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Energetics of organometallic species: the entropic factor
of
ollmal ds me?Zikc
Chemistry ELSEVIER
Journal of Organometallic
Chemistry 5 18 (1996) 167- 180
Energetics of organometallic species: the entropic factor Manuel E. Minas da Piedade a,*, Jo& A. Mat-tinho Simbes b a Crntro b Departumento
de Quimicu de Quimicu
Estruturul,
Cornp1rx-o I, Institute
e Bioquimicu,
Superior
Fuculdude
de Ci&cius,
Received
8 December
Tknico,
Univrrsidude
1096 Lishou de Lishou,
Coda,
Portugul
1700 Lishoa,
Portugul
1995
Abstract A rather simple procedure to estimate entropy changes of organometallic reactions is described. It merely consists in finding organic or inorganic reactions, for which the gas phase standard entropies are well known, that can mimic a given organometallic reaction. The merits and limitations of the method are discussed, and it is concluded that a careful use of model reactions can at least provide a reliable guideline to estimate or even to assess entropy data for many organometallic reactions. Keywords:
Gas phase reactions; Organometallic reactions; Entropy data
1. Introduction The thermodynamic driving force of a chemical reaction is measured by the Gibbs energy change A,G associated with the conversion of reactants to products, spontaneous reactions having A,G < 0. Under equilibrium conditions A,G = 0 and the standard Gibbs energy A,G” of the reaction is related to the equilibrium constant K of the reaction by
A,G”= -RT
In K
(1)
were R is the gas constant and T the absolute temperature. As K reflects the relative amounts of reactants and products present in the reaction mixture (and therefore the reaction yield), the prediction of the feasibility of a given reaction or of a postulated elementary step in a composite reaction, on thermodynamic grounds, implies that one is able to calculate A,G” for the process under study. The standard Gibbs energy of a reaction is related to the corresponding enthalpy A, Ho and entropy A, So by
A,G” = A,Ho - TArSo
(2)
In the case of reactions involving organometallic compounds much more is known about the enthalpy term than about the entropy term in Eq. (2). Most experimental studies in organometallic thermochemistry available
* Corresponding author. 0022-328X/96/$15.00 PI/
0 1996 Elsevier
SOO22-328X(96)06193-1
Science
S.A. All rights reserved
in the literature
report
the determination
reaction,
which
other
from
enthalpies
of enthalpies of reaction,
of en-
A, HO of formation and bond dissociation enthalpies DH ‘(M-L> (M = metal centre; L = ligand) were (or can be) derived [l-7]. Some methods of estimating A, H ‘, A,H” and DH’(M-L) data have also been discussed [8]. Although these estimating procedures are not as accurate and general as several existing schemes for predicting thermochemical data of organic compounds [9- 121, they are often used to assess experimental data and to discuss the energetics of bond cleavage and formation in organometallic reactions. Thus, in the absence of direct experimental measurements, it is now possible, for many organometallic reactions, to make reliable predictions of the enthalpy term in Eq. (2). Much less attention has been given to the measurement and estimation of entropy changes in organometallit reactions, despite the fact that, in some cases, the value of TA, So makes an important contribution to A,G”, or even determines if the reaction is spontaneous. For example, in the reaction (see Table 1) thalpies
Cr(C%(PCy,),(sln)
+ H,(s
-)Cr(CO),(PCy,),(r12-H2)(sln)
ln> (3)
A,Ho = -30.5 kJ mol-’ and TArSo = -31.9 kJ mol- ’, leading to A,G” = 1.4 kJ mol- ‘. Therefore, although the reaction is exothermic, the entropy change leads to a positive value for A,G”. Note that, in this
I9
16 17 18
IO II 12 13 I4 I5
4
2
1
No.
‘Si’ CH 2’
CH, ‘Me
Me (sin) + SiMe, (sln)
+ H, (sln)
Th(cp * ),(~R)H (sin) + co (sln) = Th(Cp * ),(oR)c(o)H (sln) R = CH’Bu 2 R = 2,6-C6H3’Bu2 Ukot), (g) = Ukot) (g) + cot (g) [Ti(Cp)2Cl]2 (sin) + 2C0 (sln) = 2TiCp,(CO)CI (sin) Ti(C,H,),PEt, (sin)= TX&H,), (sln)+PEt, (sin> Ti(C,H,,),L (sin) = Ti(C,H,,), (sln)+L (sin> L = PF, L=PMe, L = PEt, L = PMe,Ph L = P(OMe), L = P(OEt), HqCp),R z (sin) + CO (sin) = HACp),RC(O)R (sin> R = Me R = Bz HffCp* j2H, (sin)+ C,H, &In) = HMCp” ),(Ph)H (sInI+ H, (sin)
(sin) = (Cp’ jI<
343-387
benzene, [ 141 benzene, [ 141
270-300 313-332 224-269 276- 303 269-303 259-290
180-220 180-200 445-540 243, 268 300-318
333-373
269-307 269-307 373-444
toluene, [20]
1171 toluene, [ 181 thf, [ 191 thf, [I 9]
toluene, [ 161
cyclohexane, [ 151
323-373
benzene, [ 141
Th(Cp* ),(CH,SiMe3),
279-353 298-353
benzene, [ 131 benzene, [ 131
Sc(Cp * ),H (sin) + C,Hr, (sin) = Sc(Cp * ),Ph (sin) + H, (sln) Sc(Cp * ),(thf)H (sln) + C,H, (sln) = Sc(Cp * ),Ph (sln) + thf (sln) + H, (sin)
T/K
Solvent, Ref.
Reaction a
Table 1 Entropies of selected organometallic reactions
1.3
139.4f20.4
- 138.1 + 23.4 - 120.1 * 2.5 - 14.6& 2.6
130.5 + 10.5 142.7 * 10.0 134.7+ I.3 139.3+_ 7.9 l25.9* 13.4 ll4.6k 8.8
-49.0+ 18.0 - 100.0*31.0 272 *58 -85 +20 145.6+ 10.0
69.5 + 20.9
43.2+
4.2 8.4
Km ’mol- ’
-4.2* 100.4+
A,S/J
46 41 48
44 45
42 43
31 3x 39 40 41
22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
21
20
*
0
’ XCO),l,
* KCO),
(sin)
Mn,(CO),,
(sin)
(sin) = W(CO),(PR,)2Hz
(sin) + Hz (.sln) = 2Mn(CO),H
W(CO),(PR,),(v’-H,) R = cyyC,Ho R =‘Pr
(sln)
Mo(CO),(CD~CN), (sin)+ CpH (sin) = Mo(Cp)(CO),H (sln)+3CD,CN (sin) Mo(CO);(thf), (sin)+ PhMe (sin) = Mo(T’-PhMe)(CO), (sin)+ 3thf (sln) W(CO),Xe (sln) = W(CO), (sin)+ Xe (sln) W(CO),(PhNH,) (sInI+ L (sin) = W(CO),L (sin)+ PhNH, (sln) L = PBu, L = PPh, L = P(OBd, L = P(OPh), L = AsPh, (sin)+ H,O (sln) = W(CO),(PR;),(H,O) (sin)+ H, (sin) W(CO),(PR,),(T’~H,) R = Cy R =‘Pr W(CO),(PR,),(thf) (sin) = W(CO),(PR,), (sln)+ thf (sin) R =cy-C,H,, R =‘Pr
(sln)
(sin)
(sin) + H, (sin)
(slid + py (sln)
(sin) = 2CdCp)(CO),P(OMe),
(sin) = 2CrtCp
py (sin) = CdCO),(PCy3)2 (sln) = 2CdCp)(CO), (sin)
(CI(Cp)(CO),[P(OMe),]]~
[CdCp
CdCO),(PCyj), [CrtCp)(CO)ilz
V(Cp), 1(sln) + CO (sin) = V(Cp12(COII (sin) CdCO),(PCy,), (sin)+ L (sin) = CdCO),(PCy,),(q2-L) L = N, L = H;
HfbH
\
+a 0
[ 141
(331
[32]
supercritical
toluene,
toluene,
thf, [32]
CO,,
toluene, [23] toluene, [24] toluene, [25] toluene, [26] thf, [24] toluene, [27] toluene, [26] thf, [26] toluene, [25] thf, [26] CDJN, [28] thf, [29] liquid Xe, [30] toluene, [3 I]
toluene, [2l] thf, [22]
benzene,
[34]
273-309 265-305 353-453
193-293
203-298
283-318 291-318 278-298 208-368 298-333 283-338 208-368 241-314 273-323 223-273 243-263 198-235 316.-355 308-354 173-198 308-318
272-316
332-386
8.4 8.4
+33 +2l +2s + 8 +25
9.6 7.1 23.8 5.9 9.2 3.8 5.4 9.2 12.1 5.4 6.3 12.6 8.4 5.0 20.9
14.2
9.8
10.0+ s.o+ 35.6+
5.9 8.8 3.3
129.7 f IO.5 l42.3+ 8.4
-69.0+ -78.7k
IS1 360 222 372 280
- 148.1 k - 107.1 f 120.5 f 155.2* 212.1 k 146.9_+ 143.5+ 229.3 + 179.1 i l69.0+ 288.7k 175.7+ 214.6+ l73.6* 66.9 +
- 144.8&
78.8k
60 61 62 63 64 65 66 61 68 69 70 71 72 73 14 75 76 77 78 79
57 58 59
56
55
PPh z Me
0 I;FL--%--Me oc
PPh z Me
(sin) I+
+Le ‘0‘ 0
(sin)
0 (sln)
(sin) + H,O (sin)
Co(CO),H(sln) = CdCO),H(sln) + CO(sln) Co(CO),C(O)Prtsln) = Co(CO),C(OYPdsln) 2Me-B ,2(sln) = [Me-B ,z]z(sln) 2Rh(TMP)‘(sln)+ CH,(sln) = Rh(TMP)Me(sln) + Rh(TMP)H(sln) Rh(OEP)H(sln) + U&In) = Rh(OEP)CHO(sln) [Rh(OEP)],(sln) + H z(sln) = 2Rh(OEP)H(sln) [Rh(TXP)],(sln) + CH,(sln) = Rh(TXP)CH,(sln) + Rh(TXP)H(sln) [Rh(OEP)],(sln) + C, H&In) = (OEP)RhCH,CHMeRh(OEPXsln) [Rh(OEP)],(sln) + CO(sln) = (OEP)RhC(O)Rh(OEPXsln) [Rh(OEP)],(sln) + ZCO(sln) = (OEP)RhC(O)C(O)Rh(OEP)(sln) (OEP>RhC(O)Rh(OEP%ln) + CO(sln> = (OEP)RhC(O)C(O)Rh(OEP)(sln) [Rh(OEP)],CO(sln)+ CO(sln) = (OEP)RhC(O)C(O)Rh(OEPXsIn)
Ru(H)(~~-H~XCI)(CO)[P(~P~~)],(~I~) = Ru(HXCIXCO)[P(‘Pr,)]z(sln)+ H,(sln) Os,Cp,(g) = 2OsCp,(g) Os&CO),,(sln) + PhC=CPh(sln) = OS&CO), ,(PhC=CPh)(sln) + CO(sln) Co,(CO)&sln)+ H,(sln) = 2Co(CO),H(sln) Co,(CO),(sln)+ H,(sln) = 2Co(CO),H(sln)
[FeCo,(CO)&CPh)H] (sin) = [FeCo,(CO),(HCPh)] (sln) Ru,Cp, (8) = 2RuCpz (g) Ru(Cp * )(PMel),(OH) (sln)+PhzNH (sin) = Ru(Cp * XPMe,),(NPh,) Ru,(CO),, (sin)+ 3C0 (sin) = 3Ru(CO), &In)
PPh z Me
Me I;Fe/-CO oc
IL+
(sin) =
(sln) +
PPh z Me
o-_“go
CP’
CP”
ether, [35]
[381
decalin, [45] supercritical CO,, [46] heptane, [47] hexane, [42] heptane, [48] octane, [49] water, [50] benzene, [5 I] benzene, (521 benzene, [53] benzene, [5l] benzene, [54] toluene, [55] toluene, [55] toluene, [55] toluene, [55]
[Ml
n-hexane, [42] i-octane, [43] toluene-d,, [44]
thf, [4l]
[401
toluene, [39]
CH $I,,
C,D,. 1371
decalin, [36] supercritical CO,, [34]
2,2’-diethoxydiethyl
Mn(CO),R (sln) + CO (sin) = Mn(CO),C(O)R (sln) R=Me R = Et R = Pr R = Ph Mn,(CO),, (sln) + Re,(CO),, (sin) = 2(CO),MnRe(CO), Mn,(CO),, (sln)+ Co,(CO)s (sin> = 2(CO),MnCo(CO),
49 50 51 52 53 54 (sin) (sln)
Solvent, Ref.
Reaction a
No.
Table I (continued)
288-298 298-358 280-350 353-393 298-335 294,335 353,393 280-330
333-453 3077428
373-448 180-190 500-625
170-298 500-625
220.309
378-402
353-453
T/K
Km’ mol-’
0.8 5.9 0.8
2.0
- 114.0+ 5.0 -60.8& 2.6 97.1+ 4.1 ll8.6* 5.9 38.5 + 28.0 - 17.6* 2.1 18.4 18.4+ 2.1 121.3 8.9+ 2.5 - 138.1 - 79.5 * 20.9 -123 *I5 3.3* 8.4 - 29.3 + 12.6 -84 +21 -130 &2l -259 &30 -130 k29 -151 *I2
-5.o+ l29.9+ -25.5*
-6.5+_
- 117.1 * 16.7
- 125.5 - 64.9 - 37.2 - I 14.6 80.3 + 2.5 2.9& 3.3
I
A-S/J ,
Rh(acacXC,H,),(sln)+L(sln) = Rh(acacXC,H,)L(sln)+CzH,(sln) L = CH,CHF L = CH,CHCI L = CH,CHMe L = CH,CHEt L = cis-C,Hs L = tran.s-C,Hs L = ‘C,H, II(H),(r$H,~X)[PMe(‘Bu),],(sln) = I~H),(X)[PMe(‘Bu),],(sln)+H2(sln) x = Cl X = Br x=1 II(D)2(n2-D2)(CI)[PMe(‘Bu),]l(sln) = 1~D),(C1)[PMe(‘Bu),],(s1n)+ D,(sln) It(CO),(SiR,)(H)( @H2),(TaCp,&ln) = It(CO),( p-CH2)2(TaCp,)(sln)+R S = thf-d, R = Me S = thf-d; R = Et S = toluene-d, R = Et S = thf-d, R = Ph Ni]P(O-o-tol),l,(sln)+ C,H,(sln) = Ni[P(O-o-tol),]s(C,H,)(sln)+P(O-o-tol),(sln) Ni]P(O-o-tol),l,(C,H,Xsln) + P(O-o-toi),(sln) = Ni[P(O-o-tol),],(C,H,)(sln) Ni]P(O-o-tol),l,(sin)+ L(sln) = Ni[P(O-o-tol),],L(sln)+ P(O-o-tol),(sln) L = C,H,, L = 1-hexene r~un.s-Pt(PEt3),(Cl)Et(sln) = rruns-Pt(PEt3)2(Cl)H(sln)+ C,H,(sln) ,SiH(sln)
cyclohexane, [61]
toluene, [59] toluene, [59] benzene, [60]
toluene-d,, [57] S, ml
toluene-d,, [57]
toluene, [56]
273-3 13 2633313 253-343 294-338 2133243 2133243
260-294
250-294
a acac = acetylacetonate; C,H, = 3.methylpentadienyl; C, H,, = 2,4-dimethylpentadienyl; cot = 1,3,5,7cyclooctatetraene; Cp = n’-C,H,; Cp * = n5-C,Me,; methylcobalamine; OBP = octaethylporphyrin; py = pyridine; thf = tetrahydrofuran; TMP = tetramesitylporphyrin; to1 = tolyl; TXP = tetraxylylporphyrin.
