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Stability of transition metal bromide-aluminium bromide complexes in cyclohexane
Journal
of the Less-Common
Metals,
I37
(1988)
35
35
- 41
STABILITY OF TRANSITION METAL BROMIDE-ALUMINIUM BROMIDE COMPLEXES IN CYCLOHEXANE* F. P. EMMENEGGER
and R. RENGIER
Institute of Inorganic (Switzerland)
Chemistry,
(Received
June
University
of Fribourg,
PProlles,
1700
Fribourg
12,1987)
Summary
The equilibrium MBr,( s) + Al*Br,(sln)
constants e
for the reactions
MAlzBrs(sln)
(M = Co, Pd, Hg) have been measured at 298 K in cyclohexane. For M z Cr, Mn, Ni, Cd the equilibrium constants could not be measured but the solubilities of MAl,Brs(s) could be determined and used to calculate the equilibrium constants by means of thermodynamic cycles. The relative stabilities of MA1,Brs in the gas phase, in cyclohexane and in toluene are discussed.
1. Introduction The research dealing with the stability and structure of gaseous metal halide complexes has recently been reviewed by Schser [l] and Papatheodorou [ 21. Best known are equilibria of the type MX,(s) + Al,X,(g)
+
(1)
MAl,Xs(g)
M = alkaline earth metal, transition metal; X = Cl, Br. According to their volatility, MAl,Xs(g) are molecules and therefore they should dissolve in non-polar, poorly coordinating organic solvents. Indeed, it has recently been shown that the equilibria MBr,( s) + AlzBr,(sln)
C
MAl,Brs(sln)
(2)
(M = Cr, Mn, Co, Ni, Zn, Cd) can be studied in toluene [3]. Despite the close analogy between eqns. (1) and (2) the formation constants of MAlzBrs(g) and MAl,Brs(sln) are quite different, e.g. for M = Co, AG&,, (1) = 29.6 kJ mol-’ while in toluene AG& (2) = 2.4 kJ mol-‘. The thermodynamic cycles of Fig. 1 show that the difference is due to the difference of the free energies of solvation of Al,Br,(g) and CoAl,Brs(g). In the case of toluene the solute*Dedicated 0022-5088/88/$3.50
to Professor
Harald
Schtifer
on the occasion 0 Elsevier
of his 75th
Sequoia/Printed
birthday. in The Netherlands
36
A12Br6(sln)+ MBrz(s)Fig, 1. Thermodynamic
%q
cycles for MA12Brs.
solvent interaction will mainly be due to the n-electron therefore seemed interesting to study the equilibrium hexane where less important solute-solvent interactions
system of toluene. It in eqn. (2) in cycloare anticipated.
2. Results The formation _7i:=
constant
K of MAl,Brs in eqn. (2) is defined
by eqn. (3):
IM&%1 W&J
(3)
To determine K, MBr,(s) is equilibrated with a cyclohexane solution of Al,Br, and then the equilibrium concentrations [M] and [Al] are determined by atomic absorption spectroscopy. As MAl,Brs is the only soluble species containing M (see discussion and ref. 3) [M] = [ MAl,Br,] and [Al] = 2( bW&,, + [M&B%l). If [M] is plotted us. [AIZBrblfree, a straight line with a slope of K is obtained (Figs. 2 and 3). In general, the equi~brium in eqn. (2) can only be studied at small Al*Br, concentrations because at larger Al,Br, concentrations MBr,(s) is no longer stable but is converted to MAl,Br 3n +2(s) (n = 2 in most cases). Therefore, at elevated Al,Br, concentrations the MA12Br8 concentration will correspond to the solubility of MAl,Br,(s) and it will not change upon further increase of the Al,Br, concentration (unless new Al,Br,rich complexes were formed). mMICo”l in cvclohexane 1
0.3
mMICo”1 a in toluene
*
I
I/
0.2
a
.
l
saturated solution of [Co f2Brg1
..
.
mMIPd”l
.
15
..
Klig =
I Al2Br61
50
* .
. /
l
.
