the study of chemical reactions

State University of New York at Albany State University of New York at Albany

The Study of Chemical The Study of Chemical ReactionsReactions

Equilibrium Constants and Free Equilibrium Constants and Free EnergyEnergy

Thermodynamics:Thermodynamics: deals with the energy deals with the energy changes that accompany chemical and changes that accompany chemical and physical transformations.physical transformations.

A + B C + D

For the general reactionFor the general reaction

KeqProductsReactants

=[C] [D][A] [B]=

Where KWhere Keqeq is the equilibrium constant. is the equilibrium constant.

When KWhen Keqeq is > 1, the forward reaction is favored. is > 1, the forward reaction is favored.

When KWhen Keqeq is < 1, the reverse reaction is favored. is < 1, the reverse reaction is favored.

1. Thermodynamics1. Thermodynamics

KKeqeq is related to the Gibbs free energy is related to the Gibbs free energy

by the equation:by the equation:

G = -RT(ln Keq)= -2.303RT(log10 Keq)

Where R = ideal gas constantWhere R = ideal gas constantT = temperature in KelvinT = temperature in KelvinThe equation demonstrates that reactions with The equation demonstrates that reactions with negative negative G values are favored.G values are favored.

G = free energy of the products - free energy of the reactants.G = free energy of the products - free energy of the reactants.But don’t forget that:But don’t forget that:

1. Thermodynamics1. Thermodynamics

Enthalpy and EntropyEnthalpy and Entropy

Two factors that contribute to the GibbsTwo factors that contribute to the Gibbsfree energy are free energy are enthalpyenthalpy and and entropyentropy..

GG00 = = HH00 - T - TSS00

G = free energy of products - free energy of reactants.G = free energy of products - free energy of reactants.

HH00 = enthalpy of products - enthalpy of reactants = enthalpy of products - enthalpy of reactants

SS00 = entropy of products - entropy of reactants = entropy of products - entropy of reactants

Enthalpy:Enthalpy: the amount of heat evolve or the amount of heat evolve or consumed in the course of a reaction. A measure consumed in the course of a reaction. A measure of the strength of bonding in products and of the strength of bonding in products and reactants. Reactions favor products with lowest reactants. Reactions favor products with lowest enthalpy.enthalpy.

Exothermic reactionExothermic reaction: negative value of : negative value of HH00; weaker ; weaker bonds are broken and stronger bonds are formed. bonds are broken and stronger bonds are formed. H makes a favorable negative contribution to H makes a favorable negative contribution to GG00..

Endothermic reactionEndothermic reaction: positive value of : positive value of HH00; ; Stronger bonds are broken and weaker bonds are Stronger bonds are broken and weaker bonds are formed. formed. H makes an unfavorable positive H makes an unfavorable positive contribution to contribution to GG00..

2. Enthalpy and entropy2. Enthalpy and entropy

Entropy: Entropy: randomness or freedom of randomness or freedom of motion. Reactions favor products motion. Reactions favor products with the greatest entropy. A positive with the greatest entropy. A positive entropy means that the products entropy means that the products have more freedom of motion than have more freedom of motion than the reactants. In such a case, the reactants. In such a case, entropy makes a favorable negative entropy makes a favorable negative contribution to contribution to GG00..

2. Enthalpy and entropy2. Enthalpy and entropy

Usually, Usually, S is small, and thus, S is small, and thus, H is the driving force for H is the driving force for the reaction. the reaction.

Kinetics and Rate EquationsKinetics and Rate Equations

Kinetics: the study of reaction rates.Kinetics: the study of reaction rates.

Reaction rateReaction rate: how fast the products appear : how fast the products appear and the reactants disappear. Determined by and the reactants disappear. Determined by measuring the increase of concentration of measuring the increase of concentration of products or disappearance of reactants with products or disappearance of reactants with time. time. Rate Equation (or Rate Law)Rate Equation (or Rate Law): relationship : relationship between concentration of reactants and the between concentration of reactants and the observed reaction rate. observed reaction rate. This is determined This is determined experimentally.experimentally.

A + B C + D

For a general reaction:For a general reaction:

Rate = kRate = krr [A] [A]aa[B][B]bb

Where Where kkrr = rate constant = rate constant

aa and and bb = order with respect to each = order with respect to each reactant. Must be determinedreactant. Must be determined experimentally.experimentally.

aa + + bb = overall order of reaction. = overall order of reaction.

3. Kinetics and rate equations3. Kinetics and rate equations

Example:Example:CH3OH + BrCH3-Br + OH

H2O/Acetone

Experiments have shown that:Experiments have shown that:

1. Doubling the conc. of 1. Doubling the conc. of --OH doubles the reaction rate.OH doubles the reaction rate.2. Doubling the conc. of CH2. Doubling the conc. of CH33Br doubles the rate also.Br doubles the rate also.

Therefore, the rate is proportional to the concentration Therefore, the rate is proportional to the concentration

of both CHof both CH33Br and OHBr and OH--. Thus, the rate law can be. Thus, the rate law can be

written as:written as: Rate = kRate = krr [CH [CH33Br][OHBr][OH--]]


The rate equation is 1st order with respect to each of the twoThe rate equation is 1st order with respect to each of the tworeagents because it is proportional to the 1st power of theirreagents because it is proportional to the 1st power of theirconcentrations. The reaction is second order overall.concentrations. The reaction is second order overall.

Example # 2:Example # 2:(CH3)3C-Br + OH

H2O/Acetone(CH3)3C-Br + Br

Experiments have shown that:Experiments have shown that:

1. Doubling the conc. of 1. Doubling the conc. of --OH does not affect the rate.OH does not affect the rate.

2. Doubling the conc. of (CH2. Doubling the conc. of (CH33))33CBr doubles the rate.CBr doubles the rate.

Therefore, the rate is proportional to the concentration Therefore, the rate is proportional to the concentration

of (CHof (CH33))33CBr but not OHCBr but not OH--. Thus, the rate law can be written . Thus, the rate law can be written

as:as: Rate = kRate = krr [(CH [(CH33))33C-Br]C-Br]


The rate equation is 1st order with respect to (CHThe rate equation is 1st order with respect to (CH33))33CBr.CBr.

The reaction is first order overall.The reaction is first order overall.

Activation Energy and Activation Energy and Temperature Dependence of Temperature Dependence of

RatesