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113 Cards in this Set

  • Front
  • Back

Kinetics deals with the RATE of a reaction. What does the rate depend on?

Overcoming the energy barrier (Activation energy) for the reactants to be transformed into products.

What does a large/small activation energy imply about a reactant?

Large - Inert (Unreactive)


Small - Labile (Reactive)

Thermodynamics deals with the EQULIBRIUM position of a reaction. What does the equilibrium depend on?

Equilibrium is dependent on the relative energies of reactants and products. It does not depend on activation energy.

What can be deduced about the equilibrium of a reaction using ΔG from the equation:



ΔG = -RTlnK



If Δ G is negative, then K must be a positive value larger than 1 as ln(fraction) gives a negative number which would make ΔG positive.


If K>1 then the reaction shifts right in favour of the products

Define the mechanism of a reaction:

The pathway (or pathways) that reactants are converted into products

In a typical reaction, aside from products and reactants what are likely to be the energy maxima and minima?

At the maxima energy there is likely to be a transition state which is not directly observable


At the minima will be an intermediate which is sometimes possible to observe although only briefly as highly reactive

What is the principle of microscopic reversibility?

Lowest energy pathway must be the same for bot forward and backwards reaction

Name 3 product studies can be used for studying mechanisms:

Stoichiometric analysis


Isotopic labelling


Product structure

How can rate of reaction be used to study mechanisms as a function of:



Temperature:


Reactant Concentration:


Pressure:


Solvent:

Temperature: Activation parameters (Ea, ΔH#, ΔS#)


Reactant Concentration: Rate Law


Pressure: Activation Volume ΔV#


Solvent: Solvation of reactants, intermediates and transition states

Name 6 reaction monitoring techniques:

Mass spectrometry


Gas uptake - or gas formation


Magnetic Resonance - NMR


Absorption Spectrometry - UV/vis(beer-Lambert) and IR (absorbance proportional to concentration)


Titration - slow


Conductivity - when there are ionic reactants/products

Name 3 special techniques for fast reactions and when they're used:

Stopped flow: rapid mixing of solutions


Flash photolysis: Reactive products from photochemical reactions


NMR line shape analysis: Solvent exchange kinetics

Distinguish between associative and dissociative ligand substitution reactions.


Give examples using LnM-X + Y

Dissociative: Intermediate with a lower coordination number. LnM-X --> LnM + X


LnM + Y --> LnM-Y


Associative: Intermediate with a higher coordination number. LnM-X + Y --> LnM-XY


LnM-XY --> LnM-Y + X

Define Intergange (I)

Concerted (coordinated) M-X bond cleavage and M-Y bond formation making a transition state of an increased coordination number

Define dissociative interchange (Id)

Transition state involves substantial M-X bond extension (weakens) and weak M-Y bond interaction leading to a 'loose' transition state.

Define associative interchange (Ia)

Transition state involves strong bonding of metal to both X and Y leading to a 'tight' transition state.

How does a pseudo first order reaction work when the rate law is:



Rate = k [LnMX] [Y]

Make on of the reactants in excess so that it's concentration does not change significantly during the reaction.


kobs = k[Y]



Rate = kobs[LnMX]

What is the Arrhenius Equation?

k=A e^-Ea/RT



Where Ea is the activation energy


A is Arrhenius Constant


R is the gas constant


T is temperature


k is rate


e is exponential

What is the Eyring equation?

Relates Gibbs energy of activation ΔG# to rate constant k:



k= (kbT/h)e^-ΔG#/RT



Where kb is Boltzman constant


h is Planck's constant

How can the Eyring equation be manipulated to be in terms of the activation parameters ΔH# and ΔS#?



And what are they?

As ΔG# = ΔH# -TΔS#



k= (kbT/h) e^-ΔH#/RT * e^ΔS#/R



ln(k/T) = ln(kb/h) - ΔH#/RT + ΔS#/R



ΔS# = Entropy of activation


ΔS#H# = enthalpy of activation

How can the sign of ΔS# help us determine whether a mechanism is associative or dissociatve?

Dissociative reaction have a transition state with a higher entropy so ΔS# is positive


Associative reactions form a transition state with a lower entropy so ΔS# will be negative

What is the effect of changing the pressure on the activation parameters?

