CH4ALKANES2

CH 4 ALKANES II: HALOGENATION- the only significant reaction of the otherwise mostly inert alkane class will be discussed here

- a detailed examination of any chemical change involves elucidation of the mechanism,thermodynamics & kinetics involved in the overall reaction

MECHANISM OF ALKANE HALOGENATION

- the overall reaction for the monohalogenation of an alkane is:

- alkane halogenation falls into a more general class of reactions known as substitution % wherean atom or group in an organic molecule is removed & replaced by another atom or group:

- thus, substitution is a combination of the other two organic chemical transformation processes:

Substitution = Addition + Elimination

- the equation for an overall reaction is not always a realistic rendition of how reactants transforminto products, necessitating the use of:

Mechanism

- a complete, detailed account of the exact bond-breaking and bond-making processes whichrationalize the formation of products from reactants in a chemical transformation

- reaction mechanisms will include:

Curved Arrows % to represent the movement of electrons as bonding changes occur

Reactive Intermediates % unstable, short-lived species which react quickly with stable molecules

Elementary Steps % processes which involve reactive intermediates as reactants & products

R H + X X

alkane

or hR X + H X

halogen

X = Cl, Br = heat h = light

A B + Z A Z + B

Substitution Rxn:

organic molecule Z added B eliminated

Z substitutes for B

- a mechanism is a reasonable explanation for the outcome of a reaction; it is not always a provablefact, although modern spectroscopic techniques are now characterizing many intermediates

- the following experimental observations have been made for the chlorination of methane:

a) Heat or light is required to initiate or no reaction occurs

b) The wavelength of the light used is strongly absorbed by chlorine (not methane)

c) There is a high quantum yield % one photon of light produces many halogenated products

- based on these facts, the proposed mechanism for alkane halogenation is as follows:

Free Radical Chain Process

- a general mechanism which applies to other reactions as well; it always involves three phases:

1) Initiation

- elementary step which involves only bond-breaking & generates reactive intermediates

Free Radicals, R

- short-lived reactive intermediates which have an odd number of electrons

- free radicals are powerful electrophiles (E+), seeking another electron

EX s

- henceforth, free radicals will refer to the organic variety exclusively

2) Propagation

- elementary step in which a reactive intermediate reacts with a stable molecule producing astable molecule (of itself) and another reactive intermediate

- the reactive intermediate generated in the first propagation step reacts with another stablemolecule in a second elementary propagation step, producing the same reactive intermediatethat began the first propagation step

- the cycle regenerates itself, repeating over & over, because the product of the secondpropagation step is the reactant in the first propagation step

X X

halogen molecule

or hX + X

halogen atoms

(free radicals)

Cl , Br , CH3

2a)

2b)

- since the halogen atom (X) produced in step 2b repeats (as reactant) in step 2a one X canproduce many halogen product molecules (RX), explaining the high quantum yield

3) Termination

- elementary step which involves only bond-making; producing fewer reactive intermediates thanit consumes

- in this case, a step which consumes free radicals & produces a stable molecule

- in alkane halogenation, there are many possible termination steps; these are the most common:

3a)

3b)

3c)

- these steps are all very unlikely, based on the low probability of collision between the reactants

- reactive intermediates such as free radicals are always in extremely low concentration, sincethey react so rapidly with stable molecules which are in high concentration & more likely to beencountered

- it is only when the reactants (stable molecules), namely, the alkane (RH) & the halogenmolecule (X2), become very low in concentration does the collision frequency for the freeradicals increase & the termination steps become likely

R H X H XR+ +

stable molecule

reactive intermediate


stable molecule

(free radical)

XR + +

stable molecule



stable molecule

(free radical)

X X R X

(repeats step 2222aaaa)

X X X X+

R X R X+

R R R R+

EX. Chlorination of Methane

Overall Reaction

Mechanism

THERMODYNAMICS

- the study of energy (heat) changes involved in physical and chemical processes.

