Mechanistic Aspects of Inorganic Reactions - ACS Publications

2 Pressure Effects and Substitution Mechanisms

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T. W. SWADDLE University of Calgary, Department of Chemistry, Calgary, Alberta, T2N 1N4 Canada

An attempt i s made to account quantitatively for the volumes of a c t i v a t i o n , ΔV*, of ligand sub s t i t u t i o n processes. Causes of the pressure– dependence of ΔV* include solvational change, for which a v e r s a t i l e analysis i s developed. The pressure-independent ΔV* values of solvent ex change reactions are good measures of the non-solvational components of ΔV* for related net reac tions. For water exchange, one can predict -7 ≤ΔV*< 0 for I and 0 < ΔV* ≤ +7 for I pro cesses, with satisfactory correlation with inde pendent mechanistic assignments. The molal v o l umes of the t r a n s i t i o n states for series of water a

exchange

reactions

d

2+

3+

(M (aq), M (aq), M(NH ) OH 3+) are insensitive to the nature of M; the 3

5

2

initial,

kinetic characteristics are governed mainly by not t r a n s i t i o n , state properties.

I t i s customary to j u s t i f y the study o f pressure e f f e c t s on r e a c t i o n r a t e s on the grounds t h a t i t can e l u c i d a t e r e a c t i o n mechanisms. A somewhat d i f f e r e n t and, I t h i n k , more c o n s t r u c t i v e v i e w p o i n t i s t h a t pressure effects constitute important n a t u r a l phenomena i n themselves, and t h a t our compre hension of r e a c t i o n k i n e t i c s i s incomplete i f i t does not enable us to understand the e f f e c t s o f pressure on r e a c t i o n rates. In t h i s s p i r i t , an attempt w i l l be made t o account f o r the magnitude o f pressure e f f e c t s on l i g a n d s u b s t i t u t i o n r e a c t i o n rates. A t t e n t i o n w i l l n e c e s s a r i l y be confined t o a few simple model systems; two recent reviews ( 1 , 2) o f pressure e f f e c t s on r e a c t i o n s o f t r a n s i t i o n metal complexes i n s o l u t i o n may be consulted f o r more comprehensive surveys o f the f i e l d . 0097-6156/82/0198-0039$07.00/0 © 1982 American Chemical Society Rorabacher and Endicott; Mechanistic Aspects of Inorganic Reactions ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

40

MECHANISTIC ASPECTS OF

INORGANIC REACTIONS

K i n e t i c s i n R e l a t i o n t o Thermodynamics A c e n t r a l theme of our work i n Calgary has been t o seek connections between e q u i l i b r i u m and k i n e t i c p r o p e r t i e s — t h a t i s , between thermodynamic and extrathermodynamic q u a n t i t i e s ( 3 ) . An e q u i l i b r i u m constant Κ i s governed by (8 I n K / 8 P ) = -AV/RT

(1)

T

where the volume of r e a c t i o n AV may be independently measured by d i l a t o m e t r y , or from the a l g e b r a i c sum of the p a r t i a l molal volumes V of products and r e a c t a n t s , which can a l s o be d e t e r mined independently. AV = IV(products)

- IV(reactants)

(2)

I n k i n e t i c s , s i m i l a r r e l a t i o n s h i p s apply, but the volume of a c t i v a t i o n AV* can be determined only from the pressure dependence of the r a t e c o e f f i c i e n t k, s i n c e the p a r t i a l m o l a l volumes V* of t r a n s i t i o n s t a t e s are not d i r e c t l y ^ measurable. Conversely, however, equation 4 can y i e l d values of V*. (8 I n k / 8 P ) = -AV*/RT

(3)

AV* = V* - I V * ( r e a c t a n t s )

(4)

T

Some of our f i r s t p u b l i c a t i o n s i n t h i s f i e l d (4 - 6) d e a l t w i t h the l i n e a r c o r r e l a t i o n s t h a t e x i s t between AV* and AV f o r r e a c t i o n s of the type ( 3

M(NH ) X " 3

n ) +

5

+ H0

» M(NH ) 0H

2

3

5

3 + 2

n

+ X~

(5)

where M = Co or Cr. We have r e c e n t l y repeated some of t h a t work i n g r e a t e r d e t a i l ( 7 ) . I t was confirmed t h a t AV* f o r r e a c t i o n 5 can be markedly pressure-dependent when η = 1 or 2, i . e . , I n k i s then not a l i n e a r f u n c t i o n of P. However, I n k i s s t r i c t l y a l i n e a r f u n c t i o n of P, w i t h i n experimental un certainty, for a l l single-path s o l v e n t exchange r e a c t i o n s n

s t u d i e d t o date (e.g., X ~

= h* 0 i n eq. 5 ) . 2

This i s i l l u s t r a t e d

i n F i g u r e 1; the exchange of Ν,Ν-dimethylformamide (DMF) s o l v e n t on chromium(III) was chosen f o r the comparison simply because the 400 MPa c a p a c i t y of our equipment was f u l l y e x p l o i t e d . Pressure Dependence of Volumes of A c t i v a t i o n When, and how, does t h i s pressure-dependence of AV* a r i s e ? E m p i r i c a l l y , we f i n d f o u r r e a c t i o n types which g i v e n o n - l i n e a r In k vs. Ρ p l o t s .

Rorabacher and Endicott; Mechanistic Aspects of Inorganic Reactions ACS Symposium Series; American Chemical Society: Washington, DC, 1982.