Effects ΔV# - the volume of activation



dlnk/dp = -ΔV#/RT



ln(k/ko) = -PΔV#/RT

Using the equation ln(k/ko) = -PΔV#/RT



What happens to k with increasing p for dissociative and associative mechanisms respectively?

Dissociative: The transition state occupies more volume (long weak bond to departing ligand) so ΔV# is positive.


Increasing P therefore decreases k



Associative: Transition state occupies less volume as short tight bond ΔV# is negative. Increasing p causes increase in k

What is the advantage and disadvantage of using ΔV# in place of ΔS#?

Advantage: ΔV# is easier to visualise


Disadvantage: High pressures required to notice change

What happens to the stereochemistry of a square planar substitution?

Stereochemistry is retained. I.e. cis replaces cis, trans replaces trans

When py is the incoming ligand, and it is in excess, it can be seen from a linear plot of kobs vs [py] that:



kobs = k1 + k2[py] (y=mx + c)


What do the two k terms indicate?



There are two possible pathways

What can be varied in the reaction to alter k1? (i.e. the dissociative mechanism)

The solvent.


In some cases polar coordinating solvents cause a larger value for k1

What can be varied in the reaction to alter k2?


(i.e. the associative mechanism)


Give an example for the reaction Pt(Cl2)(py)2 + Y

Vary incoming ligand Y


e.g. for Pt(Cl2)(py)2



Pt is a relatively soft electrophile so soft nucleophiles such as PPh3 will have a much larger k value than hard nucleophiles such as Cl-

If the kinetics of a reaction is consistent with two pathways e.g:


Pt(L)3X --> (ks +sol -X) P(L)3sol -->(+Y - sol) PtL3Y



Pt(L)3X --> (k2 +Y -X) --> Pt(L)3Y



Derive the rate equation

Rate = ks[sol][PtL3X] + k2[Y][PtL3X]


ks[sol] = constant = k1


Rate = k1[PtL3X] + k2[Y][PtL3X]



Rate = kobs[PtL3X]


Where kobs = k1 + k2[Y]

What effect can spectator ligands have?

If they are bulky they will slow down the rate of associative pathways. Can be used as evidence of an associative pathway

How does the position of the R group affect the rate?

Bulky R groups cis to the leaving ligand will have a greater effect

How can two associative pathways exist in a square planar complex ligand substitution?

Through a coordinating solvent (k1 route)


or an added ligand Y (k2 route)

What can be noted about the intermediate in an associative square-planar ligand substitution reaction?

5-coordinate intermediate can change geometry (e.g. from square pyramidal to trigonal pyramid and bak again)

What effect does the leaving group X have on rate of M-X substitutions?

The weaker the M-X bond the faster the rate

What is the effect of changing the metal on the k2 of a ligand substitution reaction?

M-L bond strength increases as you go down the group of transition metals, decreasing the reactivity.


E.g. Ni>Pd>Pt as reactivity decreases 3d>4d>5d


Therefore decreasing k2

Why is k2 for [Au(CN)4]- so much larger than for [Pt(CN)4]2-?

Pt(II) complex has +1 charge


Au(III) complex has +2 charge


Au is more electrophillic


The complex has a -1 charge as opposed to -2, this causes less repulsion of CN-

Distinguish between the electronic and steric effects of trans and cis spectator ligands

Cis: Small electronic effect - large steric effect


Trans: Large electronic effect - small steric effect

What is the trans effect?

The effect of a coordinated ligand on the rate of substitution of a ligand trans to itself in a square planar or octahedral complex.


I.e. a ligand with a high trans effect accelerates the substitution of the ligand trans to itself

Which compounds have the largest trans effect?

Electron donors e.g. CN- is a good trans spectator ligand, H2O is bad.


What is important to note about the best trans spectator ligands CN-, CO, NO, C2H4?

They are all good pi acceptors

Define trans influence

The extent to which a coordinated ligand weakens the metal-ligand bond trans to itself

Explain the 'ground state' (bond weakening) effects (sigma bonding) of trans spectator ligands in the complex:



ML2TX

If T is a strong sigma donor (e.g. H-), it has a strong interaction with M and weakens the M-X bond resulting in a lowering of activation energy and a faster rate for M-X substitution.

Explain the 'transition state' effects (pi bonding) of trans spectator ligands in the complex:



ML2TX

Transition state is stabilised by pi backbonding to ligand T.