Equilibrium Constant, Keq

Reactants, Rs Products, Ps

- when Keq >> 1 ; Ps are favored & equilibrium lies to the right

- when Keq

Free Energy, Go

G = G (Ps) - G (Rs)

- when G < 0 (negative value) ; process (reaction) is favorable

- when G > 0 (positive value) ; process (reaction) is unfavorable

Go is related to Keq : Go = -RT ln Keq or Keq = e

-G/RT

- so, a favorable reaction has -G and Keq >> 1 & an unfavorable reaction has +G & Keq 0 (positive value) ; process (reaction) favors Ps

- when S < 0 (negative value) ; process (reaction) favors Rs

- favorable reaction (-G and Keq >> 1 ) would then be promoted by a -Ho & a +So

- since the TSo term is usually small and negligible, Ho is the more important factor in

determining the value of Go, Keq and whether or not a reaction is favorable.

- therefore, assuming that Go . Ho , a more exothermic reaction (stronger bonds formed) is a

more favorable reaction with a larger Keq.

Bond Dissociation Energy, BDE

- the energy required to break a bond homolytically.

Homolytic Bond Cleavage

Note For bond formation the BDE has a negative value (Exothermic process).

Heterolytic Bond Cleavage

BDEs (for homolytic bond cleavage) can be used to approximate Ho values for reactions:

Ho = BDE (Rs) - BDE (Ps) endothermic exothermic

(positive) (negative)

Table 4-2, p. 136, lists the BDE values for bonds found in some simple organic molecules.

EX. Using BDEs, approximate the value of Ho for the chlorination of methane:

CH4 + Cl2 CH3Cl + HCl

Bonds Broken BDE (kcal/mol) Bonds Formed BDE (kcal/mol)

CH 104 CCl 84ClCl 58 HCl 103

Total 162 Total 187

Ho = 162 - 187 kcal/mol

Ho = -25 kcal/mol

A B A + B Ho = BDE (Endothermic Rxn)

A B A + B

- BDEs can also be used to approximate Ho values for elementary steps.

- since propagation steps 2a & 2b provide all the energy necessary to sustain the free radicalchain reaction, the sum of the values of Ho for the propagation steps (2a & 2b) gives the same

value of Ho as for the overall reaction determined above.

Propagation Steps:

2a) CH4 + Cl@ CH3@ + HCl Ho2a = +1 kcal/mol

BDE = 104 -103 kcal/mol

2b) CH3@ + Cl2 CH3Cl + Cl@ Ho2b = -26 kcal/mol

BDE = 58 -84 kcal/mol

HoT = -25 kcal/mol

KINETICS

- the study of reaction rates (or how fast a reactant disappears or a product appears).

Rate Law

- an equation which relates rate to concentration (experimentally obtained).

For the reaction: A + B P s

Rate = k [A]a[B]b

where: k = rate constant[ ] = concentrationa,b = rate order

Activation Energy, EA

- the minimum kinetic energy required for molecules to have successful collisions and react.

- EA is related to k by the Arrhenius Equation:

k = Ae-EA/RT

where: A = frequency factorR = gas constantT = temperature

as EA9999 k 8888 Rate8888 (also as T8 k 8 Rate8)

Transition State, TS

- the energy maximum between Rs & Ps in any collision that leads to a reaction.

- the difference in energy between the Rs & the TS is the EA

- the TS is not an intermediate its bonds cannot vibrate

- the TS is symbolized with partial bonds

EX. Transition state for propagation step 2a in the chlorination of methane

Reaction Energy Profile, REP

- a graphical account of the energy change vs. structural change during the course of a reaction

For the reaction: A + B C + D Exothermic, -Ho

Note the reverse rxn would be endothermic (+Ho), & would have a larger EA.

Multistep Reaction Rates

- many reactions have several steps & intermediates.

- the REP s for these reactions will have several energy minima & maxima:

Maxima (peaks) = transition states Minima (valleys) = reactive intermediates

CH4 + Cl H C

H

H

H Cl CH3 + H Cl

TS

formingbreaking

Rate-Determining Step, RDS

- the slowest step (or bottleneck) in a multistep reaction.