-10.5 h

-10.0 h

200

s

s

k

400

0

pressure / MPa

200

3

400

-i-13.5

"1-13.0

•i-12.5

3 e

Figure L Constancy of AV* for solvent exchange reactions where AV* = —6.3 cm*/mol for Cr(DMF) *-DMF solvent exchange at 338 K (a); and pressure dependence of AV* for reactions involving charge development and, hence, solvational change where AVe* = —18.5 cm /mol for Co(NH ) SO + direct aquation at 298 K (b).

c

-9.5h

-9.0

42

(a)

MECHANISTIC ASPECTS O F INORGANIC REACTIONS

Multi-step

ligation

or

incomplete

of Cr(DMF)^

i n DMF,

reactions,

e.g., bromide i o n

i n which the i o n p a i r i n g i s

almost complete a t ~ 0.1 mol kg * Br a t atmospheric pressure but p r o g r e s s i v e l y l e s s complete, l e a d i n g t o incompletion o f the o v e r a l l r e a c t i o n , as the pressure i s r a i s e d . Cr(DMF),

3+

+ B r " i n DMF

fast 0 < AV* < +7 cm mol To t e s t t h i s , we l i s t i n Table I a l l those water-exchange r e a c t i o n s of metal ions f o r which a p o s i t i v e AV* has been found. +

+

a

Table I P r e s s u r e - d e c e l e r a t e d water exchange r e a c t i o n s and evidence f o r d i s s o c i a t i v e interchange i n corresponding net s u b s t i t u t i o n r e a c t i o n s ML(.

i n MLÔH^

AV* f o r HÔ-exchange /cm mol

Dependence of l i g a t i o n r a t e on n u c l e o p h i l e -

2 +

+7.2

(25)

very s l i g h t

2 +

+6.1

(25)

very s l i g h t

+3.8

(25)

negligible?

+7.0

(8)

R =

0.9

+1.2

(18)

R =

0.5

+5.8

(10)

3

Ni(H 0)

5

Co(H 0)

5

2

2

Fe(H 0) 2

2 + 5

Fe(H 0) 0H 2

2 +

4

Co(NH ) 3

3 + 5

t-Co(en) 0H 2

-

3 + 2

R = r e l a t i v e r a t e of l i g a t i o n , NCS~/C1


2.

SWADDLE

Pressure Effects and Substitution

49

Mechanisms

I n the l a s t column, the Langford-Gray c r i t e r i o n (19) f o r the 1^ mechanism f o r the corresponding net s u b s t i t u t i o n r e a c t i o n s i s shown t o be met i n v i r t u a l l y a l l cases, although data f o r F e ( I I ) are sparse. Where a p p l i c a b l e , S a s a k i and Sykes' v e r s i o n (24) of the Langford-Gray c r i t e r i o n i s used, v i z . , t h a t R, the r a t e of a t t a c k of NCS r e l a t i v e t o CI , should be c l o s e t o ( i n p r a c t i c e , s l i g h t l y l e s s than) u n i t y i n an I , r e a c t i o n , III disregarding

For

the

Co

(^3)5

c a s e

>

Δ ν

*

f o r

exchange (and, indeed, A V ^ * f o r r e a c t i o n 5 i n general)

water is

ion pairing.

nt

j u s t barely

p o s i t i v e , but

f o r trans-Co (en) 2 ^ ^ 2 ^ 2 ^

+

^

*

S

c l o s e r t o the p r e d i c t e d l i m i t f o r an 1^ process. In

Table

I I , markedly

negative AV*

values

f o r water

ex-

Table I I P r e s s u r e - a c c e l e r a t e d water exchange r e a c t i o n s and evidence f o r a s s o c i a t i v e interchange i n corresponding net s u b s t i t u t i o n r e a c t i o n s ML-

n+

i n ML-OH^^

AV* f o r BLO-exchange /cm mol" 3

3 +

Cr(H 0) 2

Fe(H 0) 2

5

3 + 5

Mn(H 0) 2

Cr(NH ) 3

3 + 5

Rh(NH ) 3

Ir(NH ) 3

2 + 5

3 + 5

3 + 5

Dependence of l i g a t i o n r a t e on n u c l e o p h i l e

-9.3

(26)

R = 55

-5.4

(8)

R = 19

-5.4

(25)

?

-5.8

(27)

R = 6

-4.1

(27)

R =

-3.2

(28)

0.6

change c o r r e l a t e w i t h Sasaki-Sykes c r i t e r i a f o r a s s o c i a t i v e interchange i n net s u b s t i t u t i o n r e a c t i o n s i n a t l e a s t t h r e e instances (see (29) and (30) f o r commentaries on the Cr^^îNH^)^ case). Data f o r the v e r y f a s t r e a c t i o n s of Mn(II) are l i m i t e d , but the s e n s i t i v i t y of the r a t e s t o the nature of the nucleo p h i l e may w e l l be s l i g h t , l e a d i n g t o an assignment of an 1^ mechanism even i f , as AV* suggests, a c t i v a t i o n i s a s s o c i a t i v e (20), 25); the problem here may l i e w i t h the o p e r a t i o n a l nature of the Langford-Gray and Sasaki-Sykes c r i t e r i a (30). For the R h ( I I I ) case, v a r i o u s l i n e s of evidence suggest weak a s s o c i a t i v e



50

a c t i v a t i o n (31), and the s m a l l R value might be r e l a t e d t o the greater s t a b i l i t y o f the S-thiocyanato l i n k a g e isomer f o r R h ( I I I ) , but the assignment o f mechanism i n r e a c t i o n s o f R h ( I I I ) c a t i o n s i s undoubtedly going t o remain debatable f o r some time. The r e s u l t s o f our recent study o f water exchange on i r o n ( I I I ) ( 8 ) , summarized above, s t r o n g l y i n d i c a t e a change i n the mode o f a c t i v a t i o n from a s s o c i a t i v e t o d i s s o c i a t i v e on r e 3+ moving a proton from F e O ^ O ) ^ . This c o n c l u s i o n i s not v u l n e r able t o Langford's c r i t i c i s m o f the mechanistic i n t e r p r e t a t i o n of AV* (32) ( t h a t changes i n the non-reacting m e t a l - l i g a n d bond lengths may i n f l u e n c e AV* m a t e r i a l l y ) , s i n c e a l l the bonds concerned are F e - 0 . I n a d d i t i o n , Table I I I shows t h a t AV* values f o r water exchange and f o r n e t s u b s t i t u t i o n on the con2+ jugate base FeOÔÔH are the same w i t h i n the experimental u n c e r t a i n t y , as expected f o r a mechanism i n v o l v i n g a common 2+ intermediate, Fe(H 0),0H ( a q ) . The g e n e r a l l y negative and 3+ I ] C I

9

different

AV*

values

f o r s u b s t i t u t i o n on FeCHÔ)^

itself

serve t o confirm a s s o c i a t i v e a c t i v a t i o n i n i t s r e a c t i o n s . Table I I I 3+

1

AVVicnAiol" ) x

1

1

"

Fe(H 0) 2

f o r r e a c t i o n s o f Fe 3 +

6

Fe(H 0) 0H 2

5

2 +

n

(aq) w i t h X " Ref.