Formation of 5-coordinate intermediate increases electron density on M, electron density goes into vacant Pi* orbital on ligand T stabilising intermediate

Explain why:



[PtCl4]2- + NH3 --> [PtCl3NH3]- + NH3 --> [PtCl2NH3] where NH3 are cis to each other



[PtNH3]2+ + 2Cl- --> [PtCl2(NH3)2] where Cl are trans to each other

Cl has a higher trans effect than NH3 so the second in coming ligand will go trans to Cl in both scenarios.

Why does PR3 have a higher trans effect than Cl?

It is a strong sigma donor and also a pi acceptor

How can there be a dissociative mechanism for a square planar complex?

Pt(Me)2(SMe2)2 ---> M(Me)2(SMe2)


labile ligands due to strong trans effect of methyl ligands (very strong sigma donors?)


Involves chelating ligand, allows the substitution of the other SMe2 group

What is the chelate effect?

A chelate ligand is essentially a two attached ligands. Once one of the ligands is bound to a central metal atom the other is more likely to also bond to it, i.e. may cause a substitution reaction.

What about a nucleophile can determine whether an associative or dissociative substitution reaction takes place for e.g. Pt complexes

Whether it is a hard or soft ligand (nucleophile). Pt is a soft electrophile, so for an associative mechanism requires a soft ligand, it may do both mechanisms. A hard ligand would generally only be able to do a dissociative mechanism.

How can cis-trans isomerisation occur in square-planar complexes?

2 possible routes:



1) Intramolecular route, changes from cis square planar to tetrahedral intermediate and back to trans square planar. Disfavoured as the tet. intermediate changes spin state.



2) 2 catalysed substitution reactions by traces of free ligand. Cl- substituted by NH3, NH3 substituted by Cl- but goes trans due to Cl- having a stronger trans effect than NH3

What can be noted about the ligands of an Fe(CO)5 complex?


What effect does this have on their bond angles?

They can undergo berry-pseudo rotation. 2 of the equitorial CO ligands will change positions with the axial CO ligands (with a square pyramidal intermediate in between). Only 1 C NMR peak as fast.



Change in bond angles from 180 to 120 degrees for axial and visa versa

Give three examples of ligand substitution reactions for octahedral complexes

Solvent exchange: (e.g. swap H2O for H2O*)


Anation: (e.g. swap H2O for X-) n.b. changes charge of complex


Aquation: (e.g. substitution of Cl- with H2O) May affect charge

For an [M(OH2)6] complex surrounded by bulk water a primary and secondary coordination shell exist respectively. What determines the rate and mechanism at which these H2O ligands exchange?

The charge on the metal



M n+

Which metals cause the fastest solvent exchange?

Aqua ions of group 1,2,12 and 13 metal ions are all very labile.


Solvent exchange rates are determined by charge and - large cations with small charge most labile

Why do Al and Ga cations result in dissociative solvent exchange mechanisms whilst In undergoes an associative mechanism?

In is much larger so can increase coordination number

Explain the signs of ΔS# and ΔV# for dissociative and associative mechanisms

Dissociative: ΔS# is negative, as increased species so increased disorder. ΔV# is negative as long loose weak bonds in transition state.


Assosicative: ΔS# positive as decrease in number of species so deceased disorder. ΔV# positive as short tight strong bonds in transition state

Are dissociative (Id) mechanisms associated with small or large metal ions?

Dissociative (Id) associated with small metal ions


Associative (Ia) with large metal ions

Explain why for a high spin d4 octahedral complex an dissociative mechanism is favoured

Goes from an octahedral complex to a square pyramidal complex with the loss of a ligand. There is a different crystal field splitting pattern.


dz^2 is lowered in energy (stabilised) resulting in a higher CFSE.

