Jan Lutzow H o l m
The University of Trondheim, NTH N-7034 Trondheim-NTH, Norway
Enthalpy
As has been pointed out several times in this Journal, the use of energy or enthalpy cycles to show how atomic and molecular energy factors may influence observable chemical factors, is a quite instructive method in teaching inorganic chemistry a t the undergraduate level (1, 2). Thus, valuable insieht can be obtained about stabilities of halides and oxidYes ( I ) , ahout salt solubilities (2, 3), electrode potentials (2). and also about ~ossibilitiesof formation of comoounds containing ions in unusual oxidation states. It will b'shown in this paper how such cycles have been used in the inorganic chemistry course for students of chemical engineering and metallurgy a t the University of Trondheim. History
Inorganic Chemistry Table 1. Calculation of Electron Affinity from the Born-Haber Cycle
Commound
a
-AH,"
Mean 85.2
Table 2.
The first enthalpy cycle demonstrated to the students is the s i m ~ l eBorn-Haber cycle a t O"K. The enthalw .. cycle . leads to1 AH; = S , + ?D,% I , - E x - U,, (1)
-
-
-
+
When eqn. (1) was first derived, the first four terms, AH,", S,, D,,, and I M , were all known quantities; while values for Ex and UBI. were nonexistent. If, by using Born-Haher cycles on a series of compounds with the same anion, one found an approximately constant value for the electron affinity, Ex,this might indicate that the correct lattice energy values had been used for the calculations. A tvnical e x a m ~ l eof this sort of calculation is shown in ~ a b f 1. e Todav reliable data are available for the electron affinity of thk halogens. The values generally believed to he the bext ones are given in Table 2. As the E x values are known, the theoretical lattice energy data calculated from the Boru-Land6 equation (eqn. I), can be compared to the experimental values, calculated from the Born-Haber cycle. This has been done in Table 3. Here the London, or dispersion, energy, UL, has also been taken into account. These forces were discussed by London (4) in 1930. This energy contribution is due to the fact that the forces created by the statistical fluctuation of the electron distribution in an atom induce similar displacements of the charges in the neighboring atoms, thereby leading to an extra attraction between the atoms. In nonpolar molecules, for instance the noble gases, the London forces are the only forces between the molecules. The London energy is given by the term
'/,Dxs I N (kcal mole-?
Utm
-U
8
460
/ Journal of Chemical Educafron
-Ex
Experimental Electron Affinities of the Halogens
- E d k c a l mole-'
F+e-=FCL e- = C1Br + e- = BrI e- = I-
-79.5 -85.5 -80.5 -73.6
+ +
=t2
* 1.5 +1 +1
From Ladd, M. F. C., and Lee, W. H., Prog. Solid State Chem., 1,'37 (1963); 2, 378 (1965). Table 3. Comparison of the Lattice Energy, UBH, Using the Born-Haber Cycle and the Born-Lande Equation, UBL. AH, Cmstal
a
, / * D m AH
Ix
Ex Usx UBCUG Uw kcal mole-1
(Uc0, Um)
Including the dispersion (London) energy, UL.
cally (Um) is very small. One notes that for the silver halides the difference between the two values is large. This disagreement shows that in the silver compounds there is a considerable covalent contribution to the bond. The Born-Haber cycle as presented above is only valid a t O"K, but it can easily be extended to another temperature. The extended Born-Haher cycle a t 298.15"K is
where N = Avogadro's number, C = London energy, a = polarizability, and r = atomic radius. As seen from the last column in Table 3, the difference ~
for most of the alkali halides is about 0-1.5% of the lattice energy, so that the disagreement between the experimental lattice energy (UW) and the one calculated theoreti-
UL
+ 1.2.