* of [Pd A12Br8]
[Pd AL2BrgI Kliq = IAf2Br61
10
lCoAL2Brgl
OS _
..* . . : . * .*f’ saturated solution -** *
.
5
_-, 100 mMIA12EW61
2
. . . . ., L
6
1 20
60
, 100
IL0
mM [A12Br61
Fig. 2. Formation
constant and solubility of CoAlzBrs(sln) in toluene and cyclohexane.
Fig. 3. Formation
constant and solubifity of PdA12Brs(sln) in cyclohexane.
37
The situation is illustrated in Fig. 2 for the formation of CoAl,Br, in cyclohexane and in toluene. The slopes [CoZ’]/[A1,Br,] correspond to K while the horizontal lines correspond to the solubilities of CoAl,Br, in these solvents. In the system PdBr,-Al,Br, the formation constant of PdAl,Brs(sln) can only be measured at rather low concentrations of Al,Br,, requiring a change of scale to show K and the solubility of PdAl,Br, in one figure (Fig. 3). In the systems CrBr*-AlzBr,, NiBr,-Al,Br, and CdBr,-Al,Br,, MAl,Br,(s) is formed at very low A12Br, concentrations ([Al] < 1 mM) and therefore only the solubilities of MAl,Brs(s) but not the formation constants of MAl,Br,(sln) can be measured (Table 1). The system MnBr,-Al,Br, does not quite fit into the above scheme. The data are shown in Table 2. As with CrBr*, NiBr, and CdBr,, K cannot be measured. But the solubility of MnAl*Brs(s) increases significantly with TABLE
1
Thermodynamic in cyclohexane
data of the equilibrium
M in MBr2
-
MAl,Brs(sln)
at 298 K
of (mM)
0.057 0.096 0.24 0.19 0.035 2.05 6.65
6.5 x 1O-3
11 x 10-s 1.07 2
Equilibration
1 2 3 4 5 6 7
e
Solubility MA12Br8
-
Hg Pd
Sample number
+ Al,Brs(sln)
K
Cr Mn co Ni Cd
TABLE
MBr*(s)
of MnBr?(s)
with AlzBrs(sln)
[Al, Br6] start
[AZ2 Br6] equil
[Mn*‘] equil
(mW
@W
(PM)
2.5 2.5 5.0 5.0 25.0 50.0 50.0
0.36 0.41 0.52 0.39 0.51 0.60 0.64
8.2 10.8 12.7 8.1 8.4 8.8 9.3
Conversion of MnBrz(s) to MnA12Brs(s). Average solubility of MnAl,Brs = 9.6 pm.
100 mg MnBr2 (= 0.466 hexane.
mmol)
equilibrated
in cyclohexane Sample number
8-9 10 12 14 16 18 20 -
11 13 15 17 19 21
[AZzBr,] start
[A12Br6] equil
[Mn”] equil
WV
(mW
(PM)
100 125 150 175 200 250 350
13 43 53 87 118 158 245
125 200 168 236 245 247 291
Average value of [ A12BreJstit [ A12Br6]Wuil = 90.4 mM. Theoretical values of MnAlzBrs(s) is formed = 93.2 mM. for 14 - 21 days with Al,Br, in 5 ml cyclo-
38
A similar behaviour is observed in the increasing A12Br, concentration. system ZnBr,-Al,Br,. Even in PdBrPAl,Br, (Fig. 3) an increasing solubility of PdAl,Brs(s) with increasing [Al,Br,] cannot be excluded and the visibleIR spectrum of PdAl,Br,(sln) shows slight changes when the Al,Br, concentration is increased (Fig. 4). Formation constants of MAlzBrs(sln) and solubilities of MAl,Brs(s) are listed in Table 1. For M = Co, the temperature dependence of the equilibrium constant has been determined spectrophotometrically over the temperature range 25 - 61 “C. This yielded AH”,,, and AS& for the formation of CoAl,Br,(sln) according to the reaction in eqn. (2). As a result of the lower solubility of CoAl,Br, in cyclohexane than in toluene (Fig. 2) the accuracy of the results (Table 3) is lower for the cyclohexane than for the toluene solutions [ 31,
10
15
20
.103cm-’
) gas phase, (- - - - -) cyclohexane, Fig. 4. Visible-IR spectrum of PdAlzBrs in ((- - -) cyclohexane with a large excess of A12Br,.