Cl"

-4.5

Br"

-8

NCS"

-0

+7.1

(35)

H0

-5.4

+7.0

(8)

2

+7.8

(33) (34)

Non-Aqueous Solvent Exchange Reactions I t i s u n r e a l i s t i c t o t r e a t molecules o f s o l v e n t s such as Ν,Ν-dimethylformamide (DMF) as spheres i n e s t i m a t i n g AV* f o r s o l v e n t exchange as f o r water. One can, however, a n t i c i p a t e t h a t s o l v e n t s which have unusually open s t r u c t u r e s because o f extensive hydrogen bonding (notably water) w i l l l o s e a r e l a t i v e l y l a r g e f r a c t i o n o f t h e i r molar volume V on c o o r d i n a t i o n t o a metal i o n , whereas f o r d i p o l a r a p r o t i c s o l v e n t s t h i s f r a c t i o n w i l l be much l e s s , w i t h p a r t i a l l y Η-bonded s o l v e n t s


2.


SWADDLE

Mechanisms

51

such as a l c o h o l s coming i n between. Indeed, Table IV shows t h a t |AV*|/V f o r s o l v e n t exchange decreases i n the order water > a l c o h o l s > d i p o l a r a p r o t i c s o l v e n t s , a t l e a s t f o r AV* values s u f f i c i e n t l y removed from zero. Nevertheless, the s t r i k i n g f e a t u r e o f Table IV i s t h a t AV* Table IV 3 -1 2+ AV*(cm mol ) f o r s o l v e n t exchange on M i n various solvents Solvent:

M = Mn

H 0-

ChÔH-

-5.4

-5.0

2

2+

Fe

2 +

3.8

0.4

Co

2 +

6.1

8.9

Ni

2 +

7.2

AV (Ni

)/V

- From 0 17

1

S

NMR (25)

- From H NMR (37)

0.40

DMF-

Ch^CN-

-7.0 3.0

11.4 0.28

6.7

6.7

9.1

7.3 0.14

0.12

- From *H NMR (36) - From

1 4

N NMR (38)

f o r s o l v e n t exchange v a r i e s r e l a t i v e l y l i t t l e w i t h the s o l v e n t , but s t r o n g l y w i t h the metal. This lends c r e d i b i l i t y t o attempts (20,25) t o r a t i o n a l i z e trends i n AV* f o r s o l v e n t exchange on the b a s i s o f the d - o r b i t a l occupancy, s i n c e t h i s i s the f a c t o r most c h a r a c t e r i s t i c o f each metal i o n . Thus i t i s argued (20) t h a t a s s o c i a t i v e a c t i v a t i o n may be taken as "normal" i n o c t a h e d r a l complexes, but h i g h i n t e r a x i a l ( i . e . , electron densities work a g a i n s t the attainment o f a 7-coordinate t r a n s i t i o n s t a t e because both the incoming and outgoing groups must move i n t o i n t e r a x i a l space. We can, t h e r e f o r e , expect a s s o c i a t i v e charac t e r t o become more evident as we go from N i ( I I ) C o ( I I ) -> ( 3

F e ( I I ) •* Mn(II) (high s p i n ) ; C o ( N H ) X " 3

5

n ) +

3

-> C r ( N H ) X ~ 3

5

n ) +

;

C r ( I I I ) t o Mo(III) and W(III) (because 4d and 5d o r b i t a l e are more d i f f u s e than 3d); low s p i n C o ( I I I ) t o R h ( I I I ) and I r ( I I I ) ; e t c . The degree o f a s s o c i a t i v e a c t i v a t i o n i n C r ( I I I ) and analo gous h i g h - s p i n F e ( I I I ) complexes might be expected t o be s i m i 3 l a r , both having t ~ c o n f i g u r a t i o n s , except t h a t the two e ^g & e l e c t r o n s o f the i r o n ( I I I ) w i l l l a b i l i z e the d e p a r t i n g l i g a n d so t h a t the a s s o c i a t i v e c h a r a c t e r w i l l be somewhat reduced r e l a -


52

MECHANISTIC ASPECTS O F

t i v e to C r ( I I I ) . by o b s e r v a t i o n .

In g e n e r a l , these

INORGANIC REACTIONS

e x p e c t a t i o n s are

supported

An A l t e r n a t i v e Approach t o Accounting f o r AV* Values f o r Solvent Exchange Reactions F i g u r e 5 provides a c l u e to a d i f f e r e n t , b a s i c a l l y nonm e c h a n i s t i c , way of r a t i o n a l i z i n g known AV* values f o r s o l v e n t exchange and p r e d i c t i n g new ones r a t h e r p r e c i s e l y . There i s a reasonably good i n v e r s e l i n e a r c o r r e l a t i o n of AV* f o r water 2+ exchange on corresponding

M

ions partial

of

the f i r s t

molal

t r a n s i t i o n series with

volumes

of

the

aqueous

the ions

themselves;

the slope i s about -1, and i t seems t h a t t h i s would 3+ a l s o be t r u e f o r the M (aq) ions of t h a t s e r i e s . What t h i s means i s t h a t the sum of AV* and \L i s e s s e n t i a l l y constant, M or a t l e a s t i n s e n s i t i v e t o the nature of Μ , f o r a given s e r i e s 3 -1 d e s p i t e a wide range i n AV*. T h i s sum i s -33 ί 2 cm mol for 2+ 3+ M (aq) and -66 ± 1 f o r M ( a q ) , based on i n f i n i t e - d i l u t i o n i o n i c p a r t i a l molal volumes V ° (14, 39); f o r M ( N H ) O H ( a q ) , 3 -I i t i s 56 ± 2 cm mol based on i o n i c volumes V^ a t [M] ~ 0.01 +

3+

M

3

5

2

1

mol L ( 7 ) . I t f o l l o w s from eq. 4 t h a t t h i s sum equals V* (the volume of the incoming water molecule can be ignored, being common throughout the s e r i e s - i t i s , i n any event, i n c l u d e d i n Vj^

f o r an interchange p r o c e s s ) .