X+e-=X-
+
where AHt" = enthalpy of formation, SM= sublimation enM(g), Dx, = dissociation energy Xz(g) ergy M(s) 2X(g), -Ex = electron affinity X + e = X-, I, = ionization energy M M+ e - , and the Borne-Land6 lattice enerw is
S
where S = enthalpy of sublimation of M The cycle gives
+
as AH = AE pAV (first law of thermodynamics) and C, = 5hR for an ideal gas, and one then has AH2,,;=
-u,,,,, + (n + URT
So far the use of Born-Haber cycles for calculating electron affinities, and comparing theoretical and experimental lattice energy data when the electron affinity is known have been demonstrated. A third use of the Born-Haber cycle is for calculating the enthalpy of formation of hypothetical ionic compounds. This will he discussed in some detail. This method of calculation was first used by Grimm and Herzfeld (5) in 1923, and has later been developed further. Consider the hypothetical compound Ne+CI-, neon chloride. If this compound existed, it would certainly have a NaCl structure, with the ionic radius of Ne+ close to that of Na+, probably slightly smaller. The lattice energy could then be calculated, and as the ionization potential of neon is known, AH,+"can be calculated. The result is shown in Table 4, and shows that the compound cannot exist. As AHta(NeC!) = +246 kcal mole-l, an extremely high entropy would he necessary to make AGt" negative (AGio = AH,+"- TAS,"). Table 4. Calculation of the Heat of Formation of NeCI, Compared with NaCl S
NaCl NeCl
'/aDc,l In,
-Eel kcal mole-'
24.0 29.0 118.5 0 29.0 498.2
-85.5 -85.5
-UL -183.5 --I96
or the fluor affinity of boron trifluoride or aluminium trifluoride AH = Y(MF,-) MFdg) + F-(g) = MF-(g) are both examples of complex affinities. The complex, or fluor, affinity of MFdg), Y(MF4-), can he calculated from the cycle dX,O,MF.,
+ S" + $or, 4 s )+ M F ~ i g l f FIE)
A W + F . W + MI=)
I
From this cycle one gets
When the heat of formation and lattice energy of the complex AMF4 is known, Y(MF4-) can be calculated. In calculations of this type, involving complex ions, it is common to use the lattice energy equation of Kapustinskii (7)
a," calc.
where Z = charge, v = number of ions, and r = ionic radius; when the ion is a complex one, the thermochemical ionic radius is often used. The fluor affinity of AlFdg), Y(AIF4-) can also be calculated from the following cycle
-97.5 -+246
One of the most sensational applications of this method of calculation was that used by Bartlett f6), who in the beginning of the 60's, in his laboratory in Vancouver, Canada, synthesized the first noble gas compound, XePtFs. Bartlett first isolated the compound PtOzFs, after a reaction between PtFs and Oz a t room temperature. He discovered that this compound was isomorphous to KSbFs, and that the volumes of the two unit cells were approximately equal. He therefore assumed a structural formula of Oz+ptFs- (oxygen with oxidation number +1/2) for the new compound. He further assumed that the crystal contained the ion Oz+, and that this ion was stabilized by the high electron affinity of platinum hexafluoride. Bartlett Xe+ remembered that the ionization energy of Xe (Xe e - ) is 280 kcal mole->, i.e., approximately equal to that of 0 2 ( 0 ~ 0 2 + + e - ) , 282 kcal molecl, and that the molecular diameters of Xe and Oz are about equal (400 pm). He therefore mixed Xe gas and PtF6 gas a t room temperature, and a new compound was precipitated with the composition XePtFs, as Bartlett had predicted on the basis of the enthalpy cycle. Although later X-ray examinations have shown that the new compound does not have the ionic structure X e + P t F s which Bartlett first assumed, this does not in any way diminish the value of his discovery.
-
-
+
Enthalpy Cycles of Complex Compounds Enthalov can also be used to calculate complex .- cvcles . affinities. The proton affinity of ammonia
which leads to Y(AIF,-) = AH, - AH,
- AH, -AH,
(6:
Here AH1 = 152 kcal (S), AHz = 0 kcal, and AH3 = -76 kca! (9-12). The enthalpy change AH4 must be calculated. This Coulombic bond energy is given by
By using an interionic distance of d = 310 pm in the gas molecule NaAIF4 and n = 9, one finds AH4 = -97 kcal mole-', and the fluor affinity is Y(AIF,-) = (-76 - 152 + 97) kcal mole-' = -131 kcal mole-' This value can be compared to the fluor affinity of BFs(g), -76 kcal mole-l, and shows that in the gaseous state AlFj has a much higher affinity to fluor than does BFB. If one would postulate a stable sodium tetrafluoroalum-
Table 5. Data Used in Calculating the Enthalpy of Formation of NaBF,(s) and NaAIF&)
Com~ound
Nak)
-
--
Enthalpies of reaction (kcal/mole) 2F& M(s) MF&) Na(d MFda) Fk) MF,k)
++
+ F-(g)
+
IN"
-U
AH,"
Volume 51, Number 7, July 1974 / 461