- the RDS determines the overall rate of the rxn (or overall reactivity)

- the RDS has the largest EA (highest energy TS) in the REP

- the RDS can also be identified as the elementary step with the most endothermic enthalpyvalue (most positive or least negative Ho)

For an elementary step: as Ho8888 TSE 8888 EA 8888 Rate9

EX. RDS in Alkane Halogenation = Propagation Step 2a

RH + X@ R@ + HX

XXXX EA, kcal Rate @300K Rate @500K Comments on Overall Reactivity

F 1.2 1.4 x 105 3.0 x 105 F reacts too fast explodes

Cl 4.0 1.3 x 103 1.8 x 104 Cl reacts at room temperature (with light)

Br 18 9.0 x 10-8 1.5 x 10-2 Br requires heat

I 34 2.0 x 10-19 2.0 x 10-9 I reacts too slow no reaction (NR)

Note these values are for R = CH3

Conclusion: as EA for RDS8888 Overall Rate9999 Reactvity9999

HALOGENATION OF HIGHER ALKANES

- a higher alkane is one with more than one type of carbon according to degree of substitution (that is, any alkane with three or more carbons)

- the different types of hydrogens attached to those different carbons will then produce more thanone product upon substitution by a halogen (yielding multiple monohalogenation products)

Product Distribution

- the relative amount or percentage yield (%P) of each different monohalogenation productdepends on two factors:

1) the number of hydrogens which give rise to that particular monohalogenated product

2) the relative reactivity of that type of hydrogen which upon substitution, yields that product

- the number of hydrogens is easily determined by counting, but the relative reactivity must becalculated from established experimental percentage yields

EX. Chlorination of propane, C3H8

- note that only two 2o Hs give a greater yield of product (60%) than do the six 1o Hs (only 40%)

- secondary hydrogens (2o Hs) must be therefore, more reactive than primary hydrogens (1o Hs)

TTTTyyyyppppeeeessss ooooffff HHHHyyyyddddrrrrooooggggeeeennnn

1o C

R C

H

H

H R C

R

H

H R C

R

R

H

Primary hydrogens Secondary hydrogens Tertiary hydrogen

2o C 3o C

1111oooo H's 2222oooo H's 3333oooo H

1o 1o 2o

Cl2

(1o H substd')

44440000%%%% 66660000%%%%

CH3 CH2 CH3 +h

CH3 CH CH3

Cl

CH3 CH2 CH2 Cl + + HCl

(2o H substd')

Relative Reactivity of 1o vs 2o Hydrogens

- the relative reactivity can be quantified by using the percentage yield & number of hydrogens tofind the yield per hydrogen & then simplifying the ratio:

Relative Reactivity 1o H : 2o H = 1.0 : 4.5 (towards chlorine)

- or, secondary hydrogens (2o Hs) are 4.5 times more reactive than primary hydrogens (1o Hs)

- this relative reactivity ratio of hydrogens towards chlorination is always the same regardless of thestructure of the alkane involved in the reaction

- based solely on experimental observation, there is a clear preference for one type of hydrogenover another towards substitution by halogen

- to rationalize this selectivity phenomenon, the thermodynamic & kinetic aspects of the reactionmechanism are examined:

- recall the rate-determining step (RDS) in alkane halogenation % propagation step 2a:

2a) RH + X@ R@ + HX

- the key reactive intermediate in this elementary step is the organic free radical, R

- the carbon on which the free radical forms in step 2a is the same carbon that the halogen willsubstitute in step 2b

- therefore, the structure of the free radical dictates the structure of the product, RX from whoseproduct ratio the relative reactivity of hydrogen was determined

- the reactivity of the hydrogen can be correlated to the stability of the free radical as follows:

- elimination of the more reactive hydrogen in the RDS leads to:

- the more stable free radical, R

- a more stable transition state (TS) leading to that free radical (lower TS energy)

- a lower activation energy for that elementary propagation step

- a faster overall rate of reaction for that monohalogenation product

=

1o H 40%

6 H6.7% / H

=60%

2 H30% / H

=6.7

6.7

1.0

4.5

Relative Reactivity Ratio

=

2o H

- the previous line of reasoning is only valid because it is based on a comparison of parameters inthe rate determining step

EX. Chlorination of propane

Relative Comparison: 2o to 1o

H-reactivity8 R stability8 TS stability8 TSE 9 EA 9 Rate RDS8 Overall Rate 8

- from bond dissociation energies (BDE), the enthalpy (Ho) of the rate determining steps (2a) for

2o vs 1o halogenation can be calculated

- the only difference between pathways x & y is the BDE for the breaking of a 2o CH bond vs 1o