and
TABLE 3 Thermodynamic
values of the reaction CoBr*(s) + AlzBr6 e
CoAl*Brs at 298 K
Solvent
AH”
AS’
AG”
Ref.
none (gas) cyclohexane toluene
42.4 + 2 -7.8 f 1.8 -9.4 * 0.8
42.9 + 2 -68.0 f 10 -39.5 +3
29.6 + 2.5 12.5 f 0.3 2.4 k 0.1
4 3
3. Discussion 3.1. Stoichiometry of the complexes From the visible-IR spectra of the MBr,-Al*Br, complexes in the gas phase and in solution (Figs. 4 and 5) one may conclude that the chromophores are not much influenced by the solvent. This agrees with the assumption that the stoichiometry of the complexes is MAl,Brs in the gas phase as well as in solution. Additional points to support this hypothesis have been presented in ref. 3. If the stoichiometry of the gaseous and dissolved complexes is the same, the thermodynamics of their formation may be compared.
39 I”
toluene
w in cyclohexane
jJ;~z 13
15
17
.103 cm'
Fig. 5. Visible-IR spectrum of CoAlzBrs in the gas phase, in toluene and in cyclohexane.
3.2. Computation of unmeasurable equilibrium constants The thermodynamic cycles of Fig. 1 show how the free energies of formation of MAl,Br,(g) and MAl*Br,(sln) are related to each other. In eqn. (4) the indications in parentheses refer to the corresponding process of Fig. 1. AG’(Klig) = AG”(K,,,) - AG”(s01v Al,Br&g)) + AG”(K,,) - AG “(sub1 MAl,Brs( s))
(4)
To compare the formation of MAl,Brs(sln) in the solvents toluene and cyclohexane one may calculate AGirransferi.e. the difference between eqn. (4) written for a toluene and for a cyclohexane solution: AGtOransfer = AG ‘=(&-hex) - AG ‘=(&,,) = AG”(solv Al,Br,(g),
+ AG”(&,,
tol) - AG”(solv Al,Br,(g),
-hex) - AG ‘(Kso,tol)
c-hex) (5)
In eqn. (5), AG” of the solvation of Al,Br,(g) in toluene (= AG”(solv A12Br,(g), tol) and in cyclohexane (= AG“(solv Al,Br,(g), c-hex)) are known [3, 51. Thus, from the solubility of MA12Br,(s) in cyclohexane (= AG”(K,,,c_hex)) and in toluene (= AG”(K,,, &), AGfransfer can be computed. With AGyransfer and AG’(K,,J one finds AG”(Kc_hex). This is important in those cases where the formation constant of MAl,Brs(sln) in cyclohexane cannot be measured because of the formation of MAl,Brs(s) at very low Al,Br, concentrations. Free energies of formation of MAl,Brs(sln) in cyclohexane calculated by the above procedure are presented in parentheses in Table 4. For M = Co, where both Kc_hex and Ktol have been measured, the agreement between measured and calculated (by eqn. (5)) values is excellent. Where only the calculated value of AG”(K,.hex) is available, the corresponding formation constant of MA12Brs(sln) is very small. This explains why it could not have been measured: at the low A12Br, concentrations, where MBr,(s) is the stable equilibrium phase, the concentration of MA12Brs(sln) is extremely small.
40 TABLE 4 Free energy of formation and dissolution of MAl*Brs
AG& (kJ mol-‘) formation of MA12Br8 in
M
ref.
toluene
(7.0) (7.5) 12.5 (12.8) (10.3) 11.2 -0.17
-1.95 -1.84 2.4 10.1 -4.8 -
33.5 29.6 52.0 24.7
A12Br6
30.l(sublimation)
4 6 7
formation
cyclohexane
Cr Mn co Ni Cd Rg Pd
6 -
AG;
AC&s (kJ mol-‘) solu bility in CYClO-
AG; solubility
toluene
hexane (9.0) (9.3) 10.1 (2.7) (15.1) -
[B]
24.2 22.9 20.6 21.2 25.4 15.4 12.4
14.5 12.9 9.8 17.8 9.6 -
9.7 10.0 10.8 3.4 15.8 -
+0.5a
-0.2a
0.7
aRefs. 3 and 5. Because of unintentional heating during equilibration the solubilities given in ref. 3 are slightly too high. AG&nsrer = AG&croiw,ne - AG;eoluene. Values calculated using eqn. (5) in parentheses.
