Chapter 4 The Study of Chemical Reactions

  Tools for Study

  To determine a reaction’s

• mechanism, look at:
• Equilibrium constant
• Free energy change
• Enthalpy
• Entropy
• Bond dissociation energy
• Kinetics

  =>

• Activation energy

  

Chlorination of Methane

_{H H H H + C Cl H 2}

heat or light

_{H C Cl + HCl H} Requires heat or light for initiation.

• The most effective wavelength is blue, which
• is absorbed by chlorine gas. Lots of product formed from absorption of
• only one photon of light (chain reaction).

  =>

Free-Radical Chain Reaction Initiation generates a reactive intermediate

• Propagation: the intermediate reacts with a
• stable molecule to produce another reactive intermediate (and a product molecule). Termination: side reactions that destroy the
• reactive intermediate. =>

  

Initiation Step

  A chlorine molecule splits homolytically into chlorine atoms (free radicals)

  => Cl Cl + photon (h

   ) Cl + Cl

  

Propagation Step (1)

  The chlorine atom collides with a methane molecule and abstracts (removes) a H, forming another free radical and one of the products (HCl).

  C ^{H H} _H ^H _{Cl +} ^{C H H} _H ^{+ H Cl} =>

  

Propagation Step (2)

  The methyl free radical collides with another chlorine molecule, producing the other product (methyl chloride) and regenerating the chlorine radical.

  H H

• ⁺ H C Cl Cl H C Cl ⁺

  Cl H H

  =>

  

Overall Reaction

C ^{H H} _H ^H _{Cl +} ^{C H H} _H ^{+ H Cl}

  C H H H

• ⁺ Cl Cl C H H H Cl ⁺ Cl

  C ^{H H} _H ^{H +}

_{Cl Cl C}

^H _{H H Cl + H Cl} =>

  Cl Cl + photon (h _ ) Cl + Cl

  C H H H Cl +

  Termination Steps

• Collision of any two free radicals
• Combination of free radical with contaminant or collision with wall.

  C H H H Cl Can you suggest others?

  =>

  

Equilibrium constant

_eq K = [products]

• [reactants]
_{19 eq} For chlorination K = 1.1
• Large value indicates reaction “goes to
• completion.”

  =>

  

Free Energy Change

  DG = free energy of (products -

• reactants), amount of energy available to do work. _o Negative values indicate spontaneity.
• _eq
• where R = 1.987 cal/K-mol and T = temperature in kelvins Since chlorination has a large K _eq

DG = -RT(lnK )

• energy change is large and negative. =>

  , the free

  

Problem

Given that -X is -OH, the energy difference for

• the following reaction is -1.0 kcal/mol.

  What percentage of cyclohexanol molecules

• will be in the equatorial conformer at equilibrium at 25°C?

  => Factors Determining G 

• enthalpy

  Free energy change depends on

• entropy
• 

  H

   = (enthalpy of products) - (enthalpy of reactants)

• 

  S

   = (entropy of products) - (entropy of reactants)

• 

  G

   = H - TS =>

  Enthalpy ^o

  = heat released or absorbed during DH

• a chemical reaction at standard conditions. Exothermic, (- DH), heat is released.
• Endothermic, (+ DH), heat is absorbed.
• Reactions favor products with lowest
• enthalpy (strongest bonds). =>

  

Entropy

^o

DS = change in randomness, disorder

• freedom of movement. Increasing heat, volume, or number of
• particles increases entropy. Spontaneous reactions maximize
• disorder and minimize enthalpy. ^{o o o}

  In the equation DG = DH the - T DS

• entropy value is often small. =>

  Bond Dissociation Energy

  Bond breaking requires energy (+BDE)

• Bond formation releases energy (-BDE)
• Table 4.2 gives BDE for homolytic
• cleavage of bonds in a gaseous molecule.

  A B A B +  We can use BDE to estimate H for a reaction.

  =>

Which is more likely? Estimate DH for each step using BDE

• + + Cl CH
₃ CH ₃

  CH ₄ HCl

• + Cl
₂ CH ₃ Cl + Cl or Cl + CH ₄ CH ₃ Cl + H H

  Cl ₂

  104 103

  58

  84 =>

  104

  84

• + HCl Cl +

  58 103

  

Kinetics

  Answers question, “How fast?”

• Rate is proportional to the concentration
• of reactants raised to a power. Rate law is experimentally determined.
• =>

  

Reaction Order

^{a b} For A + B
• a is the order with respect to A  a + b is the overall order

  [B]  C + D, rate = k[A]

  Order is the number of molecules of that

• reactant which is present in the rate- determining step of the mechanism.

  The value of k depends on temperature as

• given by Arrhenius: ln k = -E + lnA _a RT =>

  Activation Energy

  Minimum energy required to reach

• H the transition state.

  H C H Cl H

  At higher temperatures, more molecules

• have the required energy.

  => Reaction-Energy Diagrams

  For a one-step reaction:

• reactants

   transition state  products A catalyst lowers the energy of the

• transition state.