inate NAIF4, in the solid state, with fluorine 4-mrdinated around aluminium, it is now possible to calculate the enthalpy of formation, AHto(NaAIF4) as the complexing energy, AH6 is known. This is done most simply by using the cycle given above. The lattice energy of NaAlF4(s) calculated from eqn. (5) is 145 kcal mole-l (cf. Table 5), using a thermochemical radius of 260 pm for the tetrahedral ion AIF4-. From the enthalpy cycle, eqn. (4). one gets
Using the Kapustinskii lattice energy equation (7)
Illserting the known quantities from Table 5, one finds the enthalpy of the hypothetical compound NaA1F4, which is assumed to he isomorphous to NaBF4, with A1 tetrahedrally surrounded by F. AHf0(NaAIF,(s))= -482 kcal mole-'
and the following data: r(Al+) = 90 pm (assumed value), r(A13+) = 50 pm, r(F-) = 136 pm and r(I-) = 220 pm (Pauling (19)). 11 = 138 kcal mole-', Z2 = 434 kcal mole-l. Is = 656 kcal mole-' (Aylward (18)). and AHsubl (Al) = 77.5 kcal mole-' (13). one finds
leading to
-
AH"= 3UAx U,,
- 2H., - 2 , +I,+ Is
(10)
Using literature data for the enthalpies of formation of NaF(s) and AIFs(s) (13), one finds an enthalpy for the reaction NaF(s) + AIF8(s) NaAIF,(s) tetrahedral
-
of
By differentiation of AH" with respect tor,, one gets AH,,,,
-'+I6 kcd
showing that this compound is unstable. I t is, however, known that a metastable compound NaAlF4 can he made by quenching the gas over a molten mixture of NasAlFe and AIF3 (14). The structure of this compound is known; "AIF4" units are made by AIFs octahedra sharing corners with four other octahedra (151. Holm (16) calculated the moat probable enthalpy for the reaction
-
+
and found
NaF(s) AIFds) NaAIFds) octahedral AH,,,
= 1f 1 kcal mole-' = -4 f kcal mok-'
For the reaction NaAIF,(tetr) = NaAIFLoct) one then finds AH,,,,,
= -15
kcal mole-'
showing that aluminium has a strong preference of octahedral rather than tetrahedral coordination with regards to fluorine. In this connection i t is of interest that aluminium shows a similar preference with regard to oxygen. Calculations by Naprotsky and Kleppa (17) show that the enthalpy of the exchange reaction AI3+(tetr)= A13+(oct) in spinels is - 10 kcal mole-'. Enthalpy Cycles Used to Predict Stabilities of Subhalides
The stability of a subhalide AIX can be discussed on the basis of the enthalpy, AH", for the reaction 3A11X(s)= AI1"X&) 2Al(s) (9) where 111 is the normal valence of Al, and X is F, C1, Br, or I. This discussion is easiest when using a cycle. First one must find an expression for AHo as a function of the following known quantities: The ionic radii, r(Al+), r(Al+),and r(X-), the ionizationenergies Il,Iz, and18
+
AI = A I + + e AI+ = A s + + e-
~ p =+N3+ + e-
I, 12 13
and the sublimation enthalpy of Al(s), AHsubl. The following cycle is used 462
/ Journal of Chemical Education
As r(A13+) < r(Al+), dAW/dr, will be more positive (or less negative) with increasing rx. This means that the probability of a subhalide being formed by the reaction AIX,(s) W ( s )= 3AIX(s) will increase when the size of X is increased. The prohahility of a subbalide being formed is greatest for X = I, smallest for X = F. Thus, for X = F 2 t36) - 669 -4-313 keal mole-I AH" = - 1 5 3 6 ( ~ ~
+
while for X = I AH" =-1536(090
::2,20
+
O,a
2 +
220)
- 659 = -16 kcel mole-I
The calculations show that the formation of a subfluoride, AIF, in the solid phase will be virtually impossible; while a subiodide, All, will be easily formed in an equilibrium between solid A113 and metallic aluminium. Enthalpy Cycles and Molten Salt Equilibria
Enthalpy cycles are also useful in making a quick survey of the equilibria in molten salts. An example of this is the following cycle, valid a t 1273°K. N4F&
+
Na+AlF.(ll
+
ZAlFJa)
~ , ( I %3' ) ?yaAJF.''(l)
T h e cycle gives where the enthalpies of fusion on the right all are known quantities. 05 kcd mole-' (21) AH,(mixture) = 6l.5
*
AHf(Na&J6)= 21.1 f 05 kcal mole-' (22) AHXAIFJ = 113 f 1kcal mok-'(20,21) This gives AHM = +12 z t 3 kcal mole-', showing that this equilibrium is shifted to the left. As there are the same number of species on both sides of the equilibrium, the entropy change will be small, and the Gibbs free energy,
AG, of the reaction will be approximately equal to its enthalpy, AH. Another example of the use of cycles of this type, with gas equilibrium included, is the following cycle, valid a t
= 61 kcal
AH,,(NaF) AH,.,(ALFJ
= (67-11)
AH,
mole-' (8)
kcal mole-'= 56 kcal mole-' (21, 24) kcal mole-' (9-12),
= -78
one finds the calculated enthalpy of vaporization for molten NaAlFl AH..,(NaAIF,) = 39 kcal mole-'
Here AHM can be calculated, as the other quantities are known AH, = 3(6L3f 28) kcal mole-' = 184 + 8 kcal mole-' (12) AH, = 40 + 2 kcal mole-' (23) AH,(Na,AIF,) = 27.1 05 kcal mole-' (22) AH,(AIF,) = 113 f 15 kcal mole-' (20,21)
*
Hence AHM= AH, - 3AH, - AH,(Na,AIF,)-2AH,(AlFa) or AHM= 14 8 kca1 This value is in good agreement with that calculated from the preceeding cycle, namely AHM = 12 + 3 kcal.