3.3. The free energy of formation of MAl,Brs according to the reaction MBr,(s) + A12Br6 e
MA12Brs
(6)
becomes increasingly negative if the reaction medium changes from the gas phase to cyclohexane and finally to toluene, e.g. for the formation of CoA12Brs the corresponding equilibrium constants are Kgas= 6.4 X 10m6, In terms of = 6.4 X 10-3, I&,,, = &-hex cyclohexane than in toluene means that the difference between the free energies of solvation of A12Br,(g) and is larger in toluene than in cyclohexane. cyclohexane, and -30.3 kJ mol-’ in toluene. According to Fig. 1, the difference between AG’(solvation, MA12Brs(g)) cyclohexane and toluene equals AG~(solubility) independent of the solvent. However, Fig. 1 shows that AG’(Kiiq) + AG”(solv Al,Br,(g)) = AG”(K,,,) Equation (7) yields AG”(solv CoAl,Br,(g)) and AG”(solv CoAl~Brs~g))
+ AG”(so~v
(7) cyclohexane
CoAl,Br,(s) (Table 4). We may note that the difference between AG”(solv A12Br,(g)) in and toluene is small (0.7 kJ mol-i) while it is much larger for
41
AG”(solv CoAl,Br,(g)) (10.8 kJ mol-‘). Apparently the two solvents are more different for the more polar molecule CoAl,Brs than for A1,Br6. The difference between the two solvents in the course of the formation of CoA12Br,(sln) is brought out by the thermodynamic values of Table 3. It shows that AH” for the formation of CoA12Brs(sln) according to eqn. (2) is only slightly more negative in toluene than in cyclohexane. This observation is in line with the somewhat more negative enthalpy of solvation for Al,Br,(g) in toluene than in cyclohexane as computed from refs. 3, 5 and 8. The more negative enthalpies in toluene probably result from bonding interactions of the solute with the n-electron system of the solvent. Obviously, the enthalpy difference is not the reason for the different stabilities of CoAlzBrs(sln) in cyclohexane and in toluene, the important difference is the entropy. AS” for the reaction in eqn. (2) has a much larger negative value in cyclohexane than in toluene. We may interpret this observation in two ways: (i) CoAl,Brs is much more structure-making in cyclohexane than in toluene, or (ii) CoAl,Brs in cyclohexane is a more rigid molecule with a smaller vibrational entropy than in toluene. Unfortunately it is difficult to decide upon the relative importance of the two phenomena.
4. Experimental
details
The cyclohexane (Merck p.a.) was stored on a molecular Union Carbide). All other procedures are described in ref. 3.
sieve (48
Acknowledgment The authors wish to thank M. Piccand for technical assistance. The project has been supported by the Swiss National Science Foundation, grant 2.427.-0.82.
References 1 H. Schafer, Adu. Inorg. Chem. Rodiochem., 26 (1983) 201. 2 G. N. Papatheodorou and G. H. Kucera, Inorg. Chem., 16 (1977) 1006. (1982) 248. 3 F. P. Emmenegger, 2. anorg. allg. Chem.. 545 (1987) 56. 4 F. P. Emmenegger, Znorg. Chem., 16 (1977) 343. G. N. Papathoodorou and G. H. Kucera, Inorg. Chem., 16 (1977) 1006. 5 P. A. Leighton and J. P. Wilkes, J. Am. Chem. SOL, 70 (1948) 2600. 6 F. P. Emmenegger, unpublished results, 1986. 7 M. A. Capote and G. N. Papatheodorou, Inorg. Chem., 17 (1978) 3414. 8 JANAF, Thermochemical Tables, National Bureau of Standards, Washington, edn., 1971.