91 98 99
91 92 93 94 95 96
87 88 89 90
81 82 83 84 85 86
80
2.9
12.1 15.9 2.1 20.9 12.6 10.9 10.5
Cy = cyclohexyl;
4.2+ 12.6 8.4* 12.6 113.0+ 5.4
79.9k 6.3 103.8f 5.9 104.6k 10.5 lOO.Of 5.9 -58.6k41.8 - 175.1+ 33.4
82.4* 13.4 95.0+ 3.3 86.6f 7.5
80.3f
-3.3* -31.4* -2.1* -1.1 + - 20.5 k - 25.5 k - 10.9+
Me-B,,
=
5
2 u
2
s
s ir! 9 3, 3 \ k
37 2
-+ ‘?
% h % %‘ e
172
M.E. Minus du Pirdudr,
J.A. Murtinho
Simdes/Journul
case, K = 0.57, and ignoring the entropic contribution to A,G” (i.e. making A,G” = ArHo) results in an enormous error in the value of the equilibrium constant (K = 1.8 X lo5 instead of K = 0.57). The importance of evaluating A,S” for the thermodynamic analysis of organometallic reactions led us to search for a simple and reliable method for estimating (and assessing) A,S” data. We have found that for many of those reactions reasonable estimates of A,S” can be obtained by using entropy data for model reactions for which the standard entropy changes are well known.
2. Selected entropy data for organometallic reactions The values in Table 1 [13-611 were selected to illustrate the merits as well as the limitations of the estimation method discussed below. These data seldom refer to the reactants and products in their standard states [9], since concentrations and not activities were used to derive the equilibrium constants, but it will be assumed that the overall corrections are smaller than the experimental uncertainties. In any case, the organometallic reaction entropies presented in Table 1 and in the text below will be represented by A,S and not by A,S”. In general, A,S” values are obtained from van’t Hoff plots [9,62,63]: A,H” lnK=--
RT
ofOr,gnnometullic
Chemistry
518 (1996) 167-180
Take, for example, reaction 16, an intermolecular carbony1 insertion into a hafnium-methyl bond. As far as entropy is concerned, this reaction can be modelled by reaction Ml4 or by reaction Ml5 (“M” for model; see Table 2 [62,65]). It is seen that A,S(16) = - 138.1 + 23.4 J K-’ mall ’ is close to A,S”(M14) = - 132.3 J K-’ mall ’ and A,S”(M15) = - 137.8 J K-’ mol-‘. Consider now the a-bond metathesis reaction 1, for which A,s(l> = -4.2 i. 4.2 J K-’ mall’. In this case, the model reactions M28, M29, and M30 yield an average A,S” = - 7.8 J K- ’ mol- ’, in good agreement with the experimental value. Finally, note that the entropy of reaction 3 in Table 1, A,S(3) = 43.2 A 1.3 J K- ’ mol- ‘, which involves a cyclization process, can be modelled by reaction M3, where A,S”(M3) = 49.5 J K-’ mall’. The above three examples indicate that the entropy changes of the organometallic reactions in Table 1 can be approximated to the entropy changes of organic and inorganic reactions of the same type, in the gas phase, at 298 K. A collection of these simple model reactions, for which the entropies are known, is presented in Table 2, together with an indication of the corresponding reactions in Table 1. The deviations 6 found between the experimental and predicted TA,S data are summarized in Table 3. Before proceeding into a more detailed discussion of these results it is stressed that 6 = T 1 A,S(exp) - A,S’(model) 1, at T = 298 K, is usually less than 10 kJ mol-‘.
A,S” +-
R
(4)
The calculation of A,S” from the plot of In K vs. l/T assumes that both A,S” and A, Ho do not vary with temperature. An alternative and (in principle) more accurate method consists in combining a calorimetrically derived A,Ho value with the corresponding equilibrium constant at a single temperature T, to obtain A,S” at that temperature from Eq. (4) [9,62,63]. To our knowledge this method has not been applied to organometallic reactions. Note also that the errors of the A, S values in Table 1, which reflect the precision of the measurements, are frequently of the order of 10% or more and do not include Student’s t factors [64]. In general, not more than 10 experimental points were used to fit Eq. (4) by a linear regression. Therefore, if Student’s t factors for 95% confidence level were taken into account, the errors in Table 1 would at least double, in most cases.
4. Discussion The agreement between the experimental and predicted entropy values can be understood within the framework of statistical thermodynamics of ideal gas phase reactions [ 1Oa,ll,66]. Only a very brief analysis is given below. The entropy of a substance in the gas phase can be considered as a sum of several contributions, namely translation (S,‘), rotation (SF>, vibration (S,“>, internal rotation (Si), and electronic ($‘I: so = sp + sp + s,o + s; + s,”
(5) Other contributions may have to be accounted for [ lOa,l 11, but those in Eq. (5) are enough for the present discussion. The equations used in the computation of SF, SF, St, and S,” (in J K-’ mol-‘1, assuming a rigid rotator-harmonic oscillator model for the molecule, are 5: = -9.57577
+ 20.78628 In T + 12.47177 In M (6)
3. The estimation method SF = 877.39503 + 8.31451 In T The method used to estimate the entropy changes of organometallic reactions is rather simple and can be illustrated by considering several reactions in Table 1.
+ 8.31451 In I - 8.31451 In o
(linear molecules)
(7)
M.E. Minus du Pied&, Table 2 Standard No.
molar entrouies
J.A. Martinho
d,S’(g)/J
Reaction = 1 particle
I particle M3 M4 MS M6 M7 M8 M9 Ml0 Ml1 Ml2 Ml3 Ml4 Ml5 Ml6 Ml7
= 2 purtic1r.s CH&CH,),Ph = cy-C,H,, + C,H, C,H,=2CH, H ,01 = 20H N,H, = 2NH, C,H, + H,O, = HOCH,CH,OH CH,+CO=CHjCO C,H ,L = cy-C,Hs + CH, C,H,, = cy-C,H,, + CH, CH 4 + CO = CH ,C(O)H H 2 + CO = HC(O)H C,H, + CO = C,H,C(O)H C,H, + CO = CH,C(O)CH, C,H,, + CO = C,H,C(O)C,H, PhCH 3 + CO = CH ,C(O)Ph C,H,, = cy-Cc,H,, + H,
Ml9 M20 M2l M22 M23 M24 M25 M26 M27 2 purticlrs M28 M29 M30 M3l M32 M33
K-
’mol- ’
- 15.5 - 5.3
C,H,o=lC,H,o CsH,2
ofOr,q:anometallic
Chrmi.stty 518 (1996) 167-180
in the ideal gas state at 298 K a
of model reactions
I purticlr Ml M2
Ml8
Simde.s/Journal
=‘CsH,,
-
-
49.5 158.8 134.8 151.5 128.7 122.0 102.7 90.7 119.7 109.6 122.6 132.3 137.8 145.5 40.5 64.4
+H, 0 co CH, + N, = CH,N, CH,fH,=CH, C,H,=H,+C,H, C,H,=CH,+C,H, CH,Cl=CH,+Cl CH,F = CH, + F Si(CH,), = CH, + (CH,),SiH C,H, + C,H, = CH,CH,CH(CH,)CH, H,+C,H,=C,H, CH?(CH,J,Ph=
- 143.7 - 139.3 220.5 135.8 124.8 130.2 166.9 - 152.8 - 127.7
No. of reaction
M34 M35 M36 M37
N,H,+CH,=CH,NH,+NH, H,O>+CH,=CH,OH+H,O C,H6+OH=CH,0H+CH, cH,oH + (CH,J,NH = (CH,),N
M38
cH,oH
2 puriiclrs M39 M40 M4l
= 3 particles
2 purticlrs M42 M43 M44
= 4 particles
4 particks M45 M46 M47
= 3 purticlrs
a Standard
entropies
+ (CH,)NH,
= (CH,),NH
C,H, + 2C0 = ZCH,CO 20H + CH, = H,O + CH,OH C,H, + C,H, = PhCH, + CH,
CH(C2H,)I+H2=CH,+ CH(C,H,)? CH(C,H,),
cy-C,H, cy-C,H, cy-C,H,
+ H,O = CH,O + PhH = PhCH,
+ H,O + ~,0
3 7. 9-15, 24-33, 7, 9-15, 24-33, 7. 9-15, 24-33, 55 21,68 4 4 5, 6, 72 5, 6, 72 5, 6, 72 16,49-51,76,78 17,49951,76,78 52 I9 20 22 23 99 99 36 36 91-94 75 75
reactants
1, I8 I, I8 I, I8 48,65-67, 48, 65-67, 48, 65-67, 74 74 64 59 59
+ H,
- 85.2 - 125.2 147.4
3C,H, + 3C,Hj + 3C,H,
340.8 318.6 331.5
34, 35 34, 35 34. 35
- 87.5 - 101.9 - 70.7
60,6l 60,61 60, 61
+ 3C0 = 3CH,CO + 3HC0 = 3CH,CO + 3H, = 3CH,
of gaseous
- I I.7 - 4. I -7.5 12.2 14.2 15.7 10.3 9.5 20.6 - 36.8 -21.2
and products
were taken from Refs. [62] and [65].
I
69 69
= 2 purticles
H,O+C,H,= PhOH+H, CH, + C,H, = PhCH, + H, H,S + C,H, = PhSH + H, C,H, + H, = 2CH, H,O, + H, = 2H,O N,H,+ H,=2NH,
in Table
8 71 2
73 73 73
44, 45, 58, 63, 10 44, 45, 58, 63, 70 44, 45, 58, 63, 70
173
174
M.E. Minas da Piedade, J.A. Murtinho Simdes/Jaurnal
ofOrganomrtallic
Chemistry 518 (1996) 167-180
Table 3 Deviations 6 = I TA,S(exp) - 7’A,S”(model) 1 of the estimated values of TA,S”(model) from the corresponding experimental values TA,S(exp) for the reactions in Table 1 (T= 298 K) No. of reaction in Table 1
4
5 6 7 8 9 IO I1 12 13 14 I5 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59
TA, S(exp)/kJ
- 1.3 + 1.3 29.9 + 2.5 12.9 + 0.4 20.7 + 6.2 - 14.6 k 5.4 - 29.8 + 9.2 81.1 + 18.3 - 25.3 + 6.0 43.4 * 3.0 38.9 + 3.1 42.5 f 3.0 40.1 + 0.4 41.5 + 2.4 37.1 + 4.0 34.2 + 2.6 - 41.5 * 7.0 - 35.8 f 0.7 - 4.4 + 0.8 41.5 f 6.1 23.5 + 2.9 - 43.2 f 4.2 -44.1 k 2.9 -31.9 f 2.1 35.9 * 7. I 46.2 f 1.8 63.2 + 2.7 43.8 k 1.1 42.8 f 1.6 68.3 + 2.7 53.4 k 3.6 50.4 & 1.6 86.0 f 1.9 52.4 f 3.4 64.0 f 2.5 51.7 * 1.5 19.9 * 6.2 45.0 + 9.8 107.3 + 6.3 66.2 k 7.5 110.9 + 2.4 83.4 f 7.5 - 20.6 + 2.5 _ 23.5 + 2.5 38.7 _+3.1 42.4 k 2.5 3.0 f 1.8 1.5 f 2.6 10.6 f 1.0 -37.4 - 19.3 -11.1 - 34.2 23.9 + 0.7 0.9f 1.0 - 34.9 * 5.0 - 1.9&-0.6 - 1.5 + 0.2 38.7 f 1.8 - 7.6 + 0.2
mol
’
No. of model reaction in Table 2
TA,S”(modet)/k.I
M28, M29, M30 M41 M3 M9, Ml0 Ml 1, M12, Ml3 Mll, M12, Ml3 M4, M5, M6 M39 M4, M5, M6 M4, M5, M6 M4, M5, M6 M4, M5, M6 M4, M5, M6 M4, M5, M6 M4, M5, M6 Ml4 Ml5 M28, M29, M30 Ml7 Ml8 M8 Ml9 M20 M4, M5, M6 M4, M5, M6 M4, M5, M6 M4, M5, M6 M4, M5, M6 M4, M5, M6 M4, M5, M6 M4, M5, M6 M4, M5, M6 M4, M5, M6 M42, M43, M44 M42, M43, M44 M23, M24
-2.3 43.9 14.8 28.8 - 34.5 - 34.5 44.2 - 25.4 44.2 44.2 44.2 44.2 44.2 44.2 44.2 - 39.4 -41.1 -2.3 12.1 19.2 - 36.4 - 42.8 -41.5 44.2 44.2 44.2 44.2 44.2 44.2 44.2 44.2 442 44.2 98.4 98.4 38.0 0 0 0 0 0 0 0 44.2 44.2 0 0 4.2 - 40.3 - 40.3 - 40.3 - 43.4 0 0 - 38.4 0 0 44.2 - 8.7
b.c b.c b.c b.c b.c b.c b.c
M4, M5, M6 M4, M5, M6 c.d
c.d
M31, M14, Ml4, M14, Ml6
M32, M33 Ml5 Ml5 Ml5
b.c b.c
M7 c,d c.d
M4, M5, M6 M37, M38
mol- ’a
6/kJ mol- ’ 1.0 14.0 1.9 8.1 20.3 5.1 36.9 0.1 0.8 5.3 1.7 4.1 2.7 7.1 10.0 2.1 5.3 2.1 29.4 4.3 6.8 1.3 9.6 8.3 2.0 19.0 0.4 1.4 24. I 9.2 6.2 41.8 8.2 34.4 46.7 18.1 45.0 107.3 66.2 110.9 83.4 20.6 23.5 5.5 1.8 3.0 1.5 6.4 2.4 21.0 29.2 9.2 23.9 0.9 3.5 1.9 1.5 5.5 1.1
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Table 3 (continued) No. of reaction in Table 1
rA,S(exp)/kJ
60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99
- 34.0 * I.5 - 18.1 + 0.8 28.9 A 1.2 35.3 * I.8 II.5 + 8.3 - 5.2 & 0.6 5.5 5.5 k 0.6 36.1 2.1 f 0.7 -41.2 - 23.7 f 6.2 - 36.7 f. 4.5 I.0 f 2.5 - 8.7 k 3.8 - 25.0 k 6.3 - 38.7 & 6.3 - 77.2 * 8.9 - 38.7 + 8.6 - 45.0 & 3.6 - 1.0 k 3.6 -9.4+ 4.7 - 0.6 & 0.6 -2.1 k 6.2 -6.1 f 3.8 - 7.6 & 3.2 -3.2 k 3.1 23.9 i 0.9 24.6 & 4.0 28.3 f 1.0 25.8 If: 2.2 23.8 k 1.9 30.9 * 1.8 31.2 f 3.1 29.8 k 1.8 - 17.5 k 12.5 - 52.4 + 10.0 1.3 f 3.8 2.5 * 3.8 33.7 f 1.6
molt ’
No. of model reaction
TA,S”(model)/kJ
mol- ’a
6/kJ mol- ’
in Table 2 M45, M46, M47 M45, M46, M47 CX M4, M5, M6 M36 M31, M32, M33 M31, M32, M33 M31, M32, M33 M8 Ml, M2 M4, M5, M6 M40 Mll, Ml2 M31, M32, M33 M34, M35 M26, M27 Ml4, Ml5
c
Ml4, Ml5 M8 b.c b.c b.c b.c b.c b,c b.c
C.S c.r c.e C.C M25 M25 M25 M25 b.c
e
- 25.8 - 25.8 42 44.2 6.1 4.2 4.2 4.2 36.4 -3.1 - 44.2 - 37.3 - 34.2 4.2 3.8 -41.8 - 40.2 - 80.5 - 40.2 - 36.3 0 0 0 0 0 0 0 42 42 42 42 49.7 49.7 49.7 49.7 0 - 42 0
b.c b.c
M21, M22
0 38.2
8.2 7.7 13.1 8.9 5.4 9.4 I.3 1.3 0.3 5.8 3.0 13.6 2.5 3.2 12.5 16.8 1.5 3.3 1.5 8.7 I.0 9.4 0.6 2.1 6.1 7.6 3.2 18.1 17.4 13.7 16.2 25.9 18.8 18.5 19.9 17.5 10.4 1.3 2.5 4.5
a Average of the results obtained with different models, when applicable. b 2 particles = 2 particles. ’ See discussion in text. d 1 particle = I particle. e I particle = 2 particles.