Thus, the molal volumes of the

t r a n s i t i o n s t a t e s w i t h i n a given s e r i e s of s o l v e n t exchange reac t i o n s are e f f e c t i v e l y the same r e g a r d l e s s of the i d e n t i t y of the central ion. T h i s statement i s based on l i m i t e d data a t p r e s e n t , but, i f l i t e r a l l y t r u e , i t permits us to p r e d i c t AV* f o r s o l v e n t ex change (and hence A V ^ * f o r net l i g a n d s u b s t i t u t i o n ) from nt

values of V^, many of which are a l r e a d y a v a i l a b l e (39) ; i n p r i n c i p l e , o n l y one AV* value per s e r i e s need be measured. Even i f a l l we can l e g i t i m a t e l y say i s t h a t V* i s much l e s s s e n s i t i v e than AV* to the nature of the c e n t r a l metal i o n w i t h i n a given s e r i e s (and t h i s seems assured), we still have gained an important i n s i g h t - i t i s the p r o p e r t i e s of the i n i t i a l s t a t e , and not the t r a n s i t i o n s t a t e , t h a t determine i n l a r g e p a r t the k i n e t i c c h a r a c t e r i s t i c s of l i g a n d s u b s t i t u t i o n i n a t r a n s i t i o n metal complex. T h i s i s welcome news, as we can o b t a i n f a c t u a l i n f o r m a t i o n regarding i n i t i a l s t a t e s d i r e c t l y by numerous experimental techniques, whereas d i s c u s s i o n s of t r a n s i t i o n s t a t e p r o p e r t i e s can never be b e t t e r than h y p o t h e t i c a l .


SWADDLE


(-60)

(-55)

Mechanisms

(-50)

partial molal volumes of aqueous ions (H+-5.5) Figure 5.

Correlation between AV* for solvent exchange and V° for ions of the first transition series.


54


These conclusions are independent o f mechanistic c o n s i d e r a t i o n s of the u s u a l k i n d , and indeed provide a r a t i o n a l e f o r c e r t a i n AV* values near zero f o r s o l v e n t exchange without i n d e c i s i v e r e s o r t to the I ^ / I ^ dichotomy. One can, however, i n t e r p r e t the apparent constancy of V * to mean t h a t the t r a n s i t i o n s t a t e of water exchange i s a r e l a t i v e l y unstructured h i g h energy aggregate of water molecules h e l d together by the cen t r i p e t a l f i e l d o f an "anonymous" n+ charge; o n l y i n the lowenergy i n i t i a l s t a t e do s t r u c t u r e s c h a r a c t e r i s t i c of the p a r ticular M^ exist. Where such a s t r u c t u r e i s open ( r e l a t i v e l y p o s i t i v e V ^ ) , a s s o c i a t i v e a c t i v a t i o n i s p o s s i b l e ; where i t i s t i g h t l y packed (low V ^ ) , a c t i v a t i o n tends to the d i s s o c i a t i v e +

limit. I t may be b e t t e r , however, to speak o n l y of a c o l l a p s e or expansion, r e s p e c t i v e l y , of a s t r u c t u r e d ground s t a t e on going to a r e l a t i v e l y unstructured t r a n s i t i o n s t a t e . Acknowledgment I thank the N a t u r a l Sciences and E n g i n e e r i n g Research C o u n c i l Canada f o r t h e i r c o n t i n u i n g f i n a n c i a l support of our work i n t h i s f i e l d .

Literature Cited 1. Palmer, D. Α.; Kelm, H. Coord. Chem. Rev. 1981, 36, 89. 2. van Eldik, R.; Kelm, H. Rev. Phys. Chem. Japan 1980, 50, 185. 3. Swaddle, T. W. Coord. Chem. Rev. 1974, 17, 214. 4. Jones, W. E.; Swaddle, T. W. J. Chem. Soc. Chem. Commun. 1969, 998. 5. Jones, W. E.; Carey, L. R.; Swaddle, T. W. Can. J. Chem. 1972, 50, 2739. 6. Guastalla, G.; Swaddle, T. W. Can. J. Chem. 1973, 51, 821. 7. Sisley, M. J.; Swaddle, T. W. Inorg. Chem. 1981, 20, 2799. 8. Swaddle, T. W.; Merbach, A. E. Inorg. Chem., in press. 9. Stranks, D. R.; Vanderhoek, N. Inorg. Chem. 1976, 15, 2639. 10. Tong, S. B.; Krouse, H. R.; Swaddle, T. W. Inorg. Chem. 1976, 15, 2643. 11. Neece, G. Α.; Squire, D. R. J. Phys. Chem. 1968, 72, 128. 12. Stranks, D. R. Pure Appl. Chem. 1974, 38, 303. 13. Lohmüller, R.; Macdonald, D. D.; Mackinnon, M.; Hyne, J. B. Can. J. Chem. 1978, 56, 1739. 14. LoSurdo, Α.; Millero, F. J. J. Phys. Chem. 1980, 84, 710. 15. Shimizu, K. Bull. Chem. Soc. Japan 1979, 52, 2429. 16. Millero, F. J.; Ward, G. K.; Lepple, F. K.; Hoff, Ε. V. J. Phys. Chem. 1974, 78, 1636.