2nd
of the Less-Common
Metals,
I37
(1988)
35
35
- 41
STABILITY OF TRANSITION METAL BROMIDE-ALUMINIUM BROMIDE COMPLEXES IN CYCLOHEXANE* F. P. EMMENEGGER
and R. RENGIER
Institute of Inorganic (Switzerland)
Chemistry,
(Received
June
University
of Fribourg,
PProlles,
1700
Fribourg
12,1987)
Summary
The equilibrium MBr,( s) + Al*Br,(sln)
constants e
for the reactions
MAlzBrs(sln)
(M = Co, Pd, Hg) have been measured at 298 K in cyclohexane. For M z Cr, Mn, Ni, Cd the equilibrium constants could not be measured but the solubilities of MAl,Brs(s) could be determined and used to calculate the equilibrium constants by means of thermodynamic cycles. The relative stabilities of MA1,Brs in the gas phase, in cyclohexane and in toluene are discussed.
1. Introduction The research dealing with the stability and structure of gaseous metal halide complexes has recently been reviewed by Schser [l] and Papatheodorou [ 21. Best known are equilibria of the type MX,(s) + Al,X,(g)
+
(1)
MAl,Xs(g)
M = alkaline earth metal, transition metal; X = Cl, Br. According to their volatility, MAl,Xs(g) are molecules and therefore they should dissolve in non-polar, poorly coordinating organic solvents. Indeed, it has recently been shown that the equilibria MBr,( s) + AlzBr,(sln)
C
MAl,Brs(sln)
(2)
(M = Cr, Mn, Co, Ni, Zn, Cd) can be studied in toluene [3]. Despite the close analogy between eqns. (1) and (2) the formation constants of MAlzBrs(g) and MAl,Brs(sln) are quite different, e.g. for M = Co, AG&,, (1) = 29.6 kJ mol-’ while in toluene AG& (2) = 2.4 kJ mol-‘. The thermodynamic cycles of Fig. 1 show that the difference is due to the difference of the free energies of solvation of Al,Br,(g) and CoAl,Brs(g). In the case of toluene the solute*Dedicated 0022-5088/88/$3.50
to Professor
Harald
Schtifer
on the occasion 0 Elsevier
of his 75th
Sequoia/Printed
birthday. in The Netherlands
36
A12Br6(sln)+ MBrz(s)Fig, 1. Thermodynamic
%q
cycles for MA12Brs.
solvent interaction will mainly be due to the n-electron therefore seemed interesting to study the equilibrium hexane where less important solute-solvent interactions
system of toluene. It in eqn. (2) in cycloare anticipated.
2. Results The formation _7i:=
constant
K of MAl,Brs in eqn. (2) is defined
by eqn. (3):
IM&%1 W&J
(3)
To determine K, MBr,(s) is equilibrated with a cyclohexane solution of Al,Br, and then the equilibrium concentrations [M] and [Al] are determined by atomic absorption spectroscopy. As MAl,Brs is the only soluble species containing M (see discussion and ref. 3) [M] = [ MAl,Br,] and [Al] = 2( bW&,, + [M&B%l). If [M] is plotted us. [AIZBrblfree, a straight line with a slope of K is obtained (Figs. 2 and 3). In general, the equi~brium in eqn. (2) can only be studied at small Al*Br, concentrations because at larger Al,Br, concentrations MBr,(s) is no longer stable but is converted to MAl,Br 3n +2(s) (n = 2 in most cases). Therefore, at elevated Al,Br, concentrations the MA12Br8 concentration will correspond to the solubility of MAl,Br,(s) and it will not change upon further increase of the Al,Br, concentration (unless new Al,Br,rich complexes were formed). mMICo”l in cvclohexane 1
0.3
mMICo”1 a in toluene
*
I
I/
0.2
a
.
l
saturated solution of [Co f2Brg1
..
.
mMIPd”l
.
15
..
Klig =
I Al2Br61
50
* .
. /
l
.
* of [Pd A12Br8]
[Pd AL2BrgI Kliq = IAf2Br61
10
lCoAL2Brgl
OS _
..* . . : . * .*f’ saturated solution -** *
.