  =>

  =>

  

Energy Diagram for a

Two-Step Reaction

• Reactants  transition state  intermediate

• Intermediate  transition state  product

  

Rate-Determining Step

  Reaction intermediates are stable as long

• as they don’t collide with another molecule or atom, but they are very reactive. Transition states are at energy maximums.
• Intermediates are at energy minimums.
• _a

  The reaction step with highest E will be the

• slowest, therefore rate-determining for the entire reaction. =>

  Rate, E a

  , and Temperature X + CH

  3 X E _a Rate @ 300K Rate @ 500K F 1.2 kcal 140,000 300,000 Cl 4 kcal 1300 18,000 Br 18 kcal 9 x 10

• ^-8 0.015 I 34 kcal 2 x 10 ^-19

  2 x 10

• ^-9

  =>

Conclusions

• With increasing E _a , rate decreases.
• With increasing temperature, rate increases.
• Fluorine reacts explosively.
• Chlorine reacts at a moderate rate.
• Bromine must be heated to react.
• Iodine does not react (detectably).

  =>

  

Chlorination of Propane

1  C

  

Cl

Cl h _

  _{3 2 3 + Cl 2} CH CH CH _{2 2 3} + CH CH CH _{3 3} 2  C

  There are six 1  H’s and two 2  H’s. We

• expect 3:1 product mix, or 75% 1- chloropropane and 25% 2-chloropropane. Typical product mix: 40% 1-chloropropane
• and 60% 2-chloropropane. Therefore, not all H’s are equally reactive.
• =>

  

Reactivity of Hydrogens

  To compare hydrogen reactivity, find

• amount of product formed per hydrogen: 40% 1-chloropropane from 6 hydrogens and 60% 2-chloropropane from 2 hydrogens. 40%
•  6 = 6.67% per primary H and

  60%  2 = 30% per secondary H Secondary H’s are 30%  6.67% = 4.5

• times more reactive toward chlorination

  => than primary H’s.

Predict the Product Mix

  Given that secondary H’s are 4.5 times as reactive as primary H’s, predict the percentage of each monochlorinated product of n-butane + chlorine.

  =>

  

Free Radical Stabilities

  Energy required to break a C-H bond

• decreases as substitution on the carbon increases. Stability: 3

   > 2 > 1 > methyl

• DH(kcal) 91, 95, 98, 104

  => Chlorination Energy Diagram

  Lower E _a , faster rate, so more stable intermediate is formed faster.

  =>

  

Bromination of Propane

1  C

  Br

Br

heat

  CH CH CH Br +

  ^{3 2 3 2 CH CH CH} + _{2 2 3 3 3} 2  C

  There are six 1  H’s and two 2  H’s. We

• expect 3:1 product mix, or 75% 1- bromopropane and 25% 2-bromopropane. Typical product mix: 3% 1-bromopropane
• and 97% 2-bromopropane !!! Bromination is more selective than
• => chlorination.

  Reactivity of Hydrogens

  To compare hydrogen reactivity, find

• amount of product formed per hydrogen: 3% 1-bromopropane from 6 hydrogens and 97% 2-bromopropane from 2 hydrogens. 3%  6 = 0.5% per primary H and
• 97%  2 = 48.5% per secondary H Secondary H’s are 48.5%  0.5% = 97
• times more reactive toward bromination than primary H’s. =>
Bromination Energy Diagram
• Note larger difference in E _a
• Why endothermic?

  => Bromination vs. Chlorination =>

  Endothermic and Exothermic Diagrams =>

  

Hammond Postulate

Related species that are similar in energy are

• also similar in structure. The structure of a

  transition state resembles the structure of the closest stable species. Transition state structure for endothermic
• reactions resemble the product. Transition state structure for exothermic
• reactions resemble the reactants.

  =>

Radical Inhibitors Often added to food to retard spoilage

• Without an inhibitor, each initiation step
• will cause a chain reaction so that many molecules will react. An inhibitor combines with the free
• radical to form a stable molecule. Vitamin E and vitamin C are thought to
• protect living cells from free radicals. =>

  Carbene

  

Reactive Intermediates

• Carbocations (or carbonium ions)
• Free radicals
• Carbanions •

  =>

Carbocation Structure

  Carbon has 6 electrons,

• positive charge.
² Carbon is sp hybri
• with vacant p orbital. =>

  Carbocation Stability Stabilized by alkyl

• substituents 2 ways: (1) Inductive effect:
• donation of electron density along the sigma bonds. (2) Hyperconjugation:
• overlap of sigma bonding orbitals with empty p orbital.

  =>

  

Free Radicals

Also electron-
• deficient Stabilized by alkyl
• substituents Order of stability:
• 3  > 2 > 1 > methyl

  =>

  

Carbanions

Eight electrons on C:
• 6 bonding + lone pair Carbon has a negative
• charge. Destabilized by alkyl
• substituents. Methyl >1  > 2  > 3
• 

  

Carbenes

Carbon is neutral.
• Vacant p orbital, so
• can be electrophilic. Lone pair of
• electrons, so can be nucleophilic.

  => End of Chapter 4