WENDELLId.LATIMER AND WILLIAML. JOLLY
154% [CONTRIBUTION FROM
THE
VOl. 75
DEPARTMENT OF CHEMISTRY AND CHEMICAL ENGINEERING AND RADIATION LABORATORY, OF CALIFORNIA ] USIVERSITY
Heats and Entropies of Successive Steps in the Formation of AlF,--BY WENDELL AT. LATIMER A N D WILLIAM L. JOLLY RECEIVED OCTOBER 27, 1952 The heats of the six successive reactions of F - with A1+++ to form AlFe--- have been measured. These values with the equilibrium constants permit a calculation of the entropy change in each step. These values are ASP = 32, AS; = 26, AS: = 18, AS," = 13, A Z *= 5 and AS," = -3 cal./deg. mole. The magnitude of these values is discussed with respect to two fundamental factors and compared with the entropy of formation of other complex ions.
The six constants for the formation of AlFs--have been determined by Brosset and Orring.' Hence measurement of the heats of these reactions permits a calculation of the successive entropy changes. There are not many reliable data in the literature for the entropies of formation of complex ions, and the values which we have obtained for the aluminum fluoride complexes add considerably to an understanding of the various factors involved. Experimental Procedures The calurimeter used in this investigation has been described elsewhere.2.3 For the runs involving high concentrations of fluoride, the glass surfaces were coated with a thin layer of "Dri-Film" (dimethyldichlorosilane). Samples were contained in small glass bulbs and were introduced into the calorimetric solution by breaking the bulbs with a glass rod. All heats were measured a t 25 f. 1"and are reported in terms of the defined calorie (1 cal. = 4.1833 int. joule). The uncertainty in the heats measured is zt 0.1 calorie. The aluminum solutions were made up from reagent grade aluminum nitrate and measured amounts of standard nitric acid. The solutions were analyzed for aluminum by precipitating and igniting aluminum hydroxide. C.P. sodium fluoride was dried for 1.5 hours a t 130'. A stock solution of sodium fluoride was prepared by dissolving a .weighed amount of the solid and diluting to a known volume. A standard solution of ammonium fluoride was prepared by neutralizing reagent hydrofluoric acid with standard ammonium hydroxide. The ammonium fluoride solution used in run 19 was prepared by dissolving a weighed amount of reagent grade ammonium fluoride. The Heat of Solution of Sodium Fluoride in Water and in Aluminum Solutions Two measurements of the heat of solution of sodium fluoride in water were made. The details of the two runs are given in Table I.
Table 11. Brosset and Orring* and Kleiner4 have observed that a t low fluoride concentrations, the system Al+++-Fis very slow in attaining equilibrium. However, in the runs described in Table 11, there were no unusual lags in the absorption of heat. The reactions were calorimetrically complete in about four minutes.
TABLE I1 THEDISSOLUTION OF NaF IS A1 + + + SOLUTION
NaF, 6 .
1
1 ,063 1,759
8
+
TVater, g .
A H , cal./mole
1064
391
1042
297
Several measurements of the heat of solution of sodium fluoride in 1047 ml. of a solution 0.00973 JC in Al(S0p)s and 0.0011 M in HXO3 were made. The reactions were endothermic when less than 1.9 g. of sodium fluoride were dissolved, but exothermic for larger amounts of sodium fluoride. ( A fine precipitate, presumably some complex of AlFI and S a F , formed in the exothermic reaction. Since the composition and heat of precipitation of this precipitate are unknown, the results of the exothermic reactions are not reported.) Details for the endothermic runs are given in (1) C. Brosset and J. Orring, Pderzsk kem. Tid., 55, 101 (1913). (2) €3. J. Fontana, Tational Nuclear Energy Series, IV-IQB, McGraw-Hill Book Co., Inc., iYew Vork, N . Y . , 1050, p. 321 (3) €1. 11'. Zimmermann and U'. A f , I.atilner, TIils J U U K N A L , 61, 1550 (1939).
XaF, g.