5
_-, 100 mMIA12EW61
2
. . . . ., L
6
1 20
60
, 100
IL0
mM [A12Br61
Fig. 2. Formation
constant and solubility of CoAlzBrs(sln) in toluene and cyclohexane.
Fig. 3. Formation
constant and solubifity of PdA12Brs(sln) in cyclohexane.
37
The situation is illustrated in Fig. 2 for the formation of CoAl,Br, in cyclohexane and in toluene. The slopes [CoZ’]/[A1,Br,] correspond to K while the horizontal lines correspond to the solubilities of CoAl,Br, in these solvents. In the system PdBr,-Al,Br, the formation constant of PdAl,Brs(sln) can only be measured at rather low concentrations of Al,Br,, requiring a change of scale to show K and the solubility of PdAl,Br, in one figure (Fig. 3). In the systems CrBr*-AlzBr,, NiBr,-Al,Br, and CdBr,-Al,Br,, MAl,Br,(s) is formed at very low A12Br, concentrations ([Al] < 1 mM) and therefore only the solubilities of MAl,Brs(s) but not the formation constants of MAl,Br,(sln) can be measured (Table 1). The system MnBr,-Al,Br, does not quite fit into the above scheme. The data are shown in Table 2. As with CrBr*, NiBr, and CdBr,, K cannot be measured. But the solubility of MnAl*Brs(s) increases significantly with TABLE
1
Thermodynamic in cyclohexane
data of the equilibrium
M in MBr2
-
MAl,Brs(sln)
at 298 K
of (mM)
0.057 0.096 0.24 0.19 0.035 2.05 6.65
6.5 x 1O-3
11 x 10-s 1.07 2
Equilibration
1 2 3 4 5 6 7
e
Solubility MA12Br8
-
Hg Pd
Sample number
+ Al,Brs(sln)
K
Cr Mn co Ni Cd
TABLE
MBr*(s)
of MnBr?(s)
with AlzBrs(sln)
[Al, Br6] start
[AZ2 Br6] equil
[Mn*‘] equil
(mW
@W
(PM)
2.5 2.5 5.0 5.0 25.0 50.0 50.0
0.36 0.41 0.52 0.39 0.51 0.60 0.64
8.2 10.8 12.7 8.1 8.4 8.8 9.3
Conversion of MnBrz(s) to MnA12Brs(s). Average solubility of MnAl,Brs = 9.6 pm.
100 mg MnBr2 (= 0.466 hexane.
mmol)
equilibrated
in cyclohexane Sample number
8-9 10 12 14 16 18 20 -
11 13 15 17 19 21
[AZzBr,] start
[A12Br6] equil
[Mn”] equil
WV
(mW
(PM)
100 125 150 175 200 250 350
13 43 53 87 118 158 245
125 200 168 236 245 247 291
Average value of [ A12BreJstit [ A12Br6]Wuil = 90.4 mM. Theoretical values of MnAlzBrs(s) is formed = 93.2 mM. for 14 - 21 days with Al,Br, in 5 ml cyclo-
38
A similar behaviour is observed in the increasing A12Br, concentration. system ZnBr,-Al,Br,. Even in PdBrPAl,Br, (Fig. 3) an increasing solubility of PdAl,Brs(s) with increasing [Al,Br,] cannot be excluded and the visibleIR spectrum of PdAl,Br,(sln) shows slight changes when the Al,Br, concentration is increased (Fig. 4). Formation constants of MAlzBrs(sln) and solubilities of MAl,Brs(s) are listed in Table 1. For M = Co, the temperature dependence of the equilibrium constant has been determined spectrophotometrically over the temperature range 25 - 61 “C. This yielded AH”,,, and AS& for the formation of CoAl,Br,(sln) according to the reaction in eqn. (2). As a result of the lower solubility of CoAl,Br, in cyclohexane than in toluene (Fig. 2) the accuracy of the results (Table 3) is lower for the cyclohexane than for the toluene solutions [ 31,
10
15
20
.103cm-’
) gas phase, (- - - - -) cyclohexane, Fig. 4. Visible-IR spectrum of PdAlzBrs in ((- - -) cyclohexane with a large excess of A12Br,.