Compare the effect of ligand dissociation for d3 and d4 octahedral complexes.

d3: -1.2Δoct - (-1.0Δoct)= CFSE/Δoct -0.20


d4: -0.6Δoct - (-0.914Δoct) = CFSE/Δoct +0.314



Loss of CFSE inhibits ligand dissociation - d3 is inert


Gain of CFSE encourages ligand dissociation - d4 is labile



Also note that high spin d4 (and d9) complexes will experience Jahn-teller distortion which will weaken 2M-L bonds

Which of the following will be inert/labile (i.e. will not or will undergo ligand dissociation):


d3


d4 high spin


d6 low spin


d7 low spin


d8


d9

Inert: d3, d6 low spin, d8


Labile: d4 high spin, d7 low spin, d9



Due to gain in CFSE for labile complexes due to stabilisation of dz^2 and also J.T. distortions weakening M-L bonds

Explain why V2+ has a greater H2O exchange rate than Cr3+, but lower than V3+

Lower charge makes V2+ more labile than Cr3+ as they are both d3 complexes. V3+ is a d2 complex and has a lower CFSE than d3 so is more labile

Why do mechanisms become more dissociative as you go from left to right of the d-block?

Smaller ionic radius


Full t2g leads to repulsion, incoming ligand can't associate easily


Occupied eg (weakens M-L bond)


Favours dissociation of H2O from M

When is a pre-equilibrium formed?

Pre-equilibrium assumes reactants and intermediates of a multi-step reaction exist in a dynamic equilibrium. This is the fast step

If kobs = k2Ke[Y] / 1+ Ke[Y]



What can be deduced at high and low concentrations of Y in terms of the kobs and the order of [Y]?

At high [Y]: Ke>>1 so kobs ≈ k2


- i.e. approximately zero order for [Y]



At low [Y]: Ke<<1 so kobs ≈ k2Ke[Y]


-i.e. approximately first order for [Y]


Distinguish between anation and aquation in terms of their dependence on the identity of X-

Anation involves the substitution of a ligand by Xn-. There is a small dependence on the identity of X


Aquation involves the replacement of an H2O ligand by Xn- and depends largely on the identity of X

What does the lack of dependence on the identity of incoming ligand X- imply about anation reactions?

They are dissociative, the ligand leaves first

For an aquation reaction:


[Co(NH3)X]2+ + H2O --> [Co(NH3)5(OH2)]3+ + X-



For when identity X is changed the strength of the M-X bond changes resulting in a change in equilibrium constant K. When K is plotted against rate constant k there is a positive linear correlation. What does this suggest about aquation reactions?

That it is a dissociative mechanism as there is a faster rate when the M-X bond is weaker.

Why does I- dissociate fastest from the complex [Co(NH3)5X]2+ but F- dissociates fastest from the complex [Co(CN)5X]3- ?

When Co is N-bound it is a hard metal centre and I- is a soft nucleophile.


When Co is S-bound it is a soft centre so the hard F- nucleophile dissociates fastest

Why does reactivity of a metal decrease down a group 3d>4d>5d?

M-L bonds get stronger as you go down the group, crystal field splitting increases

What is the effect of charge in octahedral substitution?

Smaller positive charge increases lability

What are two mechanisms for the hydrolysis of [Cr(OH2)5F]2+ ?

1) aquation (i.e. -F- + H2O)



2) Acid-catalysed hydrolysis (convert F- into better leaving group using H+) Faster

What is the evidence for deprotonation in the base-catalysed hydrolysis of [Co(NH3)5Cl]2+ ?

Can show H/D exchange with the addition of D2O


No base-catalysis possible for [Co(CN)5Br]3- as there are no acidic protons


How does deprotonation of [Co(NH3)5Cl]2+ assist the dissociation of Cl- ?

Lowers the positive charge on the complex


Converts one of the ligands to NH2 which is a good pi donor

Explain how inidividual cis and trans isomers of octahedral complexes can give both isomers as products, and why the product ratio depends on spectator Y and not leaving X

Dissociative reaction so 5-coordinate intermediate is formed that can isomerise. This therefore depends on the attached Y as the x has already dissociated

What are the bond breaking mechanisms of octahedral complex isomerisation?

1) Ligand dissociation (via a non-chiral intermediate). Ligand replaced by solvent, then substituted back again by ligand resulting in a different stereochemistry.


2) Ring opening - One of a pair of chelating ligands detaches, then reattaches resulting in a different stereochemistry

What are the bond breaking (twist) mechanisms of octahedral complex isomerisation?


1) Bailar twist - rotates triangular face of octahedron (D3h symmetry).



2) Ray-Dutt twist - rhombic twist (C2v symmetry)



State a similarity and difference between Bailar and Ray-Dutt twists

Both go through trigonal prismatic transition state.