SF = 1320.85148 + 12.47177 In T + 4.157255 ln( IAIBIc) - 8.31451 In c
(8)
(non-linear molecules) 1.438Zi/T S,D=RC
i
exp( 1.438Ei/T)
- ln[ 1 - exp( - l.438ij/T)]
(9) 1
S,”= R In o,,
(10)
were T is the temperature (in K), M is the molar mass (in g mol- ’), I is the m oment of inertia of a linear molecule, I,,,Ia Zc is the product of the principal moments of inertia of a non-linear molecule, CT is the symmetry number, T;ji is the wavenumber of the ith normal mode of vibration of the molecule (in cm-‘), w0 is the electronic ground state degeneracy, and R is the gas constant. The translational entropy given by Eq. (6) refers to a standard pressure of 1 bar. According to this equation, SF is proportional to In M, and therefore it is not strongly dependent on changes of molar mass. This implies, for example, that in reactions where one parti-
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cle yields two particles, if the molar masses of the reactant and one of the products are of the same magnitude, the translational contribution to the reaction entropy will be close to the translational entropy of the second product. This is seen, for instance, in the case of intermolecular carbonyl insertion reactions and in H, oxidative additions, where the translational entropy changes are nearly identical to Sp(CO) and SF(H,) respectively. The previous discussion can be easily extended to other types of reaction involving several numbers of particles, displayed in Tables 1 and 2. It also applies to the case of the rotational contribution: Eqs. (7) and (8) show that se is rather insensitive to changes in the moment of inertia. Although the vibrational contribution to entropy can be negligible compared with $’ and SF, particularly in molecules with a small number of light atoms, such as hydrogen and carbon, in the case of most organometallit species it has to be considered. While this is true for entropies of individual species, it becomes less relevant when the vibrational entropy change A,,!$ of a reaction is calculated. In many reactions shown in Table 1, the overall change in vibration degrees of freedom is small and leads to a small A,Sf (see, however, discussion below). Another important contribution to the entropy of a large molecule comes from internal rotations [ 1Oa,l 11. However, as in the case of vibration, in many reactions the net change of the internal rotation degrees of freedom is small, leading to a small contribution to the reaction entropy. When the information about the electronic configuration of the ground state is known, it is possible to calculate the electronic contribution to the entropy by using Eq. (10) (it is assumed that the energy difference between the first electronic excited state and the ground state is much higher than k,T). In a chemical reaction where reactants and products have different ground state degeneracies, the electronic contribution to the entropy change must be considered if a very accurate value is to be derived. Take, for example, the reaction of dissociation of I,, yielding two iodine atoms. The ground state electronic degeneracies ~~(1~) = 1 and o&I) = 4 lead to TA,$’ = 3.4 kJ mol- ‘. In many organometallic reactions involving coordinatively saturated complexes, however, the variation of the ground state degeneracies is not as large and therefore neglecting the electronic contribution to the entropy leads to errors which are often comparable with the experimental uncertainties. In conclusion, A,Sp and A,$’ are frequently the most important contributions to the entropy of a reaction. Owing to their insensitivity to changes in molar mass and moments of inertia, these contributions have roughly constant values for organic, inorganic or organometallic reactions of the same type (CO inser-
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tions, a-bond metathesis, etc.). Even though the entropy of a gas phase reaction can be accurately calculated from statistical thermodynamics, the method is laborious and often the necessary structural and vibrational data for reactants and products are not available or are difficult to predict. The use of model reactions which mimic the changes in the external and internal degrees of freedom provides an alternative and easy way of estimating TA,S for organometallic reactions within ca. Other methods for predicting entropy 10 kJ mol-‘. changes avoiding detailed statistical thermodynamic calculations have been reported and applied to biochemical systems [67-721. Let us now analyse in more detail some of the reactions in Tables 1 and 2, paying particular attention to those for which 6 > 10 kJ mol- ’(Table 3). Just for a matter of convenience, the discussion below follows the classification of reactions given in Table 2, according to the number of particles as reactants and products. 4.1. I particle = 1 particle Small entropy changes for reactions where the number of particles is conserved can be predicted, particularly when only structural rearrangements are involved. This is indeed the case for reactions 46, 47, 56, 57, and 69. Although no models could be found for reactions 46, 47, 56, and 57, the reported experimental entropies are close to zero, as expected for 1 particle = 1 particle reactions. The negative value obtained for reaction 56 is probably due to the formation of the three-membered ring in the product. Note, however, that although a negative entropy value is predicted for reaction 69 based on models Ml and M2, and a positive value is experimentally found, the obtained 6 value in Table 3 is reasonably small, ca. 6 kJ mol-‘. Note also, for example, that Benson’s additivity scheme [ 101 also gives a negative value (TA, So= - 0.9 kJ mol- ‘) for the entropy of the reactions CH,CH(CH,)CH,(CO)H
= CH,(CH,),(CO)H (11)
CH,CH(CH,)CH,(CO)CH,
= CH,(CH,),(CO)CH, (12)
which may be better models for reaction 69. 4.2. I particle = 2 particles Reaction 3 corresponds to a a-bond metathesis and ring closure reaction. In this case the model M3 estimates TA, So within 2 kJ mol- ‘. A good agreement is also observed for reaction 20, where model Ml8 was used. However, it is surprising that the estimated TA, So value for reaction 19 (model M17) leads to a large
M.E.
Minus
da Pirdudr,
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Simdes/
Journul
deviation (29.4 kJ mol-‘) from the experimental value. A similar comment applies to reactions 5 and 6, which are CO insertions into M-H bonds. Although the model reactions Ml 1-Ml 3 predict TA, So for reaction 6 within the experimental error, the corresponding estimate for reaction 5 leads to a discrepancy of 20 kJ mol- ‘. Reaction 7 is a ligand dissociation reaction. Based on the model reactions M4-M6 it is expected that TA, So for reaction 7 is about 44 kJ mol- ‘. The large discrepancy found between the estimated and the experimental value (37 kJ mol- ’>, as well as the large uncertainty of the experimental value, strongly suggest that the entropy of reaction 7 in Table 1 is in error. Models M4-M6 were also used for estimating the entropies of reactions 24-33. As seen in Table 1, reactions 25-28 describe the cleavage of the Cr-Cr bond in the complex [Cr(Cp)(CO),], and were studied by different groups. The same happened with reactions 29-3 1 for the analogue Cp * complex, and reactions 32, 33 for {Cr(Cp)(CO>,[P(OMe),])l. It is noted that the experimental values of TA,S for reactions 26, 29, and 32, all measured by the same group, are considerably higher than predicted by the model and are also in disagreement with the other experimental values. The experimental value of the entropy of reaction 36 is considerably smaller than the value predicted for the model reactions M23 and M24. Both reaction 36 and the models involve the formation of a monoatomic species and a polyatomic fragment, implying identical changes in translational, rotational and vibrational degrees of freedom. From the above discussion after Eqs. (6)-(8) it is expected that the translational and rotational contributions to A,S” are similar in reactions 36, M23 and M24. However, the frequencies of the three vibration modes lost upon dissociation of the model compounds (CH,F and CH,Cl) are certainly much higher than the corresponding frequencies in the case of the dissociation of W(CO),Xe. Therefore, according to Eq. (9), the negative vibrational contribution to A,S” will be much larger for reaction 36 than for the models M23 and M24, leading to a considerably lower A,S” value in the former case [73]. The experimental values of the entropies for the CO insertion reactions 49-52 show unexpected differences. Indeed, while the models used for estimating TA,S for R = Me and Ph lead to errors smaller than 10 kJ mol- ‘, the discrepancies found for R = Et and Pr are considerably higher. The reported entropies of reactions 62 and 87-90 seem too low when compared with typical data for 1 particle = 2 particles reactions, ca. TA, So= 42 kJ mol-‘. These discrepancies must be related to the internal rotation of the q2-H2 moiety in the reactant complex and to the loss of internal rotation degrees of freedom of the phosphine group upon formation of a C-H --) M agostic interaction in the organometallic
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product [74]. Both effects act in the same direction, i.e. the former increases the entropy of the reactant and the latter reduces the entropy of the product. While the explanation seems reasonable, it could also be used to predict that reactions 46 and 47 should have negative (albeit small) entropies, which conflicts with the experimental data in Table 1. Note, however, that the error bars for the entropies of these reactions do not seem to invalidate the prediction TA, S < 0. A large deviation is found between TA,S for reaction 75 and for the model reactions M26 and M27 (16.8 kJ mol-’ ; Table 3). This discrepancy and the large experimental error quoted for TA,S(75) suggest that the reported entropy of reaction 75 is too high. The reductive elimination reactions 91-94 have entropies (79.9 _t 6.3, 103.8 k 5.9, 104.6 & 10.5, and 100.0 i 5.9 J K- ’ mol- ’ respectively), considerably smaller than expected on the basis of the data for the model reaction M25 in Table 2 (166.9 J K-’ mol- ‘), leading to an average 6 value of ca. 2 1 kJ mol- ‘. We are unable to explain this discrepancy. Steric effects in the reactant complex, hindering the internal rotations of the SiMe, group, would imply an upward correction of TA,So predicted by the model. 4.3. I particle = 3 particles No model is presented for reaction 77. Note, however, that this reaction corresponds to a double CO insertion. Therefore it is expected that A,S(77) is approximately twice the value given in Table 2 for models Ml4 and M15, which yields TATS0 = - 80.5 kJ mol- ‘. This is in good agreement with the experimental value. 4.4. 2 particles = 2 particles Reactions 37-41 should have entropies close to zero. As stated by Angelici and Ingemanson [31], the abnormally large experimental values are not understood. Kubas et al. [32] have explained the negative entropies of reactions 42 and 43 by the interaction of solvent (thf) molecules with the coordinated water. As one would expect that, in the absence of such specific interactions, TA,S = 0 and, as also one cannot rule out the solvation of free water reactant molecules, the experimental values imply that the coordination of thf to the organometallic product produces a larger entropy decrease than in the case of the free water molecule (see below for more comments on solvation). Although no specific model was used for reactions 53 and 54, the comparison between the corresponding A,S values suggests that the value reported for reaction 53 is in error. While A,S for reaction 54 is in the range found for 2 particles = 2 particles reactions (i.e. A,S = 01, the value for reaction 53 is much higher than expected.
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The entropies of reactions 65-67 are close to zero as predicted for this type of 2 particles = 2 particles reaction. The negative value of A,S for reaction 65 is, however, unexpected, judging from the positive entropies of reactions 66, 67 and of the model reactions M31-M33. The model reactions M34 and M35 predict a small positive value for the entropy of reaction 74. In contrast, the experimental value found is small but negative. This discrepancy suggests that the experimental value should be redetermined, since it is based on measurements at two temperatures only and has a large experimental error. We could not find appropriate organic analogues for reactions 80-86, where an v2-ethylene is replaced by another v2-olefin, and for reactions 95, 97, and 98. The values of A,S reported for reactions 80-86 are, however, nearly within the expected range for 2 particles = 2 particles reactions, i.e. TA,S = 0, particularly if the experimental uncertainties are considered. The same is observed for reactions 95, 97, and 98, although in the case of reaction 95 the recommended TA,S value is about 18 kJ mol- ’ higher than predicted.
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4.7. 4 particles = 3 particles The reactions M45-M47 predict, as observed experimentally, that the absolute values of the entropies of reactions 60 and 61 are smaller than the typical range for 2 particles = 1 particle reactions. The agreement between the estimated and the experimental data is fair: the prediction A,S” = - 86.7 J mol-’ K-’ leads to errors of 8.1 and 7.7 kJ mol-’ for reactions 60 and 61, respectively (Table 3). These discrepancies are within our accepted limits for the estimates. However, it is somewhat surprising that the entropies of reactions 60 and 61 differ by 53 J mol-’ K-‘. This difference is hardly justifiable by invoking solvent effects (see below). Unfortunately, the entropies of the model reactions M45-M47 vary over a wide range, making it difficult to assess which is the most reliable experimental value.
5. Final comments
Reaction 2 can be decomposed in a q-bond metathesis and a ligand dissociation reaction. It is expected that A,S = 0 for the former process (reactions M28-M30) and AJo= 130-150 J mol- ’ K- ’ for the latter (see reactions M4-M6). The model reaction M41 has A,S” = 147.4 J mol-’ K- ‘, which corresponds to TA, So= 43.9 kJ mol- ‘. The estimate exceeds the experimental TA,S value by 14.1 kJ mol- ‘. This significant difference may reflect a loosely bound thf molecule in the organometallic reactant: the internal rotation and the low frequency vibrational modes involving the coordinated thf moiety, which will increase the entropy of the organometallic adduct, are lost upon dissociation. The value of TA, So= - 37.3 kJ mol- ’for the model reaction M40 is about 14 kJ mol-’ lower than the corresponding value for reaction 71 ( - 23.7 f 6.2 kJ mol-‘). We note, however, that the experimental value relies on a van’t Hoff plot involving only three temperatures.
It is understood that the use of gas phase models at 298 K to estimate entropies of organometallic reactions in solution is somewhat crude, since a more detailed analysis of the internal and external degrees of freedom of reactants and products (whenever possible), together with temperature and solvent effects, might allow more accurate predictions. However, the method discussed above is extremely simple to apply and in most cases it is sufficiently accurate to assess or to predict entropy changes of organometallic reactions. It is of course recognized that an error of 10 kJ mol- ’ in TA,S leads to a very large error in the equilibrium constant (see Introduction) and, in this regard, the method is not satisfactory. Yet, as mentioned before, a fair amount of the experimental data is probably less reliable than the values obtained through the model reactions. Let us finally address the temperature and solvent effects on the reaction entropies. The fact that the large majority of organometallic reactions is studied in solution limits the temperature range of the experiments. For example, all reactions in Table 1, except three (7, 58, 631, were studied in solution at temperatures ranging from ca. 170-450 K. As can be concluded from
4.6. 2 particles = 4 particles
A,S(298) = A,S(T)
Reactions 34 and 35 involve changes of ligand hapticity and provide an example for which it is not possible to find suitable organic models. Therefore, large discrepancies between the entropies of models, such as M42-M44, and the entropies of those organometallic reactions could be expected.
the temperature corrections to derive A,S at 298 K are well within the uncertainty accepted for the present estimation method. A,C,, which represents the average reaction heat capacity change in the temperature range 298-T, is small for most reactions in Table 1 ( I A,C, I less than ca. 30 J mol-’ K- ’[75]) and is multiplied by
4.5. 2 particles = 3 particles
298 + A,C, lny
(13)
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a factor smaller than one. We therefore decided not to apply any temperature corrections to our model. With regard to solvation effects, the difference between the entropy of a reaction in the gas phase and in solution has been discussed, and it does not seem to be well understood [69,72,76]. It is generally agreed that the transfer from the gas phase to solution of a reaction where there is no net change in the number of particles does not lead to a significant entropy difference. However, for reactions involving a different number of particles as reactants and products there is conflicting evidence about the expected entropy differences in the gas phase and in solution [69,72,76]. According to Hammett [76], in the case of 2 particles = 1 particle reactions, it should be expected that entropies in solution are considerably less negative than in the gas phase. However, as discussed by Page [69], similar entropies should be expected for many association reactions in the gas phase and in solution. Most data in Table 1 refer to reactions involving neutral species, in solvents where solvation effects are expected to be small. The fact that the method of estimation discussed in this paper leads to a satisfactory agreement with experimental data, suggests that gas phase and solution values of TA,S for most reactions in Table 1 are similar within the maximum accepted error for the estimations (10 kJ mol- ’), even for reactions were the number of particles is not conserved.
of Organic und I91 J.D. Cox and G. Pilcher, Thermochemistry Orgunometullic Compound.s, Academic Press, London, 1970. Kinetics, Wiley, New York, [lOI (a) S.W. Benson, Thermochemicul 1976; (b) N. Cohen and S.W. Benson, Chem. Reu., 93 (1993)
Acknowledgements
D71 L.Y. Goh, S.K. Khoo and Y.Y. Lim, J. Orgunomet.
2419.
G.J. Janz, Thrrmodynumic Properties of Organic Compounds, Academic Press, New York, 1967. [121 R.C. Reid, J.M. Prausnitz and B.E. Poling, The Properties of Gu.se.s und Liquids, McGraw-Hill, Singapore, 4th edn., 1988. [I31 M.E. Thompson, S.M. Baxter, A.R. Bulls, B.J. Burger, M.C. Nolan, B.D. Santarsiero, W.P. Schaefer and J.E. Bercaw, J. Am. Chem. Sot., 109 (1987) 203. 1141 A.R. Bulls, J.E. Bercaw, J.M. Manriquez and M.E. Thompson, Polyhedron, 7 (1988) 1409. [I51 G.M. Smith, J.D. Carpenter and T.J. Marks, J. Am. Chem. SIX. [ill
108 (1986) 6805.
[I61 K.G. Moloy and T.J. Marks,
J. Am. Chem.
SW.,
106 (1984)
7051.
[I71 R.G. Bedford, J. Phys. Chem., 81 (1977) 1284. iI81 E.U. van Raaij, C.D. Schmulbach and H.H. Brintzinger, Orgunomet.
Chem.,
328
J.
(1987) 275.
[I91 L. Stahl and R.D. Ernst, J. Am. Chem. SW., 109 (1987) 5673. [201 G. Fachinetti, G. Fochi and C. Floriani, J. Chem. Sot., Dulton Truns.,
(1977) 1946.
El1 F. Calderazzo, G. Fachinetti and C. Floriani, J. Am. Chem. kc., 96 (1974) 3695.
La A.A. Gonzalez and C.D. Hoff, InorR. Chem., 28 (1989) 4295. k31 K. Zhang, A.A. Gonzalez, S.L. Mukerjee, S.-J. Chou, C.D. Hoff, K.A. Kubat-Martin, D. Bamhart and G.J. Kubas, J. Am. Chem. Sot.,
113 (1991) 9170.
[241 S.J. McLain, J. Am. Chem. SW., 110 (1988) 643. I251 L.Y. Goh and Y.Y. Lim, J. Orgunomer. Chem.,
402 (1991)
209.
WI W.C. Watkins, T. Jaeger, C.E. Kidd, S. Fortier, M.C. Baird, G. Kiss, G.C. Roper and C.D. Hoff, J. Am. Chem. Sot., 114 (1992) 907. (1990)
This work was supported by Junta National de Investigasao Cientifica e Tecnologica, Portugal (Projects PBIC/C/CEN/ 1042/92 and STRDA/C/CEN 469/92). We also thank Dr. Herminio P. Diogo for helpful comments.
References and notes [I] T.J. Marks (ed.),
Bonding
Energetics
in Orgunnmetullic
Com-
ACS Symp. Ser. 428, American Chemical Society, Washington, DC, 1990. [2] J.A. Martinho Sirnoes and J.L. Beauchamp, Chem. Rev., 90 pounds,
( 1990)629. [3] T.J. Marks (ed.), Metul-Ligund Bonding Energetics in Orgunotrunsition Metul Compound.s, Polyhedron Symposium-in-Print,
Vol. 7, 1988. [4] J.A. Martinho Simoes (ed.), Energetics of Or,gunometullic Species, NATO ASI, Ser. C, Vol. 367, Kluwer, Dordrecht, 1992. [S] C.D. Hoff, Pmg Inorg. Chem., 40 (1992) 503. [6] S.P. Nolan, Bonding Energetics of Organometallic Compounds, in Encyclopedia of Inorganic Chemistry, Wiley, New York, 1994. [7] P.B. Dias, M.E. Minas da Piedade and J.A. Martinho SimEes, Coord. Chem. Rev., 135/136 (1994) 737. [8] See, for example, Ref. [4], p. 197.
Dl
Chem.,
399
115.
G.J. Kubas, G. Kiss and C.D. Hoff, Organometullics,
IO (1991)
2870.
1291 C.D. Hoff, J. Orgunomet. Chem., 282 (1985) 201. [301 B.H. Weiller, J. Am. Chem. Six., 114 (1992) 10910. [311 R.J. Angelici and CM. Ingemanson, ZnorR. Chem., 8 (1969) 83.
[321 G.J. Kubas, C.J. Bums, G.R.K. Khalsa, L.S. van der Sluys, G. Kiss and CD. Hoff, Orgunometullic.s, II (1992) 3390. I331 G.R.K. Khalsa, G.J. Kubas, C.J. Unkefer, L.S. van der Sluys and K.A. Kubat-Martin, J. Am. Chem. Sot., 112 (1990) 3855. I341 R.J. Klinger and J.W. Rathke, Inorg. Chem., 31 (1992) 804. [351 F. Calderazzo, Anger. Chem., Int. Ed. Engl., 16 (1977) 299. [361 A. Marcomini and A. PO&, J. Chem. Sot., Dalton Truns., (1984) 95. [37] (a) K.P. Gable and T.N. Phan, J. Am. Chem. Sot., 115 (1993)
3036; (b) 116 (1994) 835. [38] C. Jablonski, G. Bellachioma, G. Cardaci and G. Reichenbach, J. Am. Chem. SK., 112 (1990) 1632. [39] R.D. Barreto, J. Puga and T.P. Fehlner, Orgunometullics, 9 ( 1990) 662. [40] A.K. Baev and A.A. Barkatin, Russ. J. Phys. Chem., 58 (1984) 195. [41] H.E. Bryndza, L.K. Fong, R.A. Paciello, W. Tam and J.E. Bercaw, J. Am. Chem. Sot., 109 (1987) 1444. [42] G. Bor, Pure Appl. Chem., 58 (1986) 543. Chem., 417 (1991) [43] R. Koelliker and G. Bor, J. Orgunomet. 439. [44] D.G. Gusev, A.B. Vymenits and V.I. Bakhmutov, Inorg. Chem., 31 (1992) 2.
180 1451
M.E.
[48]
J.A. Murtinho
Am.
Simc?rs/Journal
Chrm.
Sec.,
5459.
J.W. Rathke, R.J. Klingler and T.R. Krause, 11 (1992)
[47]
du Piedude.
A.J. Poe, C.N. Sampson and R.T. Smith, J. 108 (1986)
[46]
Minus
Orpmometullics,
585.
F. Ungvary, J. Orpwmetul. Chem., 36 (1972) 363. F. UngvLry and L. Mark& J. Orgunomrt. Chem.,
20
(1969)
205. [49] [50]
MS. Borovikov, I. Kovacs, F. Ungvary, A. Sisak and L. Mark& Orgunomrtullics, I I (I 992) 1576. J.J. Pignatello and Y.-T. Fanchiang, J. Chrm. Sot., Dalton Trans.,
(1985)
1381.
108 (1986)
3659.
[54] [55]
V.L. Coffin, W. Brennen and B.B. Wayland, J.
[68]
II0
(1988)
Chrm.,
27
[73] 8 (1989) Am.
Chem.
6063.
R. Cramer, J. Am. Chem. Sot., 89 (1967) 4621. [57] B.E. Hauser, D. Gusev and K.G. Caulton, J. Am. Chrm. Sot., 116 (1994) 208. [58] M.J. Hostetler, M.D. Butts and R.G. Bergman, Or~unometullics, 12 (1993)
65.
R.J. McKinney and D.C. Roe, J.
Am.
Chem.
Sot.,
108 (1986)
[74]
5167. [60]
CA. Tolman, J. Am. Chrm. SW., 96 (1974) 2780. R.L. Brainard and G.M. Whitesides, Orgunomrtullics,
(I 985)
[75]
D.R. Stull, E.F. Westrum, Jr. and G.C. Sinke, The Chemical Thermodynumics of Orgunic Compounds, Wiley, New York, 1969. und Eyuilihriu oj’ Organic [63] M. Frenkel (ed.), Thermochemistry Compounds, VCH, New York, 1993, Book III, Chapter 4.
[76]
[61]
4
1550. 1621
und Formulur,
Stundurd
Prohuhility
und
Stotistic.s
(1971)
1678.
W.P. Jencks, Ado. En:ymol.,
43 (1975)
219.
338.
[56]
[59]
Tubks
M.I. Page, Chem. Sot. Rrv., 2 (1973) 295. [70] Ml. Page, Anger. Chem., Int. Ed. Engl., 16 (I 977) 449. [71] A.J. Doig and D.H. Williams, J. Am. Chrm. SW., 114 (1992)
1438. Sot.,
CRC
167-180
CRC Press, Boca Raton, FL, 1991. [65] The NBS Tables of Chemical Thermodynamics Properties, /. Phys. Chrm. Ref: Dutu, II (1982) Suppl. 2. [66] See, for example, (a) G.S. Rushbrooke, Statisticul Mechanics, Oxford University Press, London, 1967; (b) B.J. McClelland, Stutisticul Thermodynamics, Chapman and Hall, London, 1979. [67] M.I. Page and W.P. Jencks, Proc. Nut. Acud. Sci. USA, 68
[72]
B.B. Wayland, V.L. Coffin and M.D. Famos, Inorg. (I 988) 2745. B.B. Wayland, Y. Feng and S. Ba, Organometullics,
[53]
[64] W.H. Beyer (ed.),
518 (1996)
[69]
[51] B.B. Wayland, S. Ba and A.E. Sherry, J. Am. Chem. Sot., 113 (1991) 5305. [52] M.D. Farnos, B.A. Woods and B.B. Wayland, J. Am. Chem. Sot.,
of Oqunometullic Chemistry
M.S. Searle and D.H. Williams, J. Am. Chem. SOL..,114 (1992) 10690. For example, typical C-F and C-Cl stretching frequencies are 1100 and 650 cm.-’ respectively [lOa], whilst a rough estimation of the W-Xe stretching frequency in W(CO),Xe leads to 227 cm-’ [estimated from v(W-CO) = 403.3 cm-’ in W(CO), Spectru, Academic Press, (P.S. Braterman, Metul Curhonyl London, 1975) and the relation (v, /vz) = ( pz /p, )‘j2, where p is the reduced mass]. Therefore, the use of Eq. (9) leads to TA,Sz = - 0. I and - 0.5 kJ mall ’ for the two organic molecules respectively, compared with TA,Sf = - 2.4 kJ mol ’ for the Xe complex. Larger differences can be expected for the two bendind modes lost upon dissociation, J. Eckert, G.J. Kubas and R.P. White, Inorg. Chem., 31 (1992) 1550 and references cited therein. Estimated from A,C, for the model reactions in Table 2. Data from Refs. [ 121, [62] and [65]. L.P. Hammett, Physicul Orgunic Chemistry, McGraw-Hill, New York, 2nd edn., 1970.