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Mechanisms

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17. Padova, J. J. Chem. Phys. 1964, 40, 691. 18. Hunt, H. R.; Taube, H. J. Am. Chem. Soc. 1958, 80, 2642. 19. Langford, C. H.; Gray, H. B. "Ligand Substitution Pro cesses"; Benjamin: New York, 1966. 20. Swaddle, T. W. Inorg. Chem. 1980, 19, 3203. 21. Palmer, D. Α.; Kelm, Η. Z. anorg. allgem. Chem. 1979, 450, 50. 22. Rindermann, W.; Palmer, D. Α.; Kelm, H. Inorg. Chim. Acta 1980, 40, 179. 23. Gutmann, V.; Mayer, H. Struct. Bonding (Berlin) 1976, 31, 49. 24. Sasaki, Y.; Sykes, A. G. J. Chem. Soc. Dalton 1975, 1048. 25. Ducommun, Y.; Newman, Κ. E.; Merbach, A. E. Inorg. Chem. 1980, 19, 3696. 26. Stranks, D. R.; Swaddle, T. W. J. Am. Chem. Soc. 1971, 93, 2783. 27. Swaddle, T. W.; Stranks, D. R. J. Am. Chem. Soc. 1972, 94, 8357. 28. Tong, S. B.; Swaddle, T. W. Inorg. Chem. 1974, 13, 1538. 29. Ferrer, M.; Sykes, A. G. Inorg. Chem. 1976, 18, 3345. 30. Swaddle, T. W. Rev. Phys. Chem. Japan 1980, 50, 230. 31. Swaddle, T. W. Can. J. Chem. 1977, 55, 3166. 32. Langford, C. H. Inorg. Chem. 1979, 18, 3288. 33. Hasinoff, Β. B. Can. J. Chem. 1976, 54, 1820. 34. Hasinoff, Β. B. Can. J. Chem. 1979, 57, 77. 35. Jost, A. Ber. Bunsenges. phys. Chem. 1976, 80, 316. 36. Meyer, F. K.; Newman, Κ. E.; Merbach, A. E. J. Am. Chem. Soc. 1979, 101, 5588. 37. Meyer, F. K.; Newman, Κ. E.; Merbach, A. E. Inorg. Chem. 1979, 18, 2142. 38. Yano, Y.; Fairhurst, M. T.; Swaddle, T. W. Inorg. Chem. 1980, 19, 3267; and unpublished work with M. J. Sisley. 39. Millero, F. J. In "Water and Aqueous Solutions"; Horne, R. Α., Ed.; Wiley-Interscience, New York, 1972; p.519. RECEIVED April 5, 1982.


General Discussion—Pressure Effects and Substitution Mechanisms

Leader: Ramesh Patel

DR. KENNETH KUSTIN (Brandeis U n i v e r s i t y ) : When a t a b l e o r a c h a r t contains o n l y a c t i v a t i o n parameters, one loses s i g h t o f what i s a c t u a l l y going on i n the system. When you r e c a l l t h a t the s o l v e n t exchange r a t e constant f o r Mn(II) i s v e r y l a r g e , I wonder i f i t i s p o s s i b l e t h a t the negative volume o f a c t i v a t i o n might have nothing t o do w i t h t h e s u b s t i t u t i o n process. I t might simply r e f l e c t t h e f a c t t h a t the s u b s t i t u t i o n i s so r a p i d t h a t i t overlaps w i t h the formation r a t e o f the i o n p a i r , and you r e a l l y couldn't d i s t i n g u i s h the two steps i n t h a t case. So what you might be seeing i s r e a l l y some squeezing down on t h e i o n p a i r formation, r a t h e r than the s u b s t i t u t i o n i t s e l f , f o r a metal i o n which i s s u b s t i t u t i n g a t almost the d i f f u s i o n con trolled limit. DR. SWADDLE: We are measuring the volume o f a c t i v a t i o n f o r s o l v e n t exchange i n a r e g i o n where i t i s i n the NMR time frame; i n other words, where t h e NMR l i n e broadening i s exchange con t r o l l e d , i . e . , k * 10 s" . 5

1

I f one goes t o s t i l l lower temperatures, one u s u a l l y sees evidence f o r outer-sphere e f f e c t s , which i s what you a r e r e ferring to. I n t h e cases which I have d i s c u s s e d here, e i t h e r one does n o t see any evidence f o r outer-sphere e f f e c t s o r e l s e one can choose t o operate i n a r e g i o n where t h e outer-sphere e f f e c t s are known t o be unimportant. DR. RAMESH PATEL (Clarkson C o l l e g e ) : Couldn't one p i c k c e r t a i n systems i n which t h e i o n p a i r i n g e f f e c t would be v e r y l a r g e ? One would then be able t o make some comments about the i n f l u e n c e o f volume changes on i o n p a i r formation f o r r a p i d l y exchanging systems. DR. SWADDLE: I n the f u t u r e , undoubtedly, we w i l l move i n t o t h i s area. We have t o do the easy t h i n g s f i r s t . I n the systems I have d i s c u s s e d , we have e s s e n t i a l l y a noncomplexing counter i o n , namely p e r c h l o r a t e , and see no evidence o f i o n p a i r i n g . Perhaps t h i s was not made c l e a r . DR. DAVID RORABACHER (Wayne S t a t e U n i v e r s i t y ) : A point which i s f r e q u e n t l y overlooked i s t h a t the c a l c u l a t i o n s gener a l l y a p p l i e d f o r determining the extent o f i o n - p a i r (or outersphere complex) formation i n s u b s t i t u t i o n r e a c t i o n s may be overly s i m p l i s t i c . There a r e many types o f i n t e r a c t i o n s which tend t o p e r t u r b the e x t e n t o f outer-sphere complex formation r e l a t i v e t o t h e p u r e l y s t a t i s t i c a l c a l c u l a t i o n commonly made which takes i n t o account o n l y the r e a c t a n t r a d i i and e l e c t r o static factors.


2.