*
Enthalpy Cycles and Evaporation Processes Finally it can be demonstrated that also in the case of evaporation processes, valuable information can be obtained from enthalpy cycles. The evaporation from the melt 50 mole % NaF 50 mole % AIF3 will be discussed. The discussion is based on the following cycle.
+
This enthalpy of vaporization has been measured by Kvande f23), who reports AH,., = 38.5 + 2.0 kcal mole-' which is in very good agreement with the calculated value. Hence, it seems possible from a simple enthalpy cycle to predict vaporization of certain molecules from a binary moltensalt mixture. Literature Cited (1) Breuer.L.. J.CHEM.EDUC.. 36.446119591. 12) HsightJ~..G.P.. J. CHEM.EDUC.. 45.42011968). (,.x,i Cihha i~r ~ T R. P and Winnermann.A...l.CHEM. EDUC. , ,~~~~~ (41 London, F . , Z Phys. Chem Ihipzigl, ~ 1 ' 1222(1930). . 151 Grimm. H.G.. and Herzfdd. K. F . . Z Phvs.. 19.141 119231. (61 ~ ~ n ~N . .~P ~tO C t c. .h r m so"., Z I R I I W ~ . (7) K a ~ u ~ t i m k iA. i , F., Quart. Re". ILondonI, 10,283119561. (6) Chao, J.. Thermoehim. Aclo. 1.71 (1970). 19) Sidomv,L.N., Erokhin. E. V..Aklshin. P.A., andKolaaov. E. N..Dobl. Akod Nouk SSSR. 73.37011967l. I101 Sidomv, L. N.. and Kololov. E. N., Z u r Fia. Khim.. 42.2617 119681: R m . J. Phrs Chem.. 42,1382(1968). (11) Sidomv. L. N.. Kolarov. E. N.. and Shol'ts. V. B.. Z u r Fiz. Khim., 42.2620 119681; Russ J. P h p . Chsm., 42.1364(1968). (12) orjotheim. K.. Motzfcldt. K.. and Rae. D. B.. in Edgeworth. T. G. (Editor). "Light Metals 1971, ProceedingsofSympaiaatfhe lWth AlME Annual Meeting," NewYork. 1971, p.223. 113) JANAFThermochemicalTahl~,Clearinghouse. Springfield. Virginia, 1971. (14) Howard. E. H..J.Amer. Chem Soc, 76.2041 119541. 115) Mashovet8,V.P.. Beletskii. M. S.. SkaLswv.Yu.G.,snd Suoboda.R.V.Ak0d. No& USSR. 113,1270l19571. (16) Holm. J.L..Acto Chem Scond.. 27.141011.973l. lnorp. Nvcl C h m . 29,2701 11967). 117) Naurahky, A . andKleppa. O.J.J. 116) Aylward. G. H..snd Find1sy.T.J.V.. "ChemiealDafaBook."2ndEd. John Wile, 'an0"Dam. LOC.. " , uyclney, I J o l . L.. '"The Nature 01 the Chemical Bond." 3rd Ed.. Cornell Univorsit) 1191&.P Prea. NewVmk. 1960. (20) Holm, .I. L.. "Thermodynamic Propertie of Molten Cvolite and other Fluoride Mirturc,"Dr.TherD.TheUniv~rsityofTrondheim.NTH, 1971. (211 Holm. l . L . Hlgh Temp. Sci. l i n ~ r i n t l . F.,ArfoChem. Scand, 27.2M3 11973). (22) J e n ~ ~ e n H o l m , BandGronvold. ., (23) Kusnde. H., "Kiyolill-aluminiumoksyd-bliidiieere fermodynomihk sfudert Wd e inorzanie chemkfrv. The dnmn,rykbmdiinssr "lricTheis. I n ~ t i f u fof ~
.
This cycle gives AH,,(NaAIF,)
=AH,
+ AH,,,(NaF) + AH,v,(AIFJ
By inserting the known quantities
~~
~
~~~
1
~~
."""
.".." d Douglas. T. B., J. P h w . C h s m . 72,475 (19681
Volume 51, Number
7.
July 1974 / 463
