosphate; IX, ethylene glycol diethyl ether; X, diethyl ether. measurements for the various solutes appear as a by-product of the heat of solution measurements. The values are appreciably more regular than in the case of the uranyl nitrate salts, and are shown in Table IV. These are rounded
TABLE IV APPARENTHEAT CAPACITIESOF COBALTOUS NITRATE HYDRATES I N VARIOUS SOLVENTS ( CALORIES/MOLE DEG.~ Dihydrate
TetraTrihydrate hydrate
Hexahydrate
Tetrahydrofuran 65 260 280 290 Diethyl ether of ethylene glycol 155 350 570 (760) Monoethyl ether of ethylene glycol 397 440 475 710 315 Isobutyl alcohol (200) 205 235 Methyl ethyl ketone 75 120 170 330 Acetone 165 185 189 220 o Rounded t o nearest 5 calories. Values in parentheses are estimated from single experiments. values (usually t o the nearest multiple of 5) of averages of two determinations, only 5 pairs out of 22 showing a difference greater than 30 cal./mole/deg., and over half differing by less than 20 cal./mole/deg. I n most cases there is little difference between the values for the trihydrate and the tetrahydrate as the solute, and in some cases this may be extended to include the dihydrate. The apparent heat capacity of Co(NOs)*.GHzO in water is about 190 cal./mole deg.
Discussion As in the case of uranyl nitrate dihydrate in the organic solvents,* the order of heats of solution approximates the ordering of the solvents by base strengths, with isobutyl alcohol out of line in appearing to be a weaker base than i t should.
Again, in complete parallel to the prior case, dilution of the alcohol with the weaker base, acetone, shows that the formation of hexasolvate is probably a factor in the discrepancy (Table 11, Fig. 1). Another confirmation of the ordering of base strengths of the solvents is given in the curves of Fig. 1. Here the heat effect of the lowest concentration of added base in admixture with acetone determines the early slope of the curve, and it is seen that in decreasing order of slope the curves are those of pyridine, water, dimethyl formamide, tetrahydrofurfuryl alcohol, monoethyl ether of ethylene glycol and isobutyl alcohol, tetrahydrofuran, diethyl ether of ethylene glycol, diethyl ether and tributyl phosphate. Evidences of the transition from tetrasolvated solute of the type (Co(N03)2S01v4jto the ionized (but not necessarily dissociated) form (CoSolvG)++(KO&- are of two types. In the cases of water and isobutyl alcohol, it is shown by the initial rise from the heat of solution in pure acetone, with increasing mater or alcohol concentration, until a maximum is reached, beyond which the heat of solution falls off with increasing water (or alcohol) concentration. This, as discussed in a previous case,8 is ascribed to the endothermic dissociation process having a larger numerical value than the exothermic solvent association process. The region of the maximum heat value (10-20% water by volume) coincides satisfactorily with the region of spectrophotometrically determined transition4 between hexahydrated and tetrahydrated solute. -4 similar incipient heat maximum is obscured, in the case of pyridine, by the heat of precipitation of solid cobaltous nitrate hexapyridine. The latter process itself serves as indicator of the transition. The formation of a solid on dissolving cobalt nitrate dihydrate in pure tetrahydrofurfuryl alcohol, and its failure to appear in the mixture of 75% alcohol and 25% acetone may indicate that here too hexasolvate is forming.2 In the case of diethyl ether, clean solution occurs with 25% by volume of ether, and a solid phase is left a t 50% by volume. It is not known whether this solid phase is the originally added hydrate or contains another phase. Relative Binding Energies of Molecular Addenda. --Since the solution of a salt such as cobaltous nitrate or uranyl nitrate in an organic