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Mechanisms

57

In p a r t i c u l a r , there are a number of s p e c i f i c i n t e r a c t i o n s between outer-sphere species and the coordinated inner-sphere groups which can s i g n i f i c a n t l y enhance the extent of o u t e r sphere complex formation. Dr. Margerum has e l u c i d a t e d the s t a c k i n g i n t e r a c t i o n s which can occur between the aromatic r i n g s of coordinated and outer-sphere l i g a n d s . S i m i l a r l y , the i n t e r n a l conjugate base (ICB) mechanism, which we formulated a number of years ago, i n v o l v e s the formation of hydrogen bonds between outer-sphere n i t r o g e n donor atoms and inner-sphere water mole cules. Both of these phenomena i n c r e a s e the extent of o u t e r sphere a s s o c i a t i o n and thereby promote complex formation of m u l t i d e n t a t e l i g a n d s . However, as Jack Vriesenga has shown i n a p o s t e r p r e s e n t a t i o n a t t h i s Conference, such outer-sphere hy drogen bond formation may r e t a r d complex formation when unident a t e l i g a n d s are i n v o l v e d by making the lone donor atom u n a v a i l able f o r inner-sphere i n s e r t i o n as long as i t remains t i e d up i n a hydrogen bond. The i n c r e a s e i n outer-sphere complex forma t i o n combined w i t h a decrease i n inner-sphere i n s e r t i o n might p r o v i d e c o n d i t i o n s of the type Dr. P a t e l suggests. In s t u d i e s on s o l v e n t e f f e c t s i n v o l v i n g v a r i a t i o n i n the composition of two component m i x t u r e s , s i m i l a r types of o u t e r sphere i n t e r a c t i o n s y i e l d p r e f e r e n t i a l s o l v a t i o n wherein the s o l v e n t composition of the outer-sphere may d i f f e r markedly from the b u l k s o l v e n t composition. Supporting e l e c t r o l y t e s p e c i e s and b u f f e r components may a l s o p a r t i c i p a t e i n outer-sphere i n t e r a c t i o n s thereby changing the apparent nature (charge, b u l k , l a b i l i t y ) of the r e a c t i n g s o l v a t e d metal i o n or metal complex as p e r c e i v e d by a r e a c t i n g l i g a n d i n the b u l k s o l v e n t . DR. ALBERT HAIM: ( S t a t e U n i v e r s i t y of New York a t Stony Brook): I guess you know as w e l l as I do, and as most people do, how d i f f i c u l t i t i s t o f i n d evidence f o r a mechanism, whether i t i s d i s s o c i a t i v e or a s s o c i a t i v e or f a l l s i n between. You have measured volumes of a c t i v a t i o n , and have obtained i n f o r m a t i o n from them. You seem t o be v e r y c e r t a i n as t o the c o n c l u s i o n s t h a t you can draw from the v a r i o u s numbers which you obtained. Suppose t h a t one were a l i t t l e s k e p t i c a l about the v a l u e of these numbers and wanted t o ask how they compared w i t h other parameters t h a t one can measure i n the same systems, such as e n t r o p i e s of a c t i v a t i o n , or energies of a c t i v a t i o n . From the p o i n t of view of volumes of a c t i v a t i o n , i s a p i c t u r e obtained which i s c o n s i s t e n t w i t h what one may d e r i v e from other measure ments? DR. SWADDLE: The problem w i t h e n t r o p i e s of a c t i v a t i o n i s t h a t they are obtained i n c o n j u n c t i o n w i t h the e n t h a l p i e s . Those of us who have worked i n NMR l i n e broadening can r e l a t e numerous s t o r i e s about e n t r o p i e s of a c t i v a t i o n which range a l l over the p l a c e , depending on e x a c t l y how one analyzes the data [See, e.g., Newman, Κ. E.; Meyer, F. K. ; Merbach, A. E. J . Am. Chem.



58

Soc. 1979, 101, 1470]. Perhaps the NMR case i s a p a r t i c u l a r l y extreme example, b u t the p o i n t i s t h a t one has two compensating parameters i n temperature e f f e c t s . I n t h e pressure e f f e c t , i t i s t r u e t h a t one a l s o has two parameters, t h e l o g k a t zero pressure (but t h a t i s something one can measure) and t h e s l o p e . The slope o f t h a t l i n e gives the volume o f a c t i v a t i o n . So, even w i t h r a t h e r poor d a t a , one can measure t h e volume o f a c t i v a t i o n q u i t e a c c u r a t e l y , w i t h i n f r a c t i o n s o f a c u b i c centimeter p e r mole. Thus, from the p o i n t o f view o f the numerical i n t e g r i t y o f these r e s u l t s , I stand by them. Of course, the i n t e r p r e t a t i o n i s , as always i n mechanistic s t u d i e s , open t o debate. DR. PATEL: I n t h e e a r l y stages o f some o f t h i s work, due t o c a l c u l a t i o n s on c r y s t a l f i e l d s t a b i l i z a t i o n e n e r g i e s , i t was thought t h a t vanadium(III) and t i t a n i u m ( I I I ) could be very good candidates f o r an a s s o c i a t i v e mechanism. Now, there has been some work done on these systems, having t o do w i t h e n t h a l p i e s o f a c t i v a t i o n , which seems t o s u b s t a n t i a t e an a s s o c i a t i v e mechan ism. What would you t h i n k about measuring volumes o f a c t i v a t i o n f o r such systems and then t r y i n g t o compare them w i t h such calculations? DR. SWADDLE: I would guess t h a t the volume o f a c t i v a t i o n f o r aquo-exchange on vanadium(III) o r t i t a n i u m ( I I I ) would be on the order o f about -7 cc p e r mole. DR. JACK VRIESENGA (Syracuse u n i v e r s i t y ) : You p o i n t e d out the dangers i n v o l v e d i n e x t r a c t i n g e n t r o p i e s and e n t h a l p i e s from NMR d a t a , not o n l y as a r e s u l t o f the c r o s s - c o r r e l a t i o n between the two, b u t a l s o t h e i r c o r r e l a t i o n t o other NMR parameters. I thought i t might be u s e f u l f o r you t o comment on t h e e f f e c t o f pressure on the other NMR parameters, besides the k i n e t i c con t r o l ? F o r example, you commented about the r o l e played by the outer-sphere r e l a x a t i o n i n the i n t e r p r e t a t i o n o f NMR r e l a x a t i o n data. How would t h i s be a f f e c t e d by pressure? DR. SWADDLE: Yes, t h a t i s c o r r e c t . As I s t a t e d , we have been c a r e f u l t o work i n areas where a t l e a s t 90 percent o f t h e l i n e broadening i s c o n t r o l l e d by s o l v e n t exchange. I t h i n k John Hunt i s t h e person t o comment on what happens t o t h e other NMR parameters under pressure. I b e l i e v e he has found some p r e s sure-dependence o f T . 2n|