CH bond (the HCl formed is the same for both)

- the BDE value for the 2o CH bond is smaller (95 kcal/mol) than the value for the 1o CH bond(98 kcal/mol) thus, it is easier to break the 2o CH bond (Ho value more exothermic)

- a summary all of the conclusions drawn from the experimental evidence & based on the rate-determining step can now be made:


as BDE9 Ho9 H-reactivity8 R stability8 TS stability8 TSE 9 EA 9 Rate RDS8 Overall Rate8

(for CH breaking)

Cl Cl

1o 1o 2o

CH3 CH2 CH3

h

CH3 CH CH3

Cl

CH3 CH2 CH2 Cl

2 Cl

Cl

-1o H

-2o H

HCl

HCl

+ Cl2

+ Cl2

(more stable)

CH3 CH2 CH2

CH3 CH CH3

+

+

+ Cl

+ Cl

1111oooo RRRR

2222oooo RRRR (more product)

1)

2a)

2b)

2b)

RDSx y

x

y

Relative Reactivity of 1o vs 3o Hydrogens

- the same comparative analysis can be made for the stability of tertiary a free radical (3o R) & itseffect on the reactivity of a tertiary hydrogen (3o H)

EX. Chlorination of isobutane, C4H10

Relative Reactivity 1o H : 3o H = 1.0 : 5.5 (towards chlorine)

- or, tertiary hydrogens (3o Hs) are 5.5 times more reactive than primary hydrogens (1o Hs)

- as before, this relative reactivity ratio of hydrogens towards chlorination is always the sameregardless of the structure of the alkane involved in the reaction

- by comparing the rate-determining steps (2a) for 1o vs 3o hydrogen elimination, a quantitativecorrelation between bond dissociation energies, free radical stability & overall reactivity can bemade as before:

RRRRDDDDSSSS ffffoooorrrr 3333oooo CCCC----HHHH

CH3 C

CH3

CH3

H ClCH3 C

CH3

CH3H Cl

BDE's => 91

H Cl

attack 3o H

+

++

+

- 103

CH3 CH

CH3

CH2 H Cl

attack 1o H

CH3 CH

CH3

CH2

(kcal/mol)

BDE's => 98 - 103

(kcal/mol)

1o R

3o R

(more stable)

RRRRDDDDSSSS ffffoooorrrr 1111oooo CCCC----HHHH

H = ----11112222 kcal/mol

H = ----5555 kcal/mol

(less stable)

1o 1o 3o

Cl2

(1o H substd')

66662222%%%% 33338888%%%%

+h

+

(3o H substd')

CH3 CH

CH3

CH3 CH3 CH

CH3

CH2 Cl

CH3 C

CH3

CH3

Cl

1o

=

1o H62%

9 H6.9% / H

=38%

1 H38% / H

=6.9

6.9

1.0

5.5


=

3o H

Calculate relative reactivities as before:

- note that the rate-determining step for 3o CH bond breaking is more exothermic because thebond dissociation energy is smaller than for 1o CH bond breaking


as BDE9 Ho9 H-reactivity8 R stability8 TS stability8 TSE 9 EA 9 Rate RDS8 Overall Rate8

(for CH breaking)

Free Radical Stabilities

- from the experimental evidence, an order of hydrogen reactivity has been established

- it follows then, that the order of stability of free radicals follows that same trend

Hydrogen Reactivity Rank

Free Radical Stability Rank

- from the previous relative comparisons, the following general inferences can be made:

- in an elementary step, (i.e. the RDS) the more stable intermediate (i.e a R) forms faster

- a more exothermic (lower Ho) elementary step has a lower activation energy (EA )

- if that more exothermic elementary step is rate-determining, then that overall reaction is faster

- a reaction energy profile clearly shows the relationship between Ho & EA

R C

R

R

R C

H

H

R C

H

R

H C

H

H

>

tertiary secondary primary methyl

3333oooo R 1111oooo R2222oooo R Me

> > >

>>

>

>>>

1o C

R C

H

H

HR C

R

H

HR C

R

R

H

2o C 3o C

1111oooo H's 2222oooo H's 3333oooo H

tertiary secondary primary methyl

Me H's

H C

H

H

H

>>

EX. Chlorination of propane Reaction Energy Profile for the Rate-Determining Step