ollmal ds me?Zikc
Chemistry ELSEVIER
Journal of Organometallic
Chemistry 5 18 (1996) 167- 180
Energetics of organometallic species: the entropic factor Manuel E. Minas da Piedade a,*, Jo& A. Mat-tinho Simbes b a Crntro b Departumento
de Quimicu de Quimicu
Estruturul,
Cornp1rx-o I, Institute
e Bioquimicu,
Superior
Fuculdude
de Ci&cius,
Received
8 December
Tknico,
Univrrsidude
1096 Lishou de Lishou,
Coda,
Portugul
1700 Lishoa,
Portugul
1995
Abstract A rather simple procedure to estimate entropy changes of organometallic reactions is described. It merely consists in finding organic or inorganic reactions, for which the gas phase standard entropies are well known, that can mimic a given organometallic reaction. The merits and limitations of the method are discussed, and it is concluded that a careful use of model reactions can at least provide a reliable guideline to estimate or even to assess entropy data for many organometallic reactions. Keywords:
Gas phase reactions; Organometallic reactions; Entropy data
1. Introduction The thermodynamic driving force of a chemical reaction is measured by the Gibbs energy change A,G associated with the conversion of reactants to products, spontaneous reactions having A,G < 0. Under equilibrium conditions A,G = 0 and the standard Gibbs energy A,G” of the reaction is related to the equilibrium constant K of the reaction by
A,G”= -RT
In K
(1)
were R is the gas constant and T the absolute temperature. As K reflects the relative amounts of reactants and products present in the reaction mixture (and therefore the reaction yield), the prediction of the feasibility of a given reaction or of a postulated elementary step in a composite reaction, on thermodynamic grounds, implies that one is able to calculate A,G” for the process under study. The standard Gibbs energy of a reaction is related to the corresponding enthalpy A, Ho and entropy A, So by
A,G” = A,Ho - TArSo
(2)
In the case of reactions involving organometallic compounds much more is known about the enthalpy term than about the entropy term in Eq. (2). Most experimental studies in organometallic thermochemistry available
* Corresponding author. 0022-328X/96/$15.00 PI/
0 1996 Elsevier
SOO22-328X(96)06193-1
Science
S.A. All rights reserved
in the literature
report
the determination
reaction,
which
other
from
enthalpies
of enthalpies of reaction,
of en-
A, HO of formation and bond dissociation enthalpies DH ‘(M-L> (M = metal centre; L = ligand) were (or can be) derived [l-7]. Some methods of estimating A, H ‘, A,H” and DH’(M-L) data have also been discussed [8]. Although these estimating procedures are not as accurate and general as several existing schemes for predicting thermochemical data of organic compounds [9- 121, they are often used to assess experimental data and to discuss the energetics of bond cleavage and formation in organometallic reactions. Thus, in the absence of direct experimental measurements, it is now possible, for many organometallic reactions, to make reliable predictions of the enthalpy term in Eq. (2). Much less attention has been given to the measurement and estimation of entropy changes in organometallit reactions, despite the fact that, in some cases, the value of TA, So makes an important contribution to A,G”, or even determines if the reaction is spontaneous. For example, in the reaction (see Table 1) thalpies
Cr(C%(PCy,),(sln)
+ H,(s
-)Cr(CO),(PCy,),(r12-H2)(sln)
ln> (3)
A,Ho = -30.5 kJ mol-’ and TArSo = -31.9 kJ mol- ’, leading to A,G” = 1.4 kJ mol- ‘. Therefore, although the reaction is exothermic, the entropy change leads to a positive value for A,G”. Note that, in this
I9
16 17 18
IO II 12 13 I4 I5
4
2
1
No.
‘Si’ CH 2’
CH, ‘Me
Me (sin) + SiMe, (sln)
+ H, (sln)
Th(cp * ),(~R)H (sin) + co (sln) = Th(Cp * ),(oR)c(o)H (sln) R = CH’Bu 2 R = 2,6-C6H3’Bu2 Ukot), (g) = Ukot) (g) + cot (g) [Ti(Cp)2Cl]2 (sin) + 2C0 (sln) = 2TiCp,(CO)CI (sin) Ti(C,H,),PEt, (sin)= TX&H,), (sln)+PEt, (sin> Ti(C,H,,),L (sin) = Ti(C,H,,), (sln)+L (sin> L = PF, L=PMe, L = PEt, L = PMe,Ph L = P(OMe), L = P(OEt), HqCp),R z (sin) + CO (sin) = HACp),RC(O)R (sin> R = Me R = Bz HffCp* j2H, (sin)+ C,H, &In) = HMCp” ),(Ph)H (sInI+ H, (sin)
(sin) = (Cp’ jI<
343-387
benzene, [ 141 benzene, [ 141
270-300 313-332 224-269 276- 303 269-303 259-290
180-220 180-200 445-540 243, 268 300-318
333-373
269-307 269-307 373-444
toluene, [20]
1171 toluene, [ 181 thf, [ 191 thf, [I 9]
toluene, [ 161
cyclohexane, [ 151
323-373
benzene, [ 141
Th(Cp* ),(CH,SiMe3),
279-353 298-353
benzene, [ 131 benzene, [ 131
Sc(Cp * ),H (sin) + C,Hr, (sin) = Sc(Cp * ),Ph (sin) + H, (sln) Sc(Cp * ),(thf)H (sln) + C,H, (sln) = Sc(Cp * ),Ph (sln) + thf (sln) + H, (sin)
T/K
Solvent, Ref.
Reaction a
Table 1 Entropies of selected organometallic reactions
1.3
139.4f20.4
- 138.1 + 23.4 - 120.1 * 2.5 - 14.6& 2.6
130.5 + 10.5 142.7 * 10.0 134.7+ I.3 139.3+_ 7.9 l25.9* 13.4 ll4.6k 8.8
-49.0+ 18.0 - 100.0*31.0 272 *58 -85 +20 145.6+ 10.0
69.5 + 20.9
43.2+
4.2 8.4
Km ’mol- ’
-4.2* 100.4+
A,S/J
46 41 48
44 45
42 43
31 3x 39 40 41
22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
21
20
*
0
’ XCO),l,
* KCO),
(sin)
Mn,(CO),,
(sin)
(sin) = W(CO),(PR,)2Hz
(sin) + Hz (.sln) = 2Mn(CO),H
W(CO),(PR,),(v’-H,) R = cyyC,Ho R =‘Pr
(sln)
Mo(CO),(CD~CN), (sin)+ CpH (sin) = Mo(Cp)(CO),H (sln)+3CD,CN (sin) Mo(CO);(thf), (sin)+ PhMe (sin) = Mo(T’-PhMe)(CO), (sin)+ 3thf (sln) W(CO),Xe (sln) = W(CO), (sin)+ Xe (sln) W(CO),(PhNH,) (sInI+ L (sin) = W(CO),L (sin)+ PhNH, (sln) L = PBu, L = PPh, L = P(OBd, L = P(OPh), L = AsPh, (sin)+ H,O (sln) = W(CO),(PR;),(H,O) (sin)+ H, (sin) W(CO),(PR,),(T’~H,) R = Cy R =‘Pr W(CO),(PR,),(thf) (sin) = W(CO),(PR,), (sln)+ thf (sin) R =cy-C,H,, R =‘Pr
(sln)
(sin)
(sin) + H, (sin)
(slid + py (sln)
(sin) = 2CdCp)(CO),P(OMe),
(sin) = 2CrtCp
py (sin) = CdCO),(PCy3)2 (sln) = 2CdCp)(CO), (sin)
(CI(Cp)(CO),[P(OMe),]]~
[CdCp
CdCO),(PCyj), [CrtCp)(CO)ilz
V(Cp), 1(sln) + CO (sin) = V(Cp12(COII (sin) CdCO),(PCy,), (sin)+ L (sin) = CdCO),(PCy,),(q2-L) L = N, L = H;
HfbH
\
+a 0
[ 141
(331
[32]
supercritical
toluene,
toluene,
thf, [32]
CO,,
toluene, [23] toluene, [24] toluene, [25] toluene, [26] thf, [24] toluene, [27] toluene, [26] thf, [26] toluene, [25] thf, [26] CDJN, [28] thf, [29] liquid Xe, [30] toluene, [3 I]
toluene, [2l] thf, [22]
benzene,
[34]
273-309 265-305 353-453
193-293
203-298
283-318 291-318 278-298 208-368 298-333 283-338 208-368 241-314 273-323 223-273 243-263 198-235 316.-355 308-354 173-198 308-318
272-316
332-386
8.4 8.4
+33 +2l +2s + 8 +25
9.6 7.1 23.8 5.9 9.2 3.8 5.4 9.2 12.1 5.4 6.3 12.6 8.4 5.0 20.9
14.2
9.8
10.0+ s.o+ 35.6+
5.9 8.8 3.3
129.7 f IO.5 l42.3+ 8.4
-69.0+ -78.7k
IS1 360 222 372 280
- 148.1 k - 107.1 f 120.5 f 155.2* 212.1 k 146.9_+ 143.5+ 229.3 + 179.1 i l69.0+ 288.7k 175.7+ 214.6+ l73.6* 66.9 +
- 144.8&
78.8k
60 61 62 63 64 65 66 61 68 69 70 71 72 73 14 75 76 77 78 79
57 58 59
56
55
PPh z Me
0 I;FL--%--Me oc
PPh z Me
(sin) I+
+Le ‘0‘ 0
(sin)
0 (sln)
(sin) + H,O (sin)
Co(CO),H(sln) = CdCO),H(sln) + CO(sln) Co(CO),C(O)Prtsln) = Co(CO),C(OYPdsln) 2Me-B ,2(sln) = [Me-B ,z]z(sln) 2Rh(TMP)‘(sln)+ CH,(sln) = Rh(TMP)Me(sln) + Rh(TMP)H(sln) Rh(OEP)H(sln) + U&In) = Rh(OEP)CHO(sln) [Rh(OEP)],(sln) + H z(sln) = 2Rh(OEP)H(sln) [Rh(TXP)],(sln) + CH,(sln) = Rh(TXP)CH,(sln) + Rh(TXP)H(sln) [Rh(OEP)],(sln) + C, H&In) = (OEP)RhCH,CHMeRh(OEPXsln) [Rh(OEP)],(sln) + CO(sln) = (OEP)RhC(O)Rh(OEPXsln) [Rh(OEP)],(sln) + ZCO(sln) = (OEP)RhC(O)C(O)Rh(OEP)(sln) (OEP>RhC(O)Rh(OEP%ln) + CO(sln> = (OEP)RhC(O)C(O)Rh(OEP)(sln) [Rh(OEP)],CO(sln)+ CO(sln) = (OEP)RhC(O)C(O)Rh(OEPXsIn)
Ru(H)(~~-H~XCI)(CO)[P(~P~~)],(~I~) = Ru(HXCIXCO)[P(‘Pr,)]z(sln)+ H,(sln) Os,Cp,(g) = 2OsCp,(g) Os&CO),,(sln) + PhC=CPh(sln) = OS&CO), ,(PhC=CPh)(sln) + CO(sln) Co,(CO)&sln)+ H,(sln) = 2Co(CO),H(sln) Co,(CO),(sln)+ H,(sln) = 2Co(CO),H(sln)
[FeCo,(CO)&CPh)H] (sin) = [FeCo,(CO),(HCPh)] (sln) Ru,Cp, (8) = 2RuCpz (g) Ru(Cp * )(PMel),(OH) (sln)+PhzNH (sin) = Ru(Cp * XPMe,),(NPh,) Ru,(CO),, (sin)+ 3C0 (sin) = 3Ru(CO), &In)
PPh z Me
Me I;Fe/-CO oc
IL+
(sin) =
(sln) +
PPh z Me
o-_“go
CP’
CP”
ether, [35]
[381
decalin, [45] supercritical CO,, [46] heptane, [47] hexane, [42] heptane, [48] octane, [49] water, [50] benzene, [5 I] benzene, (521 benzene, [53] benzene, [5l] benzene, [54] toluene, [55] toluene, [55] toluene, [55] toluene, [55]
[Ml
n-hexane, [42] i-octane, [43] toluene-d,, [44]
thf, [4l]
[401
toluene, [39]
CH $I,,
C,D,. 1371
decalin, [36] supercritical CO,, [34]
2,2’-diethoxydiethyl
Mn(CO),R (sln) + CO (sin) = Mn(CO),C(O)R (sln) R=Me R = Et R = Pr R = Ph Mn,(CO),, (sln) + Re,(CO),, (sin) = 2(CO),MnRe(CO), Mn,(CO),, (sln)+ Co,(CO)s (sin> = 2(CO),MnCo(CO),
49 50 51 52 53 54 (sin) (sln)
Solvent, Ref.
Reaction a
No.
Table I (continued)
288-298 298-358 280-350 353-393 298-335 294,335 353,393 280-330
333-453 3077428
373-448 180-190 500-625
170-298 500-625
220.309
378-402
353-453
T/K
Km’ mol-’
0.8 5.9 0.8
2.0
- 114.0+ 5.0 -60.8& 2.6 97.1+ 4.1 ll8.6* 5.9 38.5 + 28.0 - 17.6* 2.1 18.4 18.4+ 2.1 121.3 8.9+ 2.5 - 138.1 - 79.5 * 20.9 -123 *I5 3.3* 8.4 - 29.3 + 12.6 -84 +21 -130 &2l -259 &30 -130 k29 -151 *I2
-5.o+ l29.9+ -25.5*
-6.5+_
- 117.1 * 16.7
- 125.5 - 64.9 - 37.2 - I 14.6 80.3 + 2.5 2.9& 3.3
I
A-S/J ,
Rh(acacXC,H,),(sln)+L(sln) = Rh(acacXC,H,)L(sln)+CzH,(sln) L = CH,CHF L = CH,CHCI L = CH,CHMe L = CH,CHEt L = cis-C,Hs L = tran.s-C,Hs L = ‘C,H, II(H),(r$H,~X)[PMe(‘Bu),],(sln) = I~H),(X)[PMe(‘Bu),],(sln)+H2(sln) x = Cl X = Br x=1 II(D)2(n2-D2)(CI)[PMe(‘Bu),]l(sln) = 1~D),(C1)[PMe(‘Bu),],(s1n)+ D,(sln) It(CO),(SiR,)(H)( @H2),(TaCp,&ln) = It(CO),( p-CH2)2(TaCp,)(sln)+R S = thf-d, R = Me S = thf-d; R = Et S = toluene-d, R = Et S = thf-d, R = Ph Ni]P(O-o-tol),l,(sln)+ C,H,(sln) = Ni[P(O-o-tol),]s(C,H,)(sln)+P(O-o-tol),(sln) Ni]P(O-o-tol),l,(C,H,Xsln) + P(O-o-toi),(sln) = Ni[P(O-o-tol),],(C,H,)(sln) Ni]P(O-o-tol),l,(sin)+ L(sln) = Ni[P(O-o-tol),],L(sln)+ P(O-o-tol),(sln) L = C,H,, L = 1-hexene r~un.s-Pt(PEt3),(Cl)Et(sln) = rruns-Pt(PEt3)2(Cl)H(sln)+ C,H,(sln) ,SiH(sln)
cyclohexane, [61]
toluene, [59] toluene, [59] benzene, [60]
toluene-d,, [57] S, ml
toluene-d,, [57]
toluene, [56]
273-3 13 2633313 253-343 294-338 2133243 2133243
260-294
250-294
a acac = acetylacetonate; C,H, = 3.methylpentadienyl; C, H,, = 2,4-dimethylpentadienyl; cot = 1,3,5,7cyclooctatetraene; Cp = n’-C,H,; Cp * = n5-C,Me,; methylcobalamine; OBP = octaethylporphyrin; py = pyridine; thf = tetrahydrofuran; TMP = tetramesitylporphyrin; to1 = tolyl; TXP = tetraxylylporphyrin.