DR. JOHN HUNT (Washington S t a t e U n i v e r s i t y ) : With regard to determining a c t i v a t i o n parameters from NMR d a t a , i t i s mostly a matter o f doing a good j o b o f i t . I f one does a proper f i t o f the d a t a , u s i n g t h e complete Swift-Connick equations and s i g n a l averages over a long enough p e r i o d o f time, one can get q u i t e


2.

SWADDLE


Mechanisms

59

r e l i a b l e enthalpies. The e n t r o p i e s a r e then no worse than usual. With regard t o the pressure e f f e c t s , we have, as u s u a l , been i n t e r e s t e d i n systems t h a t a r e not simple. One system we have been l o o k i n g a t i n v o l v e s w a t e r - s o l u b l e p o r p h y r i n s . Ac t u a l l y , the only r e a c t i o n s we have s t u d i e d thus f a r i n v o l v e the i r o n ( I I I ) and manganese(III) tetra(4-N-methylpyridyl)porphyrin complexes. These complexes a r e i n the form o f t o s y l a t e s a l t s , which causes some problems. The r a t e constants a r e on the order of 10^ s

1

f o r a x i a l water exchange. 1

The volumes o f a c t i v a t i o n 1

are +2 ce m o l " f o r F e ( I I I ) and -2 ce m o l " f o r M n ( I I I ) . We b e l i e v e t h a t there i s one water per metal i o n i n these com p l e x e s , b u t I couldn't defend t h a t p o s i t i o n very s t r o n g l y . These systems do i n v o l v e some i n t e r p r e t a t i o n o f the e f f e c t of pressure on T ^ , but we t h i n k t h a t our r e s o l v e d volumes o f activation

are v a l i d .

The signs

a r e c o r r e c t , and they a r e

1

probably good t o 1 o r 2 ce mol , which s t i l l allows one t o keep the s i g n s . I am not going t o attempt t o i n t e r p r e t these v a l u e s . I thought Dr. Swaddle might understand why one gets a d i f f e r e n c e i n s i g n between the i r o n ( I I I ) and the manganese(III) systems. These a r e h i g h - s p i n complexes and don't show any pressuredependence on the volume o f a c t i v a t i o n , nor a temperaturedependence. The a c t u a l numbers w i l l change a l i t t l e b i t . I promised Dr. Swaddle t h a t we would look a t n i c k e l and ammonia. We have made such a study i n 15-molar aqueous ammonia which i s a mixed s o l v e n t system. I t i s r e a l l y o n l y necessary t o o b t a i n s o l v e n t interchange between the inner-sphere and the outer-sphere i n a case l i k e t h i s because outer-sphere formation i s d i f f u s i o n c o n t r o l l e d . I n t h i s system we o b t a i n a p o s i t i v e 1

AV i n the range o f 4 t o 6 ce mol , a r e g i o n o f some uncer t a i n t y because the blank data a r e not as good as we would l i k e t o have. I n c i d e n t a l l y , one o f the problems t h a t always bothers me somewhat i s t h a t I t h i n k one r e a l l y ought t o use b l a n k s , w i t h a diamagnetic i o n , t h a t resemble the s o l u t i o n one i s t r y i n g t o i n t e r p r e t , r a t h e r than simply u s i n g water i t s e l f . Even though the e f f e c t s are r e l a t i v e l y s m a l l , one might l e a r n something i n t e r e s t i n g about diamagnetic systems t h a t way. DR. JAMES ESPENSON (Iowa S t a t e U n i v e r s i t y ) : I should l i k e t o r a i s e a s l i g h t l y d i f f e r e n t aspect o f s u b s t i t u t i o n r e a c t i o n s , an aspect which r e l a t e s t o a d i f f e r e n t k i n d o f mechanism. This i n v o l v e s a change from the conventional h e t e r o l y t i c process o f metal l i g a n d bond cleavage t o one d e a l i n g w i t h homolytic bond cleavage. I have r a i s e d the question w i t h regards t o the iodochromium(III) i o n as tp whether the s u b s t i t u t i o n r e a c t i o n can occur



60

by a homolytic pathway i n s t e a d o f , o r as w e l l a s , by a heterol y t i c pathway (Scheme I ) . The h e t e r o l y t i c pathway i n t h i s p a r t i c u l a r case i s q u i t e a f a v o r a b l e r e a c t i o n , w i t h a s i z e a b l e e q u i l i b r i u m constant, although i t occurs s l o w l y . We can c a l c u l a t e the v a l u e f o r the e q u i l i b r i u m constant f o r homolytic d i s s o c i a t i o n because the r e d u c t i o n p o t e n t i a l s a r e known. I n t h i s case the e q u i l i b r i u m constant has q u i t e a s m a l l v a l u e . I t i s 10"