solvent contains largely neutral entities which can be designated MX2.4Solv, solution of cobaltous nitrate dihydrate in a weak base solvent should yield species which are largely Co(N0&.2KzO. 2Solv. The difference in the heat of solution of the dihydrate in two solvents is then a measure of the difference in the energies with which two groups of each solvent are bound. For illustration, consider a process of vaporizing the starting solid dihydrate to the ion gas, vaporizing two equivalents of the solvent, and allowing the latter to react with the gaseous cation; then allow the cations and anions to associate to a molecular gas, and dissolve the gas in the solvent. The net thermal equation for the wlution process appears as LfY
with the sum of the energy terms a t the right equal to the heat of solution, AH. The symbols represent the lattice energy of the solid (U), the heat of vaporization of S (Hv), the heat of association of the ionic to the molecular gas (Hd) and its heat of solution (Hs). The binding energy, E , is defined as the energy necessary to dissociate the gaseous cation and the bound S. To the extent i t is true that Hd is a function only of M and X, for the case under consideration, and that H, does not vary significantly with S under the situation postulated, the difference in binding energy per mole for two solvents can be represented by Esl
-
fhJ=
fTv(8,)
- I l v / ~ ,) '/z(AHl
- AHz)
(2)
which, when one removes the heat of vaporization terms by referring to the liquid rather than the gaseous state of the solvent bound becomes the relation stated above. The assumption about Ud while plausible is not immediately open to test. The assumption about H, represents an extrapolation of the generalization that heats of solution of molecular substances are generally small, and in particular that the heat of solution of water in the series of solvents under discussions varies only in the interval from -0.4 to 1.6 kcal./mole, or, if one omits the doubly functional alcohol-ethers, 0.2 to 1.6 kcal./mole (Le., kO.7 kcal.). In comparing two dihydrates, such as cobaltous nitrate dihydrate and uranyl nitrate dihydrate, and the same solvent, we see from equation 1 that the difference in the two heats of solution is AHn - AHb = U , -
L'b
- 2(E. - EL,)+ (Hd H a ) b - (ffd - Ha)a
(3)
Since all but the binding energy terms are characteristic of the pair of salts considered, if the two salts bind a series of given solvents with the same or very similar energies, the difference in heat of solution of the two salts in a given solvent will be constant. In the case of solvents like isobutyl alcohol and water, where hexasolvation occurs to a variable extent, accompanied in the latter case by ionization, a correction would have to be made. Table V shows this relationship for cobaltous nitrate and uranyl nitrate dihydrates. The clustering of the difference values around 6 kcal. is striking. The two solvents showing most deviation, isobutyl alcohol and ethylene glycol monoethyl ether, are alcohols, and it has already been shown that in the case of the former hexasolvate formation occurs. If one compares the maximum heats of solution in mixtures with acetone, as is done for isobutyl alcohol in the last row of the table, the difference is about 6 kcal. again. As will be shown below, i t seems probable that the uranyl ion binds water in the third (and presumably the fourth) coordination position with the same energy as does cobalt; from the evidence of Table V, this is largely true for other solvent groups as well. On the basis of this relationship one might predict that if solution of the cobalt salts in the solvents could be obtained, the heats of solution in ether would be about 4.6 kcal., in methyl isobutyl ketone 0 to 0.5 kcal., and in ethyl propionate approximately zero. I n tetraalcohol one would expect something 2H,O(c) $- ZS{l) = M X ~ ~ H ~ O . ~ S ~ ~ V ( S O I ~ I . hydrofurfuryl ) between 6 and 8.5 kcal., in analogy with the other I T $- 2Hv -3R -?€d -+- Hs ( I )