Ho9 R stability8 Relative TSE 9 EA 9 Rate 8

Predicting Product Distribution

- the product ratios or percentage yields (%P) obtained experimentally were used to determine therelative reactivity of different hydrogens towards chlorine:

Relative Reactivity 1o H : 2o H : 3o H = 1.0 : 4.5 : 5.5

- as before, this relative reactivity ratio of hydrogens towards chlorination is always the sameregardless of the structure of the alkane involved in the reaction

- thus, this information can be used to predict product distribution ratios (%P) for monochlorinationof any alkane

- the relative amount of each monochlorination product is found as follows:

- the percentage of each product is then determined:

Rel. Amt. P = #### HHHH''''ssss x RRRReeeellll.... RRRRccccttttvvvvttttyyyy

(producing that P) (of that H-type)

%P = Rel. Amt. P

Total P'sx 100

EX. Predict the products & percentage yields (%P) for the monochlorination of 2-methylbutane

Given % Relative Reactivity 1o H : 2o H : 3o H = 1.0 : 4.5 : 5.5

Product Type HHHH # HHHH s Relative Reactivty Relative Amount P %P

I

II

III

IV

Total =

CH3 CH

CH3

CH2 CH3Cl2

h

Selectivity vs Reactivity: Different Halogens

- it is now evident that different hydrogens have different reactivities for the same halogen

- it is also true that different halogens have different reactivities towards the same hydrogen

- for different halogens % as reactivity 9999 selectivity 8888 & as reactivity 8888 selectivity 9999

EX. Bromination of isobutane, C4H10

Relative Reactivity 1o H : 3o H = 1.0 : 900 (towards bromine)

- or, tertiary hydrogens (3o Hs) are 900 times more reactive than primary hydrogens (1o Hs)towards reaction with bromine (compared to 5.5 times more reactive towards chlorine)

- once again, this relative reactivity ratio of hydrogens towards bromination is always the sameregardless of the structure of the alkane involved in the reaction

- so, bromine (Br2) is more selective than chlorine (Cl2) the major reaction is favored by aneven greater amount

- therefore, bromine (Br2) must be less reactive than chlorine (Cl2)

Lower Reactivity: (Bromine vs Chlorine)

- comparing the enthalpies for the rate-determining steps (2a) for bromination vs chlorination ofthe tertiary hydrogen in isobutane explains the difference in reactivity between bromine & chlorine

- the same difference in reactivity would be observed for halogenation of a primary or secondaryhydrogen as well (bromine is less reactive towards any hydrogen)

1o 1o 3o

Br2

(1o H substd')

1111%%%% 99999999%%%%

+h

+

(3o H substd')

CH3 CH

CH3

CH3 CH3 CH

CH3

CH2 Br

CH3 C

CH3

CH3

Br

1o

=

1o H1%

9 H0.1% / H

=99%

1 H99% / H

=0.1

0.1

1.0

900


=

3o H

Calculate relative reactivities as before:

EX. Comparison of rate-determining steps for halogenation of the tertiary hydrogen in isobutane

- the RDS for bromination is endothermic (+Ho), so the overall reaction is slower than chlorination

whose RDS is exothermic (-Ho)

- the bromination step 2a is endothermic because the bond dissociation energy for hydrogen

bromide (HBr) is smaller than it is for hydrogen chloride (HCl)

- since the H-Br bond is being formed, the BDE is a less negative value & Ho is thus positive

Relative Comparison: Bromine to Chlorine

as BDE9 Ho8 TSE 8 EA 8 Rate RDS9 Overall Rate9 Reactivity9 (towards any H)

(for HX making)

Conclusion: bromine is less reactive than chlorine

Higher Selectivity: (Bromine vs Chlorine)

- comparing reaction-energy profiles (REPs) for the rate-determining steps (step 2a) forbromination vs chlorination of the two types of hydrogen (1o & 2o) in propane explains thedifference in selectivity between bromine & chlorine:

RRRRDDDDSSSS ffffoooorrrr SSSSuuuubbbbssssttttnnnn'''' ooooffff aaaa 3333oooo HHHH bbbbyyyy CCCChhhhlllloooorrrriiiinnnneeee