91 98 99
91 92 93 94 95 96
87 88 89 90
81 82 83 84 85 86
80
2.9
12.1 15.9 2.1 20.9 12.6 10.9 10.5
Cy = cyclohexyl;
4.2+ 12.6 8.4* 12.6 113.0+ 5.4
79.9k 6.3 103.8f 5.9 104.6k 10.5 lOO.Of 5.9 -58.6k41.8 - 175.1+ 33.4
82.4* 13.4 95.0+ 3.3 86.6f 7.5
80.3f
-3.3* -31.4* -2.1* -1.1 + - 20.5 k - 25.5 k - 10.9+
Me-B,,
=
5
2 u
2
s
s ir! 9 3, 3 \ k
37 2
-+ ‘?
% h % %‘ e
172
M.E. Minus du Pirdudr,
J.A. Murtinho
Simdes/Journul
case, K = 0.57, and ignoring the entropic contribution to A,G” (i.e. making A,G” = ArHo) results in an enormous error in the value of the equilibrium constant (K = 1.8 X lo5 instead of K = 0.57). The importance of evaluating A,S” for the thermodynamic analysis of organometallic reactions led us to search for a simple and reliable method for estimating (and assessing) A,S” data. We have found that for many of those reactions reasonable estimates of A,S” can be obtained by using entropy data for model reactions for which the standard entropy changes are well known.
2. Selected entropy data for organometallic reactions The values in Table 1 [13-611 were selected to illustrate the merits as well as the limitations of the estimation method discussed below. These data seldom refer to the reactants and products in their standard states [9], since concentrations and not activities were used to derive the equilibrium constants, but it will be assumed that the overall corrections are smaller than the experimental uncertainties. In any case, the organometallic reaction entropies presented in Table 1 and in the text below will be represented by A,S and not by A,S”. In general, A,S” values are obtained from van’t Hoff plots [9,62,63]: A,H” lnK=--
RT
ofOr,gnnometullic
Chemistry
518 (1996) 167-180
Take, for example, reaction 16, an intermolecular carbony1 insertion into a hafnium-methyl bond. As far as entropy is concerned, this reaction can be modelled by reaction Ml4 or by reaction Ml5 (“M” for model; see Table 2 [62,65]). It is seen that A,S(16) = - 138.1 + 23.4 J K-’ mall ’ is close to A,S”(M14) = - 132.3 J K-’ mall ’ and A,S”(M15) = - 137.8 J K-’ mol-‘. Consider now the a-bond metathesis reaction 1, for which A,s(l> = -4.2 i. 4.2 J K-’ mall’. In this case, the model reactions M28, M29, and M30 yield an average A,S” = - 7.8 J K- ’ mol- ’, in good agreement with the experimental value. Finally, note that the entropy of reaction 3 in Table 1, A,S(3) = 43.2 A 1.3 J K- ’ mol- ‘, which involves a cyclization process, can be modelled by reaction M3, where A,S”(M3) = 49.5 J K-’ mall’. The above three examples indicate that the entropy changes of the organometallic reactions in Table 1 can be approximated to the entropy changes of organic and inorganic reactions of the same type, in the gas phase, at 298 K. A collection of these simple model reactions, for which the entropies are known, is presented in Table 2, together with an indication of the corresponding reactions in Table 1. The deviations 6 found between the experimental and predicted TA,S data are summarized in Table 3. Before proceeding into a more detailed discussion of these results it is stressed that 6 = T 1 A,S(exp) - A,S’(model) 1, at T = 298 K, is usually less than 10 kJ mol-‘.
A,S” +-
R
(4)
The calculation of A,S” from the plot of In K vs. l/T assumes that both A,S” and A, Ho do not vary with temperature. An alternative and (in principle) more accurate method consists in combining a calorimetrically derived A,Ho value with the corresponding equilibrium constant at a single temperature T, to obtain A,S” at that temperature from Eq. (4) [9,62,63]. To our knowledge this method has not been applied to organometallic reactions. Note also that the errors of the A, S values in Table 1, which reflect the precision of the measurements, are frequently of the order of 10% or more and do not include Student’s t factors [64]. In general, not more than 10 experimental points were used to fit Eq. (4) by a linear regression. Therefore, if Student’s t factors for 95% confidence level were taken into account, the errors in Table 1 would at least double, in most cases.
4. Discussion The agreement between the experimental and predicted entropy values can be understood within the framework of statistical thermodynamics of ideal gas phase reactions [ 1Oa,ll,66]. Only a very brief analysis is given below. The entropy of a substance in the gas phase can be considered as a sum of several contributions, namely translation (S,‘), rotation (SF>, vibration (S,“>, internal rotation (Si), and electronic ($‘I: so = sp + sp + s,o + s; + s,”
(5) Other contributions may have to be accounted for [ lOa,l 11, but those in Eq. (5) are enough for the present discussion. The equations used in the computation of SF, SF, St, and S,” (in J K-’ mol-‘1, assuming a rigid rotator-harmonic oscillator model for the molecule, are 5: = -9.57577
+ 20.78628 In T + 12.47177 In M (6)
3. The estimation method SF = 877.39503 + 8.31451 In T The method used to estimate the entropy changes of organometallic reactions is rather simple and can be illustrated by considering several reactions in Table 1.
+ 8.31451 In I - 8.31451 In o
(linear molecules)
(7)
M.E. Minus du Pied&, Table 2 Standard No.
molar entrouies
J.A. Martinho
d,S’(g)/J
Reaction = 1 particle
I particle M3 M4 MS M6 M7 M8 M9 Ml0 Ml1 Ml2 Ml3 Ml4 Ml5 Ml6 Ml7
= 2 purtic1r.s CH&CH,),Ph = cy-C,H,, + C,H, C,H,=2CH, H ,01 = 20H N,H, = 2NH, C,H, + H,O, = HOCH,CH,OH CH,+CO=CHjCO C,H ,L = cy-C,Hs + CH, C,H,, = cy-C,H,, + CH, CH 4 + CO = CH ,C(O)H H 2 + CO = HC(O)H C,H, + CO = C,H,C(O)H C,H, + CO = CH,C(O)CH, C,H,, + CO = C,H,C(O)C,H, PhCH 3 + CO = CH ,C(O)Ph C,H,, = cy-Cc,H,, + H,
Ml9 M20 M2l M22 M23 M24 M25 M26 M27 2 purticlrs M28 M29 M30 M3l M32 M33
K-
’mol- ’
- 15.5 - 5.3
C,H,o=lC,H,o CsH,2
ofOr,q:anometallic
Chrmi.stty 518 (1996) 167-180
in the ideal gas state at 298 K a
of model reactions
I purticlr Ml M2
Ml8
Simde.s/Journal
=‘CsH,,
-
-
49.5 158.8 134.8 151.5 128.7 122.0 102.7 90.7 119.7 109.6 122.6 132.3 137.8 145.5 40.5 64.4
+H, 0 co CH, + N, = CH,N, CH,fH,=CH, C,H,=H,+C,H, C,H,=CH,+C,H, CH,Cl=CH,+Cl CH,F = CH, + F Si(CH,), = CH, + (CH,),SiH C,H, + C,H, = CH,CH,CH(CH,)CH, H,+C,H,=C,H, CH?(CH,J,Ph=
- 143.7 - 139.3 220.5 135.8 124.8 130.2 166.9 - 152.8 - 127.7
No. of reaction
M34 M35 M36 M37
N,H,+CH,=CH,NH,+NH, H,O>+CH,=CH,OH+H,O C,H6+OH=CH,0H+CH, cH,oH + (CH,J,NH = (CH,),N
M38
cH,oH
2 puriiclrs M39 M40 M4l
= 3 particles
2 purticlrs M42 M43 M44
= 4 particles
4 particks M45 M46 M47
= 3 purticlrs
a Standard
entropies
+ (CH,)NH,
= (CH,),NH
C,H, + 2C0 = ZCH,CO 20H + CH, = H,O + CH,OH C,H, + C,H, = PhCH, + CH,
CH(C2H,)I+H2=CH,+ CH(C,H,)? CH(C,H,),
cy-C,H, cy-C,H, cy-C,H,
+ H,O = CH,O + PhH = PhCH,
+ H,O + ~,0
3 7. 9-15, 24-33, 7, 9-15, 24-33, 7. 9-15, 24-33, 55 21,68 4 4 5, 6, 72 5, 6, 72 5, 6, 72 16,49-51,76,78 17,49951,76,78 52 I9 20 22 23 99 99 36 36 91-94 75 75
reactants
1, I8 I, I8 I, I8 48,65-67, 48, 65-67, 48, 65-67, 74 74 64 59 59
+ H,
- 85.2 - 125.2 147.4
3C,H, + 3C,Hj + 3C,H,
340.8 318.6 331.5
34, 35 34, 35 34. 35
- 87.5 - 101.9 - 70.7
60,6l 60,61 60, 61
+ 3C0 = 3CH,CO + 3HC0 = 3CH,CO + 3H, = 3CH,
of gaseous
- I I.7 - 4. I -7.5 12.2 14.2 15.7 10.3 9.5 20.6 - 36.8 -21.2
and products
were taken from Refs. [62] and [65].
I
69 69
= 2 purticles
H,O+C,H,= PhOH+H, CH, + C,H, = PhCH, + H, H,S + C,H, = PhSH + H, C,H, + H, = 2CH, H,O, + H, = 2H,O N,H,+ H,=2NH,
in Table
8 71 2
73 73 73
44, 45, 58, 63, 10 44, 45, 58, 63, 70 44, 45, 58, 63, 70
173
174
M.E. Minas da Piedade, J.A. Murtinho Simdes/Jaurnal
ofOrganomrtallic
Chemistry 518 (1996) 167-180
Table 3 Deviations 6 = I TA,S(exp) - 7’A,S”(model) 1 of the estimated values of TA,S”(model) from the corresponding experimental values TA,S(exp) for the reactions in Table 1 (T= 298 K) No. of reaction in Table 1
4
5 6 7 8 9 IO I1 12 13 14 I5 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59
TA, S(exp)/kJ
- 1.3 + 1.3 29.9 + 2.5 12.9 + 0.4 20.7 + 6.2 - 14.6 k 5.4 - 29.8 + 9.2 81.1 + 18.3 - 25.3 + 6.0 43.4 * 3.0 38.9 + 3.1 42.5 f 3.0 40.1 + 0.4 41.5 + 2.4 37.1 + 4.0 34.2 + 2.6 - 41.5 * 7.0 - 35.8 f 0.7 - 4.4 + 0.8 41.5 f 6.1 23.5 + 2.9 - 43.2 f 4.2 -44.1 k 2.9 -31.9 f 2.1 35.9 * 7. I 46.2 f 1.8 63.2 + 2.7 43.8 k 1.1 42.8 f 1.6 68.3 + 2.7 53.4 k 3.6 50.4 & 1.6 86.0 f 1.9 52.4 f 3.4 64.0 f 2.5 51.7 * 1.5 19.9 * 6.2 45.0 + 9.8 107.3 + 6.3 66.2 k 7.5 110.9 + 2.4 83.4 f 7.5 - 20.6 + 2.5 _ 23.5 + 2.5 38.7 _+3.1 42.4 k 2.5 3.0 f 1.8 1.5 f 2.6 10.6 f 1.0 -37.4 - 19.3 -11.1 - 34.2 23.9 + 0.7 0.9f 1.0 - 34.9 * 5.0 - 1.9&-0.6 - 1.5 + 0.2 38.7 f 1.8 - 7.6 + 0.2
mol
’
No. of model reaction in Table 2
TA,S”(modet)/k.I
M28, M29, M30 M41 M3 M9, Ml0 Ml 1, M12, Ml3 Mll, M12, Ml3 M4, M5, M6 M39 M4, M5, M6 M4, M5, M6 M4, M5, M6 M4, M5, M6 M4, M5, M6 M4, M5, M6 M4, M5, M6 Ml4 Ml5 M28, M29, M30 Ml7 Ml8 M8 Ml9 M20 M4, M5, M6 M4, M5, M6 M4, M5, M6 M4, M5, M6 M4, M5, M6 M4, M5, M6 M4, M5, M6 M4, M5, M6 M4, M5, M6 M4, M5, M6 M42, M43, M44 M42, M43, M44 M23, M24
-2.3 43.9 14.8 28.8 - 34.5 - 34.5 44.2 - 25.4 44.2 44.2 44.2 44.2 44.2 44.2 44.2 - 39.4 -41.1 -2.3 12.1 19.2 - 36.4 - 42.8 -41.5 44.2 44.2 44.2 44.2 44.2 44.2 44.2 44.2 442 44.2 98.4 98.4 38.0 0 0 0 0 0 0 0 44.2 44.2 0 0 4.2 - 40.3 - 40.3 - 40.3 - 43.4 0 0 - 38.4 0 0 44.2 - 8.7
b.c b.c b.c b.c b.c b.c b.c
M4, M5, M6 M4, M5, M6 c.d
c.d
M31, M14, Ml4, M14, Ml6
M32, M33 Ml5 Ml5 Ml5
b.c b.c
M7 c,d c.d
M4, M5, M6 M37, M38
mol- ’a
6/kJ mol- ’ 1.0 14.0 1.9 8.1 20.3 5.1 36.9 0.1 0.8 5.3 1.7 4.1 2.7 7.1 10.0 2.1 5.3 2.1 29.4 4.3 6.8 1.3 9.6 8.3 2.0 19.0 0.4 1.4 24. I 9.2 6.2 41.8 8.2 34.4 46.7 18.1 45.0 107.3 66.2 110.9 83.4 20.6 23.5 5.5 1.8 3.0 1.5 6.4 2.4 21.0 29.2 9.2 23.9 0.9 3.5 1.9 1.5 5.5 1.1
M.E. Minus da Piedude,
J.A. Martinho
Sim&s/Journal
of Organomrtullic
Chemistry
518 (1996) 167-180
175
Table 3 (continued) No. of reaction in Table 1
rA,S(exp)/kJ
60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99
- 34.0 * I.5 - 18.1 + 0.8 28.9 A 1.2 35.3 * I.8 II.5 + 8.3 - 5.2 & 0.6 5.5 5.5 k 0.6 36.1 2.1 f 0.7 -41.2 - 23.7 f 6.2 - 36.7 f. 4.5 I.0 f 2.5 - 8.7 k 3.8 - 25.0 k 6.3 - 38.7 & 6.3 - 77.2 * 8.9 - 38.7 + 8.6 - 45.0 & 3.6 - 1.0 k 3.6 -9.4+ 4.7 - 0.6 & 0.6 -2.1 k 6.2 -6.1 f 3.8 - 7.6 & 3.2 -3.2 k 3.1 23.9 i 0.9 24.6 & 4.0 28.3 f 1.0 25.8 If: 2.2 23.8 k 1.9 30.9 * 1.8 31.2 f 3.1 29.8 k 1.8 - 17.5 k 12.5 - 52.4 + 10.0 1.3 f 3.8 2.5 * 3.8 33.7 f 1.6
molt ’
No. of model reaction
TA,S”(model)/kJ
mol- ’a
6/kJ mol- ’
in Table 2 M45, M46, M47 M45, M46, M47 CX M4, M5, M6 M36 M31, M32, M33 M31, M32, M33 M31, M32, M33 M8 Ml, M2 M4, M5, M6 M40 Mll, Ml2 M31, M32, M33 M34, M35 M26, M27 Ml4, Ml5
c
Ml4, Ml5 M8 b.c b.c b.c b.c b.c b,c b.c
C.S c.r c.e C.C M25 M25 M25 M25 b.c
e
- 25.8 - 25.8 42 44.2 6.1 4.2 4.2 4.2 36.4 -3.1 - 44.2 - 37.3 - 34.2 4.2 3.8 -41.8 - 40.2 - 80.5 - 40.2 - 36.3 0 0 0 0 0 0 0 42 42 42 42 49.7 49.7 49.7 49.7 0 - 42 0
b.c b.c
M21, M22
0 38.2
8.2 7.7 13.1 8.9 5.4 9.4 I.3 1.3 0.3 5.8 3.0 13.6 2.5 3.2 12.5 16.8 1.5 3.3 1.5 8.7 I.0 9.4 0.6 2.1 6.1 7.6 3.2 18.1 17.4 13.7 16.2 25.9 18.8 18.5 19.9 17.5 10.4 1.3 2.5 4.5
a Average of the results obtained with different models, when applicable. b 2 particles = 2 particles. ’ See discussion in text. d 1 particle = I particle. e I particle = 2 particles.