2 7

As a consequence, even i f the reverse r e a c t i o n occurred a t S 10

S " ) , the rate of -17 homolytic d i s s o c i a t i o n should be immeasurably s m a l l (k- ύ 10 s ) ; the unimportance o f homolysis was confirmed some years ago [Schmidt, A. R. ; Swaddle, T. W. J . Chem. S o c , D a l t o n Trans. 1970, 1927]. However, c o n s i d e r the corresponding s i t u a t i o n f o r a c l o s e l y r e l a t e d complex i n which, i n s t e a d o f an i o d i d e i o n bound t o pentaaquo chromium, t h e r e i s an a l i p h a t i c fragment such as an a l k y l group. As one example, we may c o n s i d e r the h y d r o x y i s o p r o p y l chromium c a t i o n . Here the p o s s i b i l i t y f o r both homolytic and h e t e r o l y t i c s u b s t i t u t i o n e x i s t s (Scheme I I ) . With proper experiments, one can evaluate s e p a r a t e l y t h e r a t e constant values f o r cleavage by each o f these pathways. The pathway corresponding t o h e t e r o l y t i c metal l i g a n d cleavage can be evaluated by suppressing the homolysis r e a c t i o n 2+ by a d d i t i o n o f an excess o f Cr , p r o v i d i n g a measurement o f the h e t e r o l y t i c chromium-carbon bond cleavage r e a c t i o n . On the other hand, t h e homolysis r e a c t i o n , an unfavorable e q u i l i b r i u m , can be drawn t o the r i g h t by adding scavenging 2+ reagents f o r Cr o r carbon-centered r a d i c a l s . I n t h a t case we can measure the r a t e constant f o r homolytic d i s s o c i a t i o n , which i n t h i s p a r t i c u l a r i n s t a n c e i s 0.127 s \ accompanied by a l a r g e p o s i t i v e entropy o f a c t i v a t i o n and a l a r g e enthalpy o f a c t i v a tion. Since M e y e r s t e i n has measured the reverse r e a c t i o n r a t e constant, i . e . , the combination r a t e constant between C r and the h y d r o x y i s o p r o p y l r a d i c a l , the r a t i o o f those values a f f o r d s the e q u i l i b r i u m constant f o r homolytic d i s s o c i a t i o n , 2.5 χ -9 10 M i n the case o f t h i s p a r t i c u l a r complex. By s t u d y i n g a s e r i e s o f complexes i n which the v a r i o u s sub s t i t u e n t s on the alpha-carbon atom a r e v a r i e d , we can look a t the change i n t h e magnitude o f the r a t e constant f o r homolytic d i s s o c i a t i o n as a f u n c t i o n o f these s u b s t i t u e n t s . The v a l u e s range from 3.5 χ 1θ" s " f o r C r C H 0 H t o -3 χ 1 0 s " f o r the d i f f u s i o n c o n t r o l l e d r a t e (k

1 0

M"

1

1

2 +

5

1

2+

2

2

CrC(CH )(CMe )0H 3

3

2+

o r l i f e t i m e s from 7.5 hours t o -3 ms.


1

2.


SWADDLE

Scheme I :

Cr(H 0) 2

h e t

T

2

5

2

K

hom eq

10

-27

M

=

2

/

k

2 +

+ I*

6

,2+ (H 0) CrOH^ + (CH ) CHOH 2

(H 0) Cr-C(CH ) OH 5

3

2+

5

3

2+ C r ( H 0 ) " + -C(CH ) iOH 2

k

het

^hom

3

6

3

3

+

3.3 χ 1θ" + 4.7 χ 1 0 " [ H ] s "

=

2

+ hy)

2

horn

At 25.0°C:

k

1' -1

Cr(H 0)

2

+ I"

= 1.4 χ ΙΟ M

=

Scheme I I :

3 + 6

4

K eq

2+ ( H 0 ) C r - r + H 0)

61

Mechanisms

Q 227 s

1

(homolysis)

2

1

3

AH* = 27.4 kcal/mol 1

AS* = 29.4 c a l m o l " Κ"

-1

= 5.1 χ 10^ M

K

eq,298

AG

AH

2 9 g

=

2

'

5

1

X

s

1

1 0

~

1

(pulse r a d i o l y s i s ) ^

9

M

= 12 kcal/mol

= 27 kcal/mol

Bakac, Α.; K i r k e r , G. W.; Espenson, J . H., unpublished

results

^Cohen, H.; M e y e r s t e i n , D. Inorg. Chem. 1974, 13, 2434



62

In a q u a l i t a t i v e sense, the r a t e constants c o r r e l a t e w i t h the change i n degree o f s t e r i c hindrance provided by the i n c r e a s i n g b u l k o f the s u b s t i t u e n t s . We can r e l a t e those changes, which span a f a c t o r o f 10^ i n the homolytic d i s s o c i a t i o n r a t e constant, t o the f r e e energy o f a c t i v a t i o n f o r the homolytic cleavage o f c o r r e s p o n d i n g l y s u b s t i t u t e d ethanes. There i s a s u b s t a n t i a l c o r r e l a t i o n f o r every system except the b e n z y l com p l e x (Figure 1). The slope o f the l i n e i s 0.3. I f the c o r r e l a t i o n were e x a c t , one would have expected a v a l u e o f 0.5, there being a square root r e l a t i o n s h i p i n the r a t e c o n s t a n t s , o r a f a c t o r of 2 i n the f r e e e n e r g i e s , because i n the ethanes we s u b s t i t u t e s y m m e t r i c a l l y on both s i d e s and i n the chromium complexes on one s i d e o n l y . These observations suggest t h a t bond d i s s o c i a t i o n reac t i o n s , o c c u r r i n g i n a homolytic f a s h i o n f o r t h i s f a m i l y o f complexes, are c o n t r o l l e d l a r g e l y , i f not e n t i r e l y , by s t e r i c f a c t o r s , provided t h a t one stays w i t h i n a f a m i l y o f complexes i n which s p e c i a l e l e c t r o n i c e f f e c t s , such as might be found i n the b e n z y l chromium i o n , do not p l a y an important r o l e .

ÛG*c_

c

Figure 1. Plot of AG M8 * for the homolysis of organochromium cations vs. AG* for the homolysis of the correspondingly substituted ethanes (with OH replaced by CH ). Key for organochromium ions: O, CrC(R R')OH +; · , CrC(R,R')OR" +; V, CrCH(CH ) +; and +, CrCH Ph \ S

2

f

s

2

t

2

2

2


Mechanistic Aspects of Inorganic Reactions - ACS Publications

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