+
Dec. 5, 19.52
HEATSO F %LUTION
OF
COBALTOUS NITRATEHYDRATES
6043
by 0.345/RIwhere R is an ion-distance parameter this by the approximation that R equals the cube root of the DIHYDRATE AND URANYL NITRATE DIHYDRATE’ mean ionic volume, Le., - A H for - A H for CdN0a)r. UO,(NOI)I* R = 10’/(3 X 6.023 X 1028 X p / M ) ’ / # ( 5 ) Solvent 2Hi0 2HlO (2) - (1) In the case of fluorite, CaF2, for example, the agreeEthylene glycol diethyl ment between R and the Ca-F radius sum is within 6.0 ether 4.90 10.87 1%, affecting the calculated lattice energy to perTetrahydrofuran 6.4 4.30 10.71 haps 0.1%. Diethyl ether .. ... 10.60 From equation (4)one sees that given a specific Tributyl phosphate 10.46 4.74 5.7 gravity for a known salt, its lattice energy is pro6.67 1.65 5.0 Acetone portional to the Madelung constant, and that when 5.98 6.3 Methyl ethyl ketone -0.30 determining the solvent binding energy values for 6.46 Methyl isobutyl ketone .. ... two solvates of the same structure type, by equa6.03 Ethyl propionate .. ... tion (6), the lattice energy difference term is also Ethylene glycol monotherefore proportional to the value of the Madelung 6.56 8.97 2.4 ethyl ether constant. This point is emphasized, since small 8.51 Tetrahydrofurfuryl .. ... errors or uncertainties in the Madelung constants alcohol give only mall effects on the calculated binding 1.3 2.58 1.28 Isobutyl alcohol energies. To such a limit one can therefore make Isobutyl alcoholuse of rather sketchy information on the crystal6.1 4.20 io. 30 acetone mixturesb Data on uranyl nitrate dihydrate from reference 8. structures of the solids involved. It seems significant that of the 2-1 nitrates inb Mixtures giving peak AH values (25% alcohol for cobalt, 50y0 alcohol for uranyl nitrate). vestigated crystallographically (calcium, strontium, alcohols, and in fact the data on mixtures with barium and lead(I1)) all show the fluorite structureIL1even though the radius ratio is below the acetone (Table 11)bear this out. The existence of cases such as this, where direct limit usually taken for that structure (Ca++ racomparisons between salts may be made, is a matter dius, 0.99 A., nitrate, 2.1 A.), while with the chloof pure chance. In other cases, such as the corre- rides one finds a layer structure even for the hexasponding hydrates of cobaltous nitrate and chloride, hydrated chlorides of the alkaline earths” similar although one knows that the binding energies €or to the CdClz and CdIz structures (anhydrous SrClz additional molecular groups in the same coardina- is an exception, showing a fluorite structure). tion positions should be the same, actual values of Nickelous hexammino nitrate and all the hexamthe heats of solution ( e . g . , in water) are different, mino compounds of the halides show fluorite strucand little can be done with respect to general rela- ture. As a working basis for our calculations, i t tionships. This points up the need for absolute val- seems justifiable to assume the fluorite Madelung ues of binding energies for molecular groups. The constant for the hydrated nitrates, even though incomplete studies on the uranyl nitrate hexahydrate heat for a reaction such as structure12seem to indicate that this nitrate does M X ~ . U H P(O c ) = MXi(c) + nHsO) (g) not have the fluorite pattern. can be seen to differ from a true binding energy by Table VI contains density and calculated lattice the difference in crystal energy of the initial and energy values for the hydrates of cobaltous nitrate, product salts. iln essential part of the problem uranyl nitrate and cupric nitrate. The specific therefore is the estimation of lattice energies of gravities of the hydrates have been obtained by salts. In what follows we shall detail a method of pycnometric measurement under xylene. The estimating these energies with a minimum of data, fluorite Madelung constant ( A d = 7.3306) was used and shall show that in the particular case consid- in the lattice energy calculations. Values for the ered the method can be applied successfully to cal- cobaltous chloride hydrates are aIso shown, the culations of binding energies. CdIn layer lattice Madelung constant ( A d = 6.21) Calculation of Lattice Energies.