They differ in the arrangement of bridging groups


Comment on the values of ΔS# and ΔV# for:



Ligand dissociation racemisation


Ring-opening racemisation


Twist racemisation

Ligand dissociation: Large positive ΔS# and ΔV#


Ring-opening: Smaller positive ΔS# and ΔV#


Twist racemisation: ΔS# and ΔV# values close to 0

What kind of substitution reactions do neutral binary 18 electron metal carbonyl complexes do, and what can be deduced about the rate determining and step and the values for ΔS# and ΔH#?



e.g. [Ni(CO)4] + L --> [Ni(CO)3L] + CO

Dissociative mechanism. Rate determining step therefore Ni-CO bond breakage and is independent of L. Large positive values for ΔS# and ΔH#

What are the effects of metal/charge and number of substitutions on rate of substitution?

Metal/charge: more negative charge causes stronger backbonding with CO resulting in slower substitution. due to more e- density on metal.


More substitutions: more sigma donation from ligand more e- density stronger backbond so slower

What is the effect of position of metal in the group on rate of CO substitution?

Varies, weakest backbonding for 2nd row metals so fastest substitution, 3rd row slow than 1st as associative mechanism can compete for larger metals

How can dissoicative Co substitution be promoted?

Photochemical reactions (16 e- can be observed at low T or by flash photolysis)


Chemical activation by oxygen transfer (nucleophillic attack on CO ligand - leaves as CO2)

For an octahedral complex Mn(CO)5Br where the Br is axial; explain why the CO is lost from an equitorial position



CHECK

The halide Br has a lone pair in a p orbital that pushes electron density into the filled M orbitals, this pushes more electron density into the trans CO pi* orbital making it less labile resulting in the loss of a cis equitorial CO group

What are going to be the values for ΔS# and ΔH# for the substitution of a 17-electron metal carbonyl?



E.g. [V(CO)6

Electron deficient so will be an associative mechanism with positive ΔH# and large negative ΔS#

How can CO substitution of an 18-electron metal carbonyl be accelerated?



e.g. [Fe(CO)5]

1 electron oxidation/reduction



e.g. 17e [Fe(CO)5]+' (radical)

If the rate of CO substitution changes for [Ni(CO)3NO] changes depending on the incoming ligand, what can be deduced? Why is this important?

It follows an associative mechanism. NO+ is isolectronic with CO and it is an 18 electron complex so would expect dissociative.

How does NO+ allow 18 electron complexes to undergo associative CO substitution (e.g. in [Ni(CO)3NO])?

NO+ is linear M-N≡O


NO- is bent M-N=O


Conversion of NO+ to NO- requires formal transfer of 2e from M to NO, allows another ligand to come in and coordinate to M.


Oxidation state of metal changes and charge of complex, but stays 18 electron. Can convert back after loss of CO



What is the evidence for dissociative mechanisms for dinuclear metal carbonyl as opposed to M-M bond hydrolysis?


E.g. Re2(CO)10

Isotopic labelling using Re(185) and Re(187) show no Re(185)-Re(187) bond in the products, indicating that the original Re-Re bonds do not break

What are the two types of electron transfer mechanisms between metal centres?

Inner sphere: Involves the sharing of at least one bridging ligand between metal centres



Outer sphere: involves the transfer of an electron from one metal ion to another without a change in the primary coordination sphere of either metal ion

What does inner sphere electron transfer between two metal centres involve?

Bonds being broken and reformed


One of the reactant complexes has to be labile

What evidence is there that inner sphere electron transfer between two metal centres occurs using a bridging ligand?


Use complex [Co(NH3 )5Cl] 2+ + [Cr(OH2 )6 ] 2+ ---> [Co(OH2 )6 ] 2+ + [Cr(OH2 )5Cl] 2+ as an example

If Cl-(36) is added to the solution it does not show up in the product. This shows it is the same chlorine atom being passed from one complex to the other

Why is electron transfer slower for V(II) complexes than Cr(II)?

Cr(II) is labile d4, V(II) is less labile d3 so bridging step is rate determining step as opposed to electron transfer

Under what conditions can H2O and NH3 take part in inner sphere electron transfer reactions?

In high pH as they can be deprotonated

What must be available for bridging ligands for inner sphere electron transfer processes?

A lone pair of electrons

Why are unsaturated organic with conjugated pi systems good bridging ligands for inner sphere electron transfer?