Calories absorbed
2 :3 4
0.0970 ,8225 ,3160 1.262
3.09 23.78 9.98 30.97
7
The Heat of Mixing Al+++(aq)and F-(aq) A series of calorimetric measurements were made in which 4.983 ml. of a solution 0.983 M in AI(N03)s and 0.0098 M in HK03 were mixed with 1047 ml. of aqueous fluoride solution of varying concentrations. The details are given in Table 111. TABLE IrI HEATOF MIXINGAI+++A N D FRun
10 11 12 13 11 19 21
Total fluoride, mole
Calories absorbed
0.00620 S a F ,0155 XaF
2.16 5.42 5.74 3.63 5.35 1.28 0 . 95
,0310 NaF ,0975 PiH4F .01951 NH4F ,1919 KH4F .1951 NHiF
In order to correct the heats for the heat of dilution of M Al(iX03)(, it was necessary to measure the heat of mixing of 4.983 ml. of the solution 0.983 M in Al( Noah and 0.0098 M in H N 0 3 with 1047 ml. of dilute aqueous Hr\;Oa. The details are given in Table IT'. 0.983
TABLEI V HEATO F DILUTION O F AI( r\;Os)a
TABLE I THEDISSOLUTIOX OF S a F I N WATER We takc A H o = 294 + *5 cal./mole for wdF(s) = S a + ( a q ) Run
Run
Run
Final molarity of HNOI
Calories evolved
9
0.00464
15
,00446
4.84 3.10 4 . 9 7 i 0.15
Average
Calorimetric experiments showed that the mixing of 4.983 nil. of 0.0)98 d1 H X 0 3 with 1047 ml. of aqueous fluoride involved a negligible amount of heat.
Calculations The data presented in Tables I-IV may be used to calculate the heats for eleven reactions of the type Al+3
+ xF-
+
+
+
x1AlF+2 x*AlFZ+' . . . xdlFe-3 ( X - XI - 2x2 . . . -6xc)F-
= xoAl+3
+
For each reaction, the coefficient x may be obtained from the experimental data. The coefficients xn, ( 4 ) K. IC, Kleiner, J . Geii. Chein. U.S.S.R., 20, 1809 (1950), Consultants Bureau Translation.
1549
HEATSAND ENTROPIES ON FORMATION OF AlFs---
April 5, 1953
which add up to 1, may be calculated from the complexing constants at 25' reported by Brosset and Orring.' We shall report our heats using a function a, which is the number of complexed fluorine atoms per aluminum atom, or the total concentration of complexed fluoride divided by the total concentration of aluminum. In Table V and Fig, 1 we have tabulated and plotted the heat absorbed per mole of aluminum as a function of fi (for the general reaction discussed above).
I
I
I
I
I
I
TABLEV Run
?z
Cal. absorbed per mole AI
2 3 4 7 10 11
0.227 1.919 0.739 2.908 1.265 3.045
240 1770 760 2170 1460 2120
Run
n
Cal. absorbed per mole AI
12 13 14 19 21
4.17 4.91 3.55 5.20 5.20
2190 1750 2110 1275 1210
Fig. 1.
+
+
reaction H20(bound) NHa(aq) = HZO(1) The smooth curve through the points in Fig. 1 NHa(bound), As0 = -5.5 cal./deg. mole. I n has been calculated using the heats of reaction order to evaluate this ASo we have used the data of summarized in Table VI. Our estimated accu- Hart and Partington@on the entropy of dissociaracies are f50 caI. for reaction (I), f100 cal. for tion of 32 solid ammines to obtain the value 13.5 reactions ( 2 ) , (3), (4) and (5) and k 2 0 0 cal. for cal./deg. mole for the entropy of ammonia bound to a positive ion. The other values, HzO(bound), 9.4, reaction (6). NHjfaq), 26.3 and HzO(l), 16.7, are those given TABLEVI by Latimer.6 Using AS" = -5.5 units per ammonia, we may make the following comparison with THERMODYNAMIC FUNCTIONS FOR ALUMINUM-FLUORIDE the experimental values : COMPLEXES~ AH0
(1) A l + + +4- F -
AIF++ (2) AIF++ F - = AlFz+ (3) AIFz+ F - = AlFs(aq) (4) AIFs(aq) f F - = AIFP(5) A l F d - f F- = AlFaC(0) AIFs-- f F AlFs--AI+++ 6F- = AlFs---
+ +
2
1150 780 190 280 -750 -1550 100
AFO
AS0
Charge effect
-8370 -6850 -5250 -3740 -2220 -640 -27070
32 26 18 13 5 -3 91
18 12 3 -3 --I1 -19 0
+ +
Exptl.