SF = 1320.85148 + 12.47177 In T + 4.157255 ln( IAIBIc) - 8.31451 In c
(8)
(non-linear molecules) 1.438Zi/T S,D=RC
i
exp( 1.438Ei/T)
- ln[ 1 - exp( - l.438ij/T)]
(9) 1
S,”= R In o,,
(10)
were T is the temperature (in K), M is the molar mass (in g mol- ’), I is the m oment of inertia of a linear molecule, I,,,Ia Zc is the product of the principal moments of inertia of a non-linear molecule, CT is the symmetry number, T;ji is the wavenumber of the ith normal mode of vibration of the molecule (in cm-‘), w0 is the electronic ground state degeneracy, and R is the gas constant. The translational entropy given by Eq. (6) refers to a standard pressure of 1 bar. According to this equation, SF is proportional to In M, and therefore it is not strongly dependent on changes of molar mass. This implies, for example, that in reactions where one parti-
176
M.E. Minus da Pie&&,
J.A. Murtinho
Sim&.s/Journul
cle yields two particles, if the molar masses of the reactant and one of the products are of the same magnitude, the translational contribution to the reaction entropy will be close to the translational entropy of the second product. This is seen, for instance, in the case of intermolecular carbonyl insertion reactions and in H, oxidative additions, where the translational entropy changes are nearly identical to Sp(CO) and SF(H,) respectively. The previous discussion can be easily extended to other types of reaction involving several numbers of particles, displayed in Tables 1 and 2. It also applies to the case of the rotational contribution: Eqs. (7) and (8) show that se is rather insensitive to changes in the moment of inertia. Although the vibrational contribution to entropy can be negligible compared with $’ and SF, particularly in molecules with a small number of light atoms, such as hydrogen and carbon, in the case of most organometallit species it has to be considered. While this is true for entropies of individual species, it becomes less relevant when the vibrational entropy change A,,!$ of a reaction is calculated. In many reactions shown in Table 1, the overall change in vibration degrees of freedom is small and leads to a small A,Sf (see, however, discussion below). Another important contribution to the entropy of a large molecule comes from internal rotations [ 1Oa,l 11. However, as in the case of vibration, in many reactions the net change of the internal rotation degrees of freedom is small, leading to a small contribution to the reaction entropy. When the information about the electronic configuration of the ground state is known, it is possible to calculate the electronic contribution to the entropy by using Eq. (10) (it is assumed that the energy difference between the first electronic excited state and the ground state is much higher than k,T). In a chemical reaction where reactants and products have different ground state degeneracies, the electronic contribution to the entropy change must be considered if a very accurate value is to be derived. Take, for example, the reaction of dissociation of I,, yielding two iodine atoms. The ground state electronic degeneracies ~~(1~) = 1 and o&I) = 4 lead to TA,$’ = 3.4 kJ mol- ‘. In many organometallic reactions involving coordinatively saturated complexes, however, the variation of the ground state degeneracies is not as large and therefore neglecting the electronic contribution to the entropy leads to errors which are often comparable with the experimental uncertainties. In conclusion, A,Sp and A,$’ are frequently the most important contributions to the entropy of a reaction. Owing to their insensitivity to changes in molar mass and moments of inertia, these contributions have roughly constant values for organic, inorganic or organometallic reactions of the same type (CO inser-
of OrgunometullicChrmistry
518 119961 167-I 80
tions, a-bond metathesis, etc.). Even though the entropy of a gas phase reaction can be accurately calculated from statistical thermodynamics, the method is laborious and often the necessary structural and vibrational data for reactants and products are not available or are difficult to predict. The use of model reactions which mimic the changes in the external and internal degrees of freedom provides an alternative and easy way of estimating TA,S for organometallic reactions within ca. Other methods for predicting entropy 10 kJ mol-‘. changes avoiding detailed statistical thermodynamic calculations have been reported and applied to biochemical systems [67-721. Let us now analyse in more detail some of the reactions in Tables 1 and 2, paying particular attention to those for which 6 > 10 kJ mol- ’(Table 3). Just for a matter of convenience, the discussion below follows the classification of reactions given in Table 2, according to the number of particles as reactants and products. 4.1. I particle = 1 particle Small entropy changes for reactions where the number of particles is conserved can be predicted, particularly when only structural rearrangements are involved. This is indeed the case for reactions 46, 47, 56, 57, and 69. Although no models could be found for reactions 46, 47, 56, and 57, the reported experimental entropies are close to zero, as expected for 1 particle = 1 particle reactions. The negative value obtained for reaction 56 is probably due to the formation of the three-membered ring in the product. Note, however, that although a negative entropy value is predicted for reaction 69 based on models Ml and M2, and a positive value is experimentally found, the obtained 6 value in Table 3 is reasonably small, ca. 6 kJ mol-‘. Note also, for example, that Benson’s additivity scheme [ 101 also gives a negative value (TA, So= - 0.9 kJ mol- ‘) for the entropy of the reactions CH,CH(CH,)CH,(CO)H
= CH,(CH,),(CO)H (11)
CH,CH(CH,)CH,(CO)CH,
= CH,(CH,),(CO)CH, (12)
which may be better models for reaction 69. 4.2. I particle = 2 particles Reaction 3 corresponds to a a-bond metathesis and ring closure reaction. In this case the model M3 estimates TA, So within 2 kJ mol- ‘. A good agreement is also observed for reaction 20, where model Ml8 was used. However, it is surprising that the estimated TA, So value for reaction 19 (model M17) leads to a large
M.E.
Minus
da Pirdudr,
J.A. Murtinho
Simdes/
Journul
deviation (29.4 kJ mol-‘) from the experimental value. A similar comment applies to reactions 5 and 6, which are CO insertions into M-H bonds. Although the model reactions Ml 1-Ml 3 predict TA, So for reaction 6 within the experimental error, the corresponding estimate for reaction 5 leads to a discrepancy of 20 kJ mol- ‘. Reaction 7 is a ligand dissociation reaction. Based on the model reactions M4-M6 it is expected that TA, So for reaction 7 is about 44 kJ mol- ‘. The large discrepancy found between the estimated and the experimental value (37 kJ mol- ’>, as well as the large uncertainty of the experimental value, strongly suggest that the entropy of reaction 7 in Table 1 is in error. Models M4-M6 were also used for estimating the entropies of reactions 24-33. As seen in Table 1, reactions 25-28 describe the cleavage of the Cr-Cr bond in the complex [Cr(Cp)(CO),], and were studied by different groups. The same happened with reactions 29-3 1 for the analogue Cp * complex, and reactions 32, 33 for {Cr(Cp)(CO>,[P(OMe),])l. It is noted that the experimental values of TA,S for reactions 26, 29, and 32, all measured by the same group, are considerably higher than predicted by the model and are also in disagreement with the other experimental values. The experimental value of the entropy of reaction 36 is considerably smaller than the value predicted for the model reactions M23 and M24. Both reaction 36 and the models involve the formation of a monoatomic species and a polyatomic fragment, implying identical changes in translational, rotational and vibrational degrees of freedom. From the above discussion after Eqs. (6)-(8) it is expected that the translational and rotational contributions to A,S” are similar in reactions 36, M23 and M24. However, the frequencies of the three vibration modes lost upon dissociation of the model compounds (CH,F and CH,Cl) are certainly much higher than the corresponding frequencies in the case of the dissociation of W(CO),Xe. Therefore, according to Eq. (9), the negative vibrational contribution to A,S” will be much larger for reaction 36 than for the models M23 and M24, leading to a considerably lower A,S” value in the former case [73]. The experimental values of the entropies for the CO insertion reactions 49-52 show unexpected differences. Indeed, while the models used for estimating TA,S for R = Me and Ph lead to errors smaller than 10 kJ mol- ‘, the discrepancies found for R = Et and Pr are considerably higher. The reported entropies of reactions 62 and 87-90 seem too low when compared with typical data for 1 particle = 2 particles reactions, ca. TA, So= 42 kJ mol-‘. These discrepancies must be related to the internal rotation of the q2-H2 moiety in the reactant complex and to the loss of internal rotation degrees of freedom of the phosphine group upon formation of a C-H --) M agostic interaction in the organometallic
ofOrgunometallicChemistry
518 (1996)
167-180
177
product [74]. Both effects act in the same direction, i.e. the former increases the entropy of the reactant and the latter reduces the entropy of the product. While the explanation seems reasonable, it could also be used to predict that reactions 46 and 47 should have negative (albeit small) entropies, which conflicts with the experimental data in Table 1. Note, however, that the error bars for the entropies of these reactions do not seem to invalidate the prediction TA, S < 0. A large deviation is found between TA,S for reaction 75 and for the model reactions M26 and M27 (16.8 kJ mol-’ ; Table 3). This discrepancy and the large experimental error quoted for TA,S(75) suggest that the reported entropy of reaction 75 is too high. The reductive elimination reactions 91-94 have entropies (79.9 _t 6.3, 103.8 k 5.9, 104.6 & 10.5, and 100.0 i 5.9 J K- ’ mol- ’ respectively), considerably smaller than expected on the basis of the data for the model reaction M25 in Table 2 (166.9 J K-’ mol- ‘), leading to an average 6 value of ca. 2 1 kJ mol- ‘. We are unable to explain this discrepancy. Steric effects in the reactant complex, hindering the internal rotations of the SiMe, group, would imply an upward correction of TA,So predicted by the model. 4.3. I particle = 3 particles No model is presented for reaction 77. Note, however, that this reaction corresponds to a double CO insertion. Therefore it is expected that A,S(77) is approximately twice the value given in Table 2 for models Ml4 and M15, which yields TATS0 = - 80.5 kJ mol- ‘. This is in good agreement with the experimental value. 4.4. 2 particles = 2 particles Reactions 37-41 should have entropies close to zero. As stated by Angelici and Ingemanson [31], the abnormally large experimental values are not understood. Kubas et al. [32] have explained the negative entropies of reactions 42 and 43 by the interaction of solvent (thf) molecules with the coordinated water. As one would expect that, in the absence of such specific interactions, TA,S = 0 and, as also one cannot rule out the solvation of free water reactant molecules, the experimental values imply that the coordination of thf to the organometallic product produces a larger entropy decrease than in the case of the free water molecule (see below for more comments on solvation). Although no specific model was used for reactions 53 and 54, the comparison between the corresponding A,S values suggests that the value reported for reaction 53 is in error. While A,S for reaction 54 is in the range found for 2 particles = 2 particles reactions (i.e. A,S = 01, the value for reaction 53 is much higher than expected.
178
M.E. Minus du Piedude,
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Si&es/Journal
The entropies of reactions 65-67 are close to zero as predicted for this type of 2 particles = 2 particles reaction. The negative value of A,S for reaction 65 is, however, unexpected, judging from the positive entropies of reactions 66, 67 and of the model reactions M31-M33. The model reactions M34 and M35 predict a small positive value for the entropy of reaction 74. In contrast, the experimental value found is small but negative. This discrepancy suggests that the experimental value should be redetermined, since it is based on measurements at two temperatures only and has a large experimental error. We could not find appropriate organic analogues for reactions 80-86, where an v2-ethylene is replaced by another v2-olefin, and for reactions 95, 97, and 98. The values of A,S reported for reactions 80-86 are, however, nearly within the expected range for 2 particles = 2 particles reactions, i.e. TA,S = 0, particularly if the experimental uncertainties are considered. The same is observed for reactions 95, 97, and 98, although in the case of reaction 95 the recommended TA,S value is about 18 kJ mol- ’ higher than predicted.
of OrganometullicChemistry
518 (19961167-180
4.7. 4 particles = 3 particles The reactions M45-M47 predict, as observed experimentally, that the absolute values of the entropies of reactions 60 and 61 are smaller than the typical range for 2 particles = 1 particle reactions. The agreement between the estimated and the experimental data is fair: the prediction A,S” = - 86.7 J mol-’ K-’ leads to errors of 8.1 and 7.7 kJ mol-’ for reactions 60 and 61, respectively (Table 3). These discrepancies are within our accepted limits for the estimates. However, it is somewhat surprising that the entropies of reactions 60 and 61 differ by 53 J mol-’ K-‘. This difference is hardly justifiable by invoking solvent effects (see below). Unfortunately, the entropies of the model reactions M45-M47 vary over a wide range, making it difficult to assess which is the most reliable experimental value.