Delocalisation of pi electrons helps transfer electron across bridge

What affects the rate of outer sphere electron transfer?

Rate is slower if eg levels involved


Rate is faster for ligands with a conjugated pi system

What are the three necessary steps for outer sphere electron transfer?

1) Reactants move to within required distance


2) Reorganisation of surrounding solvent molecules


3) Distortion of primary coordination spheres (i.e. M-L bond elongation/compression) through bond vibrations

Why is the distortion of the primary coordination sphere necessary?

Typically M-L bonds are a shorter length for more highly charged complexes

Why would instantaneous e- transfer not work for outer sphere electron transfer?

Would give products of wrong geometry and require instantaneous energy input

Why do similar M-L bond distances Δd lead to faster electron transfer for outer sphere electron transfers and visa versa?

Less distortion needed therefore small ΔG# needed and a fast electron transfer

What about the d-electron configuration may slow down rate of outer sphere electron transfer?

Movement of electrons too or from eg* orbitals as requires greater reorganisation (e.g. Cr(III) t2g3 --> Cr(II) t2g3 eg1


Especially if spin state is changed e.g. Co(III) t2g6 ---> Co(II) t2g5 eg2

What is Marcus's theory:

Self-exchange rates can be used to predict rates of other outer sphere electron transfer reactions

What is the Marcus cross relation?

Of two separate self-exchange reactions for M and M' where rate = k11 and k22 respectively, can work out the rate of exchange between M and M' k12.


k12 = (k11*k22*K12*f12)^1/2


Where K12 is the equilibrium constant of M and M' electron exchange and f12 is a function of other parameters which normally = approx 1

What is the reverse of an oxidative addition reaction?

Reductive elimination

What happens in an oxidative addition reaction?

A coordinately unsaturated metal (i.e. has vacant sites) donates two electrons to X-Y to give X- and Y- ligands. Coordination and oxidation number of M increase by 2

What does the tendency for an oxidative addition depend on?

Stability of higher oxidation states (preferred for heavier metals)


Strength of M-X, M-Y bonds relative to X-Y


Ligand electronic and steric properties - oxidation favoured by strong sigma donor ligands and inhibited by bulky ligands

Describe nucleophillic oxidative addition mechanisms

Metal acts as nucleophile, end on approach of X-Y. Forms linear transition state, then ionic intermediate with X, before Y- is coordinated to M to form product. Can be cis or trans.

Describe concerted oxidative addition mechanisms

Side on approach of X-Y, forms triangular 3-centre transition state. X-Y bond breaking concerted with M-X and M-Y bond formation. Specific cis-addition

Which polents will be most effective for nucleophillic oxidative addition?

Polar solvents as they can help stabilise ionic transition state and intermediate

Why is there a large decrease in ΔS# for nucleophillic oxidative addition?

Increased solvation of dipolar transition state

What are the electronic and steric ligand effects on oxidative addition

Electronic effect: strongly donating ligands promote oxidative addition by increasing nucleophilicity of the metal centre e.g. phosphines



Steric effect: Bulky ligands inhibit oxidative addition by crowding the Sn2 transition state e.g. PPr3 strong donor but slow rate due to large cone angle

Why are solvent effects relatively small for concerted oxidative addition mechanisms?

Non-polar transition state

Which ligands are most likely to favour concerted oxidative addition mechanisms?

Electronegative ligands e.g. X-

Why does M-L sigma bond strength increases down a group of transition metals, i.e. Pd-X is a stronger bond than Pt-X, and why does reactivity decreases 3d>4d>5d

Due to stabilisation of the complex from crystal field splitting, which increases from 3d<4d<5d

Why do V2+ and Ni2+ aqua ions behave differently in solvent exchange?

V2+ has a larger ionic radius and is d3 so the t2g orbitals are only half-full, and there is not too much repulsion for an incoming H2O. So a more associative (Ia) subs mechanism is favoured (evidenced by negative volume of activation)


Ni2+ has a smaller ionic radius so there is less room to associate an extra H2O. It is d8 so the t2g orbitals are full, resulting in greater repulsion for an incoming H2O. Also there are 2 electrons in the eg orbitals which have M-L anti bonding character so M-L bonding is weakened and a more dissociative (Id) subs mechanism is favoured (evidenced by positive volume of activation).