CH3 C

CH3

CH3

H Cl CH3 C

CH3

CH3H Cl

BDE's => 91

+ +

- 103

(kcal/mol)

H = ----11112222 kcal/mol

CH3 C

CH3

CH3

H Br CH3 C

CH3

CH3H Br

BDE's => 91

+ +

- 88

(kcal/mol)

H = ++++3333 kcal/mol

RRRRDDDDSSSS ffffoooorrrr SSSSuuuubbbbssssttttnnnn'''' ooooffff aaaa 3333oooo HHHH bbbbyyyy BBBBrrrroooommmmiiiinnnneeee

EX. Comparison of reaction-energy profiles for rate-determining steps of halogenation of propane

- note that the transition state for endothermic bromination is more towards the product side(right) of the REP the difference in transition state energy for 1o vs 2o hydrogens is more thantwice as large

- because the transition state energy & the activation energy are so much higher for abstraction ofthe 1o hydrogen, the overall reaction for bromination of a 1o hydrogen is much slower than for a 2o hydrogen

- thus, bromination of the 2o hydrogen is much faster & becomes the dominant reaction, renderingbromine more selective for one type of hydrogen (2o in this case)

Relative Comparison: Bromine to Chlorine

as Ho8 TSE 8 EA 8 Rate RDS8 Overall Rate8 Selectivity8 (for 1o vs 2o H)

- by the same reasoning, the preference for tertiary hydrogens towards substitution by bromine iseven greater (see bromination of isobutane above)

Conclusion: bromine is more selective than chlorine

Overall bromine is less reactive but more selective than chlorine

- the inverse relation between selectivity & reactivity is a general phenomenon which is based theenthalpy of any elementary step in a chemical process

- the relative value of Ho actually determines the position of the transition state on the reactioncoordinate

THE HAMMOND POSTULATE

- related species which are similar in energy are also similar in structure

- the transition state structure resembles the structure of the closest stable species (either thereactant or the product of an elementary step)

Endothermic Reaction, +Ho

- the transition state resembles the products (Ps)

- the transition state is closer in energy and structure to the products (Ps)

- so, for an endothermic reaction it is a: P-like TS

Exothermic Reaction, -Ho

- the transition state resembles the reactants (Rs)

- the transition state is closer in energy and structure to the reactants (Rs)

- so, for an exothermic reaction it is a: R-like TS

EX. Endothermic Rxn % AB + C A + BC +Ho

E

RC

EA

TS

+ H

P's

R's

R's P's

AB + C

A + BC

TS

TS

closer in energy

closer in structure

TS Structure = A B C

very broken mostly formed

Product-Like

EX. Exothermic Rxn % AB + D A + BD -Ho

REACTIVE INTERMEDIATES

- as previously described, they are short-lived, labile species which are the reactants & products ofelementary mechanistic steps

A. Free Radicals, RRRR

- have three bonds & an unpaired, single electron on the carbon

- the bonds are constructed from sp2 HOs, giving a trigonal planar geometry & the odd electronresides in a p AO

E

RC

EA

TS

- H

P's

R's

R's P's

AB + D

A + BD

TS

TS

closer in energy

closer in structure

TS Structure = Reactant-Like A B D

not very broken not very formed

C

Order of Stability 3o R > 2o R > 1o R > Me (as before)

- free radicals are stabilized by the two electron-donating effects of other carbons (R grps):

Inductive Effect % a through-bond stabilizing interaction with the free radical carbon

Hyperconjugation % a through-space stabilizing interaction with the free radical carbon

B. Carbocations, RRRR+

- have three bonds & no other electrons on the carbon

- similar in structure & stability to free radicals, carbocations will be examined in Chapter 6

C. Carbanions, R:R:R:R:

- have three bonds & a lone pair of electrons on the carbon

- similar in structure, but opposite in stability to free radicals & carbocations, carbanions will betreated in Chapter 10

D. Carbenes,

- have two bonds & two electrons (paired or unpaired) on the carbon

- although uncharged, carbenes are extremely unstable reactive intermediates

- carbenes will investigated in Chapter 8

C

CC alkyl grp C's can donate e- density

through the bond

C

C

CH4ALKANES2

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