5. Final comments
Reaction 2 can be decomposed in a q-bond metathesis and a ligand dissociation reaction. It is expected that A,S = 0 for the former process (reactions M28-M30) and AJo= 130-150 J mol- ’ K- ’ for the latter (see reactions M4-M6). The model reaction M41 has A,S” = 147.4 J mol-’ K- ‘, which corresponds to TA, So= 43.9 kJ mol- ‘. The estimate exceeds the experimental TA,S value by 14.1 kJ mol- ‘. This significant difference may reflect a loosely bound thf molecule in the organometallic reactant: the internal rotation and the low frequency vibrational modes involving the coordinated thf moiety, which will increase the entropy of the organometallic adduct, are lost upon dissociation. The value of TA, So= - 37.3 kJ mol- ’for the model reaction M40 is about 14 kJ mol-’ lower than the corresponding value for reaction 71 ( - 23.7 f 6.2 kJ mol-‘). We note, however, that the experimental value relies on a van’t Hoff plot involving only three temperatures.
It is understood that the use of gas phase models at 298 K to estimate entropies of organometallic reactions in solution is somewhat crude, since a more detailed analysis of the internal and external degrees of freedom of reactants and products (whenever possible), together with temperature and solvent effects, might allow more accurate predictions. However, the method discussed above is extremely simple to apply and in most cases it is sufficiently accurate to assess or to predict entropy changes of organometallic reactions. It is of course recognized that an error of 10 kJ mol- ’ in TA,S leads to a very large error in the equilibrium constant (see Introduction) and, in this regard, the method is not satisfactory. Yet, as mentioned before, a fair amount of the experimental data is probably less reliable than the values obtained through the model reactions. Let us finally address the temperature and solvent effects on the reaction entropies. The fact that the large majority of organometallic reactions is studied in solution limits the temperature range of the experiments. For example, all reactions in Table 1, except three (7, 58, 631, were studied in solution at temperatures ranging from ca. 170-450 K. As can be concluded from
4.6. 2 particles = 4 particles
A,S(298) = A,S(T)
Reactions 34 and 35 involve changes of ligand hapticity and provide an example for which it is not possible to find suitable organic models. Therefore, large discrepancies between the entropies of models, such as M42-M44, and the entropies of those organometallic reactions could be expected.
the temperature corrections to derive A,S at 298 K are well within the uncertainty accepted for the present estimation method. A,C,, which represents the average reaction heat capacity change in the temperature range 298-T, is small for most reactions in Table 1 ( I A,C, I less than ca. 30 J mol-’ K- ’[75]) and is multiplied by
4.5. 2 particles = 3 particles
298 + A,C, lny
(13)
M.E. Minus da Piedude,
J.A. Martinho
Simde.s/Journul
of Orgunometullic
Chemistry
179
518 (1996) 167-180
a factor smaller than one. We therefore decided not to apply any temperature corrections to our model. With regard to solvation effects, the difference between the entropy of a reaction in the gas phase and in solution has been discussed, and it does not seem to be well understood [69,72,76]. It is generally agreed that the transfer from the gas phase to solution of a reaction where there is no net change in the number of particles does not lead to a significant entropy difference. However, for reactions involving a different number of particles as reactants and products there is conflicting evidence about the expected entropy differences in the gas phase and in solution [69,72,76]. According to Hammett [76], in the case of 2 particles = 1 particle reactions, it should be expected that entropies in solution are considerably less negative than in the gas phase. However, as discussed by Page [69], similar entropies should be expected for many association reactions in the gas phase and in solution. Most data in Table 1 refer to reactions involving neutral species, in solvents where solvation effects are expected to be small. The fact that the method of estimation discussed in this paper leads to a satisfactory agreement with experimental data, suggests that gas phase and solution values of TA,S for most reactions in Table 1 are similar within the maximum accepted error for the estimations (10 kJ mol- ’), even for reactions were the number of particles is not conserved.
of Organic und I91 J.D. Cox and G. Pilcher, Thermochemistry Orgunometullic Compound.s, Academic Press, London, 1970. Kinetics, Wiley, New York, [lOI (a) S.W. Benson, Thermochemicul 1976; (b) N. Cohen and S.W. Benson, Chem. Reu., 93 (1993)
Acknowledgements
D71 L.Y. Goh, S.K. Khoo and Y.Y. Lim, J. Orgunomet.
2419.
G.J. Janz, Thrrmodynumic Properties of Organic Compounds, Academic Press, New York, 1967. [121 R.C. Reid, J.M. Prausnitz and B.E. Poling, The Properties of Gu.se.s und Liquids, McGraw-Hill, Singapore, 4th edn., 1988. [I31 M.E. Thompson, S.M. Baxter, A.R. Bulls, B.J. Burger, M.C. Nolan, B.D. Santarsiero, W.P. Schaefer and J.E. Bercaw, J. Am. Chem. Sot., 109 (1987) 203. 1141 A.R. Bulls, J.E. Bercaw, J.M. Manriquez and M.E. Thompson, Polyhedron, 7 (1988) 1409. [I51 G.M. Smith, J.D. Carpenter and T.J. Marks, J. Am. Chem. SIX. [ill
108 (1986) 6805.
[I61 K.G. Moloy and T.J. Marks,
J. Am. Chem.
SW.,
106 (1984)
7051.
[I71 R.G. Bedford, J. Phys. Chem., 81 (1977) 1284. iI81 E.U. van Raaij, C.D. Schmulbach and H.H. Brintzinger, Orgunomet.
Chem.,
328
J.
(1987) 275.
[I91 L. Stahl and R.D. Ernst, J. Am. Chem. SW., 109 (1987) 5673. [201 G. Fachinetti, G. Fochi and C. Floriani, J. Chem. Sot., Dulton Truns.,
(1977) 1946.
El1 F. Calderazzo, G. Fachinetti and C. Floriani, J. Am. Chem. kc., 96 (1974) 3695.
La A.A. Gonzalez and C.D. Hoff, InorR. Chem., 28 (1989) 4295. k31 K. Zhang, A.A. Gonzalez, S.L. Mukerjee, S.-J. Chou, C.D. Hoff, K.A. Kubat-Martin, D. Bamhart and G.J. Kubas, J. Am. Chem. Sot.,
113 (1991) 9170.
[241 S.J. McLain, J. Am. Chem. SW., 110 (1988) 643. I251 L.Y. Goh and Y.Y. Lim, J. Orgunomer. Chem.,
402 (1991)
209.
WI W.C. Watkins, T. Jaeger, C.E. Kidd, S. Fortier, M.C. Baird, G. Kiss, G.C. Roper and C.D. Hoff, J. Am. Chem. Sot., 114 (1992) 907. (1990)
This work was supported by Junta National de Investigasao Cientifica e Tecnologica, Portugal (Projects PBIC/C/CEN/ 1042/92 and STRDA/C/CEN 469/92). We also thank Dr. Herminio P. Diogo for helpful comments.
References and notes [I] T.J. Marks (ed.),
Bonding
Energetics
in Orgunnmetullic
Com-
ACS Symp. Ser. 428, American Chemical Society, Washington, DC, 1990. [2] J.A. Martinho Sirnoes and J.L. Beauchamp, Chem. Rev., 90 pounds,
( 1990)629. [3] T.J. Marks (ed.), Metul-Ligund Bonding Energetics in Orgunotrunsition Metul Compound.s, Polyhedron Symposium-in-Print,
Vol. 7, 1988. [4] J.A. Martinho Simoes (ed.), Energetics of Or,gunometullic Species, NATO ASI, Ser. C, Vol. 367, Kluwer, Dordrecht, 1992. [S] C.D. Hoff, Pmg Inorg. Chem., 40 (1992) 503. [6] S.P. Nolan, Bonding Energetics of Organometallic Compounds, in Encyclopedia of Inorganic Chemistry, Wiley, New York, 1994. [7] P.B. Dias, M.E. Minas da Piedade and J.A. Martinho SimEes, Coord. Chem. Rev., 135/136 (1994) 737. [8] See, for example, Ref. [4], p. 197.
Dl
Chem.,
399
115.
G.J. Kubas, G. Kiss and C.D. Hoff, Organometullics,
IO (1991)
2870.
1291 C.D. Hoff, J. Orgunomet. Chem., 282 (1985) 201. [301 B.H. Weiller, J. Am. Chem. Six., 114 (1992) 10910. [311 R.J. Angelici and CM. Ingemanson, ZnorR. Chem., 8 (1969) 83.
[321 G.J. Kubas, C.J. Bums, G.R.K. Khalsa, L.S. van der Sluys, G. Kiss and CD. Hoff, Orgunometullic.s, II (1992) 3390. I331 G.R.K. Khalsa, G.J. Kubas, C.J. Unkefer, L.S. van der Sluys and K.A. Kubat-Martin, J. Am. Chem. Sot., 112 (1990) 3855. I341 R.J. Klinger and J.W. Rathke, Inorg. Chem., 31 (1992) 804. [351 F. Calderazzo, Anger. Chem., Int. Ed. Engl., 16 (1977) 299. [361 A. Marcomini and A. PO&, J. Chem. Sot., Dalton Truns., (1984) 95. [37] (a) K.P. Gable and T.N. Phan, J. Am. Chem. Sot., 115 (1993)
3036; (b) 116 (1994) 835. [38] C. Jablonski, G. Bellachioma, G. Cardaci and G. Reichenbach, J. Am. Chem. SK., 112 (1990) 1632. [39] R.D. Barreto, J. Puga and T.P. Fehlner, Orgunometullics, 9 ( 1990) 662. [40] A.K. Baev and A.A. Barkatin, Russ. J. Phys. Chem., 58 (1984) 195. [41] H.E. Bryndza, L.K. Fong, R.A. Paciello, W. Tam and J.E. Bercaw, J. Am. Chem. Sot., 109 (1987) 1444. [42] G. Bor, Pure Appl. Chem., 58 (1986) 543. Chem., 417 (1991) [43] R. Koelliker and G. Bor, J. Orgunomet. 439. [44] D.G. Gusev, A.B. Vymenits and V.I. Bakhmutov, Inorg. Chem., 31 (1992) 2.
180 1451
M.E.
[48]
J.A. Murtinho
Am.
Simc?rs/Journal
Chrm.
Sec.,
5459.
J.W. Rathke, R.J. Klingler and T.R. Krause, 11 (1992)
[47]
du Piedude.
A.J. Poe, C.N. Sampson and R.T. Smith, J. 108 (1986)
[46]
Minus
Orpmometullics,
585.
F. Ungvary, J. Orpwmetul. Chem., 36 (1972) 363. F. UngvLry and L. Mark& J. Orgunomrt. Chem.,
20
(1969)
205. [49] [50]
MS. Borovikov, I. Kovacs, F. Ungvary, A. Sisak and L. Mark& Orgunomrtullics, I I (I 992) 1576. J.J. Pignatello and Y.-T. Fanchiang, J. Chrm. Sot., Dalton Trans.,
(1985)
1381.
108 (1986)
3659.
[54] [55]
V.L. Coffin, W. Brennen and B.B. Wayland, J.
[68]
II0
(1988)
Chrm.,
27
[73] 8 (1989) Am.
Chem.
6063.
R. Cramer, J. Am. Chem. Sot., 89 (1967) 4621. [57] B.E. Hauser, D. Gusev and K.G. Caulton, J. Am. Chrm. Sot., 116 (1994) 208. [58] M.J. Hostetler, M.D. Butts and R.G. Bergman, Or~unometullics, 12 (1993)
65.
R.J. McKinney and D.C. Roe, J.
Am.
Chem.
Sot.,
108 (1986)
[74]
5167. [60]
CA. Tolman, J. Am. Chrm. SW., 96 (1974) 2780. R.L. Brainard and G.M. Whitesides, Orgunomrtullics,
(I 985)
[75]
D.R. Stull, E.F. Westrum, Jr. and G.C. Sinke, The Chemical Thermodynumics of Orgunic Compounds, Wiley, New York, 1969. und Eyuilihriu oj’ Organic [63] M. Frenkel (ed.), Thermochemistry Compounds, VCH, New York, 1993, Book III, Chapter 4.
[76]
[61]
4
1550. 1621
und Formulur,
Stundurd
Prohuhility
und
Stotistic.s
(1971)
1678.
W.P. Jencks, Ado. En:ymol.,
43 (1975)
219.
338.
[56]
[59]
Tubks
M.I. Page, Chem. Sot. Rrv., 2 (1973) 295. [70] Ml. Page, Anger. Chem., Int. Ed. Engl., 16 (I 977) 449. [71] A.J. Doig and D.H. Williams, J. Am. Chrm. SW., 114 (1992)
1438. Sot.,
CRC
167-180
CRC Press, Boca Raton, FL, 1991. [65] The NBS Tables of Chemical Thermodynamics Properties, /. Phys. Chrm. Ref: Dutu, II (1982) Suppl. 2. [66] See, for example, (a) G.S. Rushbrooke, Statisticul Mechanics, Oxford University Press, London, 1967; (b) B.J. McClelland, Stutisticul Thermodynamics, Chapman and Hall, London, 1979. [67] M.I. Page and W.P. Jencks, Proc. Nut. Acud. Sci. USA, 68
[72]
B.B. Wayland, V.L. Coffin and M.D. Famos, Inorg. (I 988) 2745. B.B. Wayland, Y. Feng and S. Ba, Organometullics,
[53]
[64] W.H. Beyer (ed.),
518 (1996)
[69]
[51] B.B. Wayland, S. Ba and A.E. Sherry, J. Am. Chem. Sot., 113 (1991) 5305. [52] M.D. Farnos, B.A. Woods and B.B. Wayland, J. Am. Chem. Sot.,
of Oqunometullic Chemistry
M.S. Searle and D.H. Williams, J. Am. Chem. SOL..,114 (1992) 10690. For example, typical C-F and C-Cl stretching frequencies are 1100 and 650 cm.-’ respectively [lOa], whilst a rough estimation of the W-Xe stretching frequency in W(CO),Xe leads to 227 cm-’ [estimated from v(W-CO) = 403.3 cm-’ in W(CO), Spectru, Academic Press, (P.S. Braterman, Metul Curhonyl London, 1975) and the relation (v, /vz) = ( pz /p, )‘j2, where p is the reduced mass]. Therefore, the use of Eq. (9) leads to TA,Sz = - 0. I and - 0.5 kJ mall ’ for the two organic molecules respectively, compared with TA,Sf = - 2.4 kJ mol ’ for the Xe complex. Larger differences can be expected for the two bendind modes lost upon dissociation, J. Eckert, G.J. Kubas and R.P. White, Inorg. Chem., 31 (1992) 1550 and references cited therein. Estimated from A,C, for the model reactions in Table 2. Data from Refs. [ 121, [62] and [65]. L.P. Hammett, Physicul Orgunic Chemistry, McGraw-Hill, New York, 2nd edn., 1970.