and
TABLE 3 Thermodynamic
values of the reaction CoBr*(s) + AlzBr6 e
CoAl*Brs at 298 K
Solvent
AH”
AS’
AG”
Ref.
none (gas) cyclohexane toluene
42.4 + 2 -7.8 f 1.8 -9.4 * 0.8
42.9 + 2 -68.0 f 10 -39.5 +3
29.6 + 2.5 12.5 f 0.3 2.4 k 0.1
4 3
3. Discussion 3.1. Stoichiometry of the complexes From the visible-IR spectra of the MBr,-Al*Br, complexes in the gas phase and in solution (Figs. 4 and 5) one may conclude that the chromophores are not much influenced by the solvent. This agrees with the assumption that the stoichiometry of the complexes is MAl,Brs in the gas phase as well as in solution. Additional points to support this hypothesis have been presented in ref. 3. If the stoichiometry of the gaseous and dissolved complexes is the same, the thermodynamics of their formation may be compared.
39 I”
toluene
w in cyclohexane
jJ;~z 13
15
17
.103 cm'
Fig. 5. Visible-IR spectrum of CoAlzBrs in the gas phase, in toluene and in cyclohexane.
3.2. Computation of unmeasurable equilibrium constants The thermodynamic cycles of Fig. 1 show how the free energies of formation of MAl,Br,(g) and MAl*Br,(sln) are related to each other. In eqn. (4) the indications in parentheses refer to the corresponding process of Fig. 1. AG’(Klig) = AG”(K,,,) - AG”(s01v Al,Br&g)) + AG”(K,,) - AG “(sub1 MAl,Brs( s))
(4)
To compare the formation of MAl,Brs(sln) in the solvents toluene and cyclohexane one may calculate AGirransferi.e. the difference between eqn. (4) written for a toluene and for a cyclohexane solution: AGtOransfer = AG ‘=(&-hex) - AG ‘=(&,,) = AG”(solv Al,Br,(g),
+ AG”(&,,
tol) - AG”(solv Al,Br,(g),
-hex) - AG ‘(Kso,tol)
c-hex) (5)
In eqn. (5), AG” of the solvation of Al,Br,(g) in toluene (= AG”(solv A12Br,(g), tol) and in cyclohexane (= AG“(solv Al,Br,(g), c-hex)) are known [3, 51. Thus, from the solubility of MA12Br,(s) in cyclohexane (= AG”(K,,,c_hex)) and in toluene (= AG”(K,,, &), AGfransfer can be computed. With AGyransfer and AG’(K,,J one finds AG”(Kc_hex). This is important in those cases where the formation constant of MAl,Brs(sln) in cyclohexane cannot be measured because of the formation of MAl,Brs(s) at very low Al,Br, concentrations. Free energies of formation of MAl,Brs(sln) in cyclohexane calculated by the above procedure are presented in parentheses in Table 4. For M = Co, where both Kc_hex and Ktol have been measured, the agreement between measured and calculated (by eqn. (5)) values is excellent. Where only the calculated value of AG”(K,.hex) is available, the corresponding formation constant of MA12Brs(sln) is very small. This explains why it could not have been measured: at the low A12Br, concentrations, where MBr,(s) is the stable equilibrium phase, the concentration of MA12Brs(sln) is extremely small.
40 TABLE 4 Free energy of formation and dissolution of MAl*Brs
AG& (kJ mol-‘) formation of MA12Br8 in
M
ref.
toluene
(7.0) (7.5) 12.5 (12.8) (10.3) 11.2 -0.17
-1.95 -1.84 2.4 10.1 -4.8 -
33.5 29.6 52.0 24.7
A12Br6
30.l(sublimation)
4 6 7
formation
cyclohexane
Cr Mn co Ni Cd Rg Pd
6 -
AG;
AC&s (kJ mol-‘) solu bility in CYClO-
AG; solubility
toluene
hexane (9.0) (9.3) 10.1 (2.7) (15.1) -
[B]
24.2 22.9 20.6 21.2 25.4 15.4 12.4
14.5 12.9 9.8 17.8 9.6 -
9.7 10.0 10.8 3.4 15.8 -
+0.5a
-0.2a
0.7
aRefs. 3 and 5. Because of unintentional heating during equilibration the solubilities given in ref. 3 are slightly too high. AG&nsrer = AG&croiw,ne - AG;eoluene. Values calculated using eqn. (5) in parentheses.