AS0
Ag+ 2r\j& = Ag(NH3)2+ -11.9 f 0 . F CU++ 4NH3 = CU(NHD)~" -18 f 38
Calcd
-11 -22
I n view of the approximate nature of the entropies of the bound molecules, the agreement is sufficient to indicate that this is the prineipal factor in the + entropy of formation of these ions. The A F o values were measured a t an ionic strength of The second factor in the entropy of formation 0.50, whereas the A H o values were measured a t ionic strengths from 0.06 to 0.2. of complex ions is the effedt of a change in total charge on the ion by the addition of a charged ion. Discussion of Results In the case of the ammonia complex ions discussed There are two general factors which determine above, this effect is zero since the ammonia molethe entropy change in complex ion formation: cule is neutral. However, in the formation of (1) the entropy change involved in replacing a water aluminum fluoride complexes, the charge changes molecule bound to the aqueous ion' by the complex- from + 3 in AI+++ to - 3 in AlFe---. Powell and ing ion or molecule; (2) the effect upon the sur- Latimere have shown that for monatomic ions the rounding water of changing the charge on the ion. partial molal entropies may be represented by an Fur the first factor, we have in the case of complex equation which contains the term -270Z/(r x)~~, ffuurides where Z is the charge, r the crystal radius in A. units and x is 2 for positive ions and 1 for negative HtO(bound) F-(aq) = HtO(1) F-(bound) ions. This term represents the decrease in partial ASo = 15.6 cal./deg. mole molal entropy due to the tying up of water by the This A s 0 has been calculated using the values (in interaction of the charge on the ion with water cal./deg. mole) of 9.4 for bound water, - 2 . 3 for dipoles. F- (aq), 16.7 for H,O(I) and 6 for F- bound to the The agreement for the monatomic ions is exaluminum. These values, previously given by cellent, but the quantitative application t o complex Latimer,5 are only approximate since the entropy ions fails because in general the total charge on the uf the bound water and fluoride will vary somewhat ion does not represent the effective charge for the with the charge on the ion and with the coordina- solvent molecules in contact with the ion. Howtion number, but they do give the magnitude of (6) A B Hart and J R. Partington, J. Chem. Soc , 1943, 104. the entropy change associated with this process. (7) W.V Smith, 0. L. I. Brown and K S. Pitzer, THISJOURNAL, 89, As an example of the reliability of such calcula- 1213 (1937). (8) Calculated from the thermal data of Bouzat, A n n . chim. p h y s . , tions we may cite the entropy changes in the forma[7L119,305 (1903),and the equilibrium constants given by J. Bjerrum, tion of Ag(NH&+ and Cu(NH3)4++. For the Ckem. R e v s , 46, 384 (1950).
+
+
+
(5) W.M.Latimer, "Oxidation Potentials," 2nd edition, Prentice Hall, Inc., New York, N. Y.,1952, pp. 37, 52, 363.
(9) R . E. Powell and W M. Latimer, J. Chem P h y s . , 19, 1139
(1951).
ROBERTL. SCOTT
1550
ever it is of interest to use our data for the aluminum fluoride complex ions to evaluate the charge effect for this series of reactions. For the over-all reaction A1(Hz0)6++* GF- = AlFs--6H20, A S o = 91. In our discussion above, we calculated 15.6 entropy units for the replacement of a water molecule by fluoride. For six fluorides this would be 93.6. The agreement with the experimentalvalue of 91 is, of course, accidental but the calculation does show that in this case the charge effect is small. From the Powell and Latimer equation, one would predict about -15 for the effect since in general the solvation of negative ions is greater than positive ions because of the smaller value of x and the radii of Al(H20)!+++ and AlFs--- are about equal. It is not surprising that the hydration of AlFs--- is less than that predicted by the equation, as the effective charge on the surface of the ion is doubtless less than - 3. In the last column of Table VI the charge effect has been calculated for each step by subtracting the replacement entropy from the experimental entropy. I t will be noted that the charge effect is symmetrical about the neutral molecule, again indicating that the effect is the same for the positive
+
+
[CONTRIBUTIOX FROM THE
DEPARTMENT OF
Vol. 75
and negative ions. At present we have no method of estimating the hydration entropy for ions such as AlF++ or AlFZ’, but the values calculated in Table VI form a basis for future comparisons. The recent work of Jonte and Martinlo on AgCl and AgClz- may be employed for such a comparison. These authors give
+
Ag+ C1- = AgCl(aq) AgCl(aq) C1- = AgC12-
+
ASo = 5 AS0 = 5
Using 10 for the entropy of bound C1- in AgCl and 11 for the value in AgClz -, we calculate the replacement entropy as 4 for the first reaction and 6 for the second. The charge effect thus is 2 for the first and -1 for the second. These values are to be compared with 3 and - 3 for the corresponding reaction of A1F2+ and AIFa with F-. One would not expect that the charge effect would be exactly the same for ions of different size, such as AgC1,and AlFI-, but the agreement appears to confirm our interpretation that the contribution from the charge effect is small for reactions of this general type. (IO) J. H. Jonte and D. S. Martin, THISJ O ~ R N A L ,‘74, 2052 (1952).