-Equations for being used for these. It should be emphasized a t crystal lattice energy are found in a form in which this point that inherent in this calculation is the molecular volumes, rather than ionic distances, assumption that the binding is largely ionic; this are the parameter. In this form i t is necessary to point will be returned to later. know only the specific gravity and formula weight Absolute Binding Energies.-Consider two solof the substance, in addition to the crystal type, to vates of a given salt, and their solution in the same calculate the lattice energy,pviz. solvent t o the same terminal concentration of L’ = 279.0 ( p / - ? ! f ) ’ / I .Ad (1 - l/n) (4) anhydrous salt. The difference between the two where the Madelung constant appropriate to the heats of solution, on considering a hypothetical case is A d , and n is a number of the order of magni- process similar to that leading to equation (I), tude of 10, related to the ionic repulsions in the is given by the relation derivation of the lattice energy equation. For our AH. - AHL, = U. - ub - (a - b)Hv f ( a - b)E (6) purposes, it is convenient to take the form devel(11) R. W. G. Wyckoff, “Crystal Structures,” Vol. I, Interscience oped by Verwey and de Boer,l0 which replaces l / n Publishers, Inc., New York, N. Y . , 1948; Vol 11, 1951, Chaps VI1 TABLEV
C O M P A R X OF S OHEATS ~ ~ OF SOLUTION OF COBALTOUS NITRATE (in Angstriims). We c h o s e to replace
(9) J Sherman, Chcm R e v s , 11, 93 (1932) (10) E J . W Verwey and J H de, Boer, Rcc. (rqv
(1936),
and X
c h i a . , 65, 431
(12) L. Pallling
(lQ24!,
and R. G. Rickinson, THIS JOURNAL, 46, 1615
6044
1,EONARI)
I. KATZINA N D
JOHN
R. FERRARO
VOl. 74
TABLE VI WATERBINDINGENERGIESOF HYDRATES OF COBALTOUS NITRATE,URANYL NITRATE,C U ~ R I C NITRATEAND COBALTOUS CHLORIDE' Solid
Density
U,
kcal./mole
AHS
kcal /m;leU
Water binding energy, kca1.h
Transition
CO(NO&.GHzO 1.87* 350.8 4.96 Hexahyd + tetra 47.0 CO(NOa)i*4Hz0 2.05 375 * 3 3.50 Tetrahyd trihyd 33.6 CO(N01)1'3H~O 2.24 393.9 -0.98 Trihyd + dihyd 32.7 CO(NOa)n*ZHzO 2.40b 411.8 -5.28 ............... .. UOz(NOi)n.bHeO 2.742' 333.5 5.48 Hexahyd + trihyd 54.0 UOz( NOi)a.3H10 2.93 352.2 -1.66 Trihyd + dihyd 33.7 UOn(N0&*2HzO 3.35 371.7 -5.37 ............... .. CU(NOa)r*6HzO 1.92 361.9 -10.71 Ilexahyd + trihyd 65.8 CU(NO,)~-~HZO 2. 047d 381.0 -2.5 ............... .. C~ClztiHzO 1.924' 322.1 2.85 IIexahyd .-c tetra 50.0 CoCln.4HaO 2.216' 349.3 (-1.0) Tetrahyd + dihyd 64.9 CoC1~.2H~0 2.477' 382.3 -9.85 Dihyd + anhyd 95.8 COClz 3.356' 448.5 -18.4 ............... .. Fluorite Madelung constant (da = 7.33) used for nitrates, layer structure ( A d = 6.21) for cobaltous chloride and its hydrates. b G. L. Clark and H. K. Buckner, THISJOURNAL, 44, 230 (1922), give 1.883 for the hexahydrate and 2.397 for the dihydrate. Reference 12. L. Playfair and J. P. Joule, Mem. Chem. SOC.,2, 401 (1845); 3, 57 (1848). ' G. L. Clark, A. J. Quick and W. D. Harkins, THISJOURNAL, 42,2483 (1920). A. Neuhaus, Chem. Erde, 5,554 (1930). 0 Heats of solution of uranyl nitrate hydrates from reference 8, cupric nitrate and cobaltous chloride from reference 16, except for CoCl2.4H20 which was estimated from values for the nitrate hydrates. Heat of vaporization of water = 10.48 kcal./mole.
TABLE VI1 ENERGY OF BINDINGPYRIDINE TO COBALTOUS ION Salt
Density," g./cc.
U,d kcal./mole
AH$; acetone
AHsJ
HCI
Transition
Pyridinr binding energy, kcal. Acetone HCI
CO(NOa)z6Py 1.25 240.2 16.00 -19.43 Hexa - + t e t r a 54.4 54.6 CO(NOa)i.4Py 1.36 268.7 10.35 - 8.93 Tetra + tri 38.3 .... 39.8 ... Co(NOa)z.3Py 1.47 290.6 - 7.00 Tri + di Co(NOa)n.2Py 1.52 313.2 -5.43 - 5.91 Tetra + di 78.1 80.5 C0Cln.6Py 1.30 211.5 .... -20.1 Hexa + t e t r a .. 53.3 .... - 12 .40b Tetra + di .. 80.1 CoC1*.4Py 1.36 235.9 CoCl2.2Py 1.61 284.5 .... - 7.33b Di + anhyd .. 211.3 .... -18.4" .......... .. ... COClZ 3.356 448.5 " Pycnometrically determined in mineral oil; c o c h value from Clark, Quick and Harkins (1920). * From reference 14. Terminal pyridine formal conFluorite Madelung constant for nitrates, layer (CdI1) for chlorides. From reference 16. centration, 5% by volume. Terminal acidity, PH 2, except 1abt .? values; heat of solution of pyridine in HCl to pH 2, -8.2 kcal./mole (see also reference 14).
...
'
in which the subscripts refer t o the solids with solvation a and b, respectively. The binding energy E is a mean energy for the (a - b) solvent groups involved, since i t may vary from coordination position to coordination position, and in general may be dependent on the other molecular groups bound. In this formulation E represents the energy necessary to dissociate the solvent molecules from the gaseous solvated cation, with the end-products also being in the gaseous state. Coupling the available data on heats of solution and vaporization with electrostatic lattice energy calculations of the type above, values for ( a - b)E are derived for a series of hydrates in Table VI. The first point of interest in the binding energies of Table VI is that where they overlap (dihydrate through hexahydrate) the binding energies for water in corresponding hydration states of the cation in the cases of cobalt chloride and cobalt nitrate check closely. For this comparison at least, the method of calculation of lattice energies introduces an error not appreciably greater than the uncertainty introduced with the experimental specific gravity and heat of solution values, even though the two series of salts are of different structure type. One
can make a similar calculation for the p y r i d i n a t e ~ ' ~ of cobaltous nitrate and cobaltous chloride, using the heats of solution in HC1 to a fixed terminal acidity and concentration, for which the relationship is (nz
- n)E,,
=
(U,,
- U,) + ( m - n)Hv - ( m -
+
n)Hneut (AHrn- AFTn) (7)
where H , is the heat of vaporization of pyridine and H n e l , t is its heat of solution14in HCI. Another experimental procedure is t o dissolve the pyridinates in acetone to a fixed composition in terms of pyridine and cobalt, in which case equation (6) can be used. We have made measurements with both procedures, and the heats of solution have been used to calculate binding energies for pyridine to cobaltous ion. The data in Table VI1 show that the agreement between values obtained for coordination positions 3 through 6 for cobaltous nitrate and chloride check very well, considering the possible errors in the method. The success with the hydrates and pyridinates lends confidence t o deductions from other binding energy relations found in this manner. (13) L. I. Katzin. J. R . Ferraro and E. Gebert. THIS JOURNAL. 74, 5471 (1950). (14) W. Hieber and A. Woerner, Z. Ekktrochcm., 40, 256 (1934).
Dec. 5, 1952
HEATSOF SOLUTION OF COBALTOUS NITRATE HYDRATES
One such relation of interest (Tables VI and VII) is the essential equality for the energy to bind a given group in coijrdination positions 3 and 4. The energy to bind water in the two positions is 33 kcal. each, and for pyridine, 40 kcal. Another interesting value is the energy calculated (Table VI) for the binding of water in the third coordination position of uranyl ion, which is essentially the same as the corresponding value for cobalt. Combined with the assumption that the binding is the same for the fourth coordination position, and the material of Table V and equation (3), there seems to be basis for the assertion that the corresponding energies for binding groups other than water in these two positions are essentially equal for the two cations. On the basis of unpublished data on the specific gravities and heats of solution of the monohydrate and monopyridinate of cobaltous chloride i t seems that although the binding energies for the third and fourth coordination positions are equal, the binding in the first coordination position is most energetic, and that in the second position, while on the order of 60% as large, is still greater than that in the third and fourth positions. Conversion of Relative Binding Energies to Absolute Values.-As a preliminary step, the values of (H, - 0.5 AH)for the heats of solution of cobalt nitrate dihydrate may be tabulated (Table VIII) according to equation (2). With the absolute binding energy known for one of these solvents,
6045
ficulty is twofold: i t is hard to define the heat of solution for either of the two possible reference solvents, water or pyridine, with the precision with which their binding energies can be calculated; and for the apparently reasonable heat values of either, the binding energy calculated for the second is apparently in error.
Thus, the heat of solution curve for the dihydrate in pyridine-acetone mixtures shows -9.51 kcal. for a solution with 2.0 molecules of pyridine per molecule of salt, -14.4 kcal. for the solution with 4 t o 5 pyridines per salt molecule, and a slow change from this t o a plateau of about -17.7 kcal. before precipitation of Co( NO&6Py a t higher pyridine concentrations. From the spectrophotometric data on the chloride,‘ it might be judged that the pyridine addition is almost complete at the stoichiometric ratio of pyridine t o salt, and has proceeded somewhat toward the stage of Co(NOa)z.4Py at the ratio of 4-5 pyridines per molecule of salt. The heat value desired therefore probably lies somewhere between -9.5 and -14.4 kcal.; -17 kcal. is certainly too high. The situation for water is much less clear, although it may be considered that the maximum point in the water-acetone mixtures (-13.4 kcal. a t 13 vol. % water) corresponds to the plateau of the pyridine curve, and is therefore a maximum possible value for the addition of water in the third and fourth coordination positions. The -8.5 kcal. value at 2.9 vol. % water may be analogous t o the -14.4 value in the pyridine series. Because of the variation in point of intrusion of hexasolvation and ionization due t o larger ionic radius, the constant-difference relation of the uranyl nitrate data is no assistance here. The data on isobutyl alcohol-acetone mixtures, free of the dielectric constant influence of water, indicate only that the water value is probably below 11 kcal. The significant point is that no combination of the reasonable values for pyridine and water, with almost identical heats of vaporization, will show a difference approximating the 1 S 1 4 kcal. in the heats of solution that would match a difference in the binding energies of 6 7 kcal. per molecule bound. TABLE VI11 A further limitation is introduced on considering that the BASES TO binding energy for water probably should not be less than ENERGIESOF BINDINGVARIOUSMOLECULAR COORDINATION POSITIONS 3 A N D 4 OF COBALTOUS NITRATE the value for the alcohols, or a value of (H, - 0.5AH) on the order of 14.5. This is satisfied by the -8.5 kcal. AH (KCAL./BOND) value at 2.9 vel.-% water, which is therefore the value used - 1/tAE(x = in Table VIII. Because the -17.7 kcal. value of the pyriMolecular base Hv ffdihyd.a E -X 18.3) dine series certainly includes a water replacement component, the value 14.4 kcal. (for the 4: 1 mole ratio of pyriWater 10.5 4.2 14.7 33.0 dine) is used. This leaves only a 2.6 kcal. difference in the Tetrahydrofurfuryl binding energies for water and pyridine. By an arbitrary 12.2c*d < 4 . 4 x16.6