3.3. The free energy of formation of MAl,Brs according to the reaction MBr,(s) + A12Br6 e
MA12Brs
(6)
becomes increasingly negative if the reaction medium changes from the gas phase to cyclohexane and finally to toluene, e.g. for the formation of CoA12Brs the corresponding equilibrium constants are Kgas= 6.4 X 10m6, In terms of = 6.4 X 10-3, I&,,, = &-hex cyclohexane than in toluene means that the difference between the free energies of solvation of A12Br,(g) and is larger in toluene than in cyclohexane. cyclohexane, and -30.3 kJ mol-’ in toluene. According to Fig. 1, the difference between AG’(solvation, MA12Brs(g)) cyclohexane and toluene equals AG~(solubility) independent of the solvent. However, Fig. 1 shows that AG’(Kiiq) + AG”(solv Al,Br,(g)) = AG”(K,,,) Equation (7) yields AG”(solv CoAl,Br,(g)) and AG”(solv CoAl~Brs~g))
+ AG”(so~v
(7) cyclohexane
CoAl,Br,(s) (Table 4). We may note that the difference between AG”(solv A12Br,(g)) in and toluene is small (0.7 kJ mol-i) while it is much larger for
41
AG”(solv CoAl,Br,(g)) (10.8 kJ mol-‘). Apparently the two solvents are more different for the more polar molecule CoAl,Brs than for A1,Br6. The difference between the two solvents in the course of the formation of CoA12Br,(sln) is brought out by the thermodynamic values of Table 3. It shows that AH” for the formation of CoA12Brs(sln) according to eqn. (2) is only slightly more negative in toluene than in cyclohexane. This observation is in line with the somewhat more negative enthalpy of solvation for Al,Br,(g) in toluene than in cyclohexane as computed from refs. 3, 5 and 8. The more negative enthalpies in toluene probably result from bonding interactions of the solute with the n-electron system of the solvent. Obviously, the enthalpy difference is not the reason for the different stabilities of CoAlzBrs(sln) in cyclohexane and in toluene, the important difference is the entropy. AS” for the reaction in eqn. (2) has a much larger negative value in cyclohexane than in toluene. We may interpret this observation in two ways: (i) CoAl,Brs is much more structure-making in cyclohexane than in toluene, or (ii) CoAl,Brs in cyclohexane is a more rigid molecule with a smaller vibrational entropy than in toluene. Unfortunately it is difficult to decide upon the relative importance of the two phenomena.
4. Experimental
details
The cyclohexane (Merck p.a.) was stored on a molecular Union Carbide). All other procedures are described in ref. 3.
sieve (48
Acknowledgment The authors wish to thank M. Piccand for technical assistance. The project has been supported by the Swiss National Science Foundation, grant 2.427.-0.82.
References 1 H. Schafer, Adu. Inorg. Chem. Rodiochem., 26 (1983) 201. 2 G. N. Papatheodorou and G. H. Kucera, Inorg. Chem., 16 (1977) 1006. (1982) 248. 3 F. P. Emmenegger, 2. anorg. allg. Chem.. 545 (1987) 56. 4 F. P. Emmenegger, Znorg. Chem., 16 (1977) 343. G. N. Papathoodorou and G. H. Kucera, Inorg. Chem., 16 (1977) 1006. 5 P. A. Leighton and J. P. Wilkes, J. Am. Chem. SOL, 70 (1948) 2600. 6 F. P. Emmenegger, unpublished results, 1986. 7 M. A. Capote and G. N. Papatheodorou, Inorg. Chem., 17 (1978) 3414. 8 JANAF, Thermochemical Tables, National Bureau of Standards, Washington, edn., 1971.
2nd