BERKELEY 4, CALIFORNIA
CHEMISTRY, UNIVERSITY OF CALIFORNIA AT L O S AXGELES]
The Acid Strength of Halogens BY ROBERT L. SCOTT RECEIVED SOVEMBER 3, 1952
A consideration of the free energy of trihalide ions shows that the halogens can be classed as Lewis acids (electron acceptors) with decreasing acid strength as: IC1 >> BrCl > IBr >> 12>Br2 >> Cln, a classification which agrees with measurements on halogen complexes with aromatic hydrocarbons as well. A calculation of the free energy of isomerization of trihalide ions illuminates the fact that only those trihalide ions which have the heaviest atom in the middle position are known.
The molecular coniplexes between aromatic hydrocarbons and halogens which have been the subject of much interest in the last few are generally accepted to be examples of Lewis acidbase interactions in which the benzene, etc., acts as an electron donor (“base”) and the halogen as an electron acceptor (‘‘acid’]). Of the three halogens whose complexes with benzene and other aromatic “bases” have been studied, IC1 is the strongest “acid,” followed by I2 and then Brz. This general rule is illustrated in Table I, which gives equilibrium constants4s6for the reaction Ar
+ X? = Ar.&
TABLE I EQUILIBRIUM CONSTANTS FOR COMPLEX FORM4TION
KO in liters/mole CCI, solution a t 25’
Base -+ Acid
Benzene
I c1
0.54 .15 .11
I2
Bra
+Xylene
1.51 0.31 .23
Hexamethylbenzene
Naphthalene
22.7 1.35
1.39 0.25
since IC1 is a stronger acid than I-. As a result, the stability of the trihalides is usually discussed in terms of a number of empirical rules.’ This difficulty is resolved when we recognize that an unsymmetrical trihalide ion can be formed (and conversely, decompose) in two different ways
The formation of trihalide ions can also be reKl K2 garded as a similar complexirig reaction between a x-Y z- _r [X-Y-z1-; x- + Y - z If [X-Y-21halide ion (base) and a halogen molecule (acid). Superficially, however, no regularity is found ; The equilibrium constant K1 measures the acid for example, Is- is the stablest trihalide ion, al- strength of XU and the base strength though we might expect IzCl- to be more stable of Z.-; K z , on the other hand, measures the acid strength of YZ and the base strength (1) H . A. Benesi and J. H. Hildebrand, THIS JOURNAL, TO, 2832 of X-. The experimentally reported values are (1948); 71, 2703 (1949). (2) R. S. Mulliken. ibid., 73, 600 (1950): 74, 811 (1952). invariably for the reaction with smaller K ; the (3) T. M. Cromwell and R. L. Scott, ibid., 72, 3825 (1950). other one can however be calculated by standard (4) R. M . Keefer and L.J . Andrews, ibid.. 73,4677, 5170 (1950). thermodynamic methods if the free energies of C S ) N. W. Blake, H . Winston and J , A. Patterson, ibid., 79, 4337
+
(. 1951)
.
( 6 ) L. J, Andrews and R M. Keefer, t b r d . , 74, 4600 (1952).
( 7 ) See, for examide, X. V . Sidpwick, “ T h e Chemical Elements and Their Compounds.” Vol. 11, Oxford University Press, pp. 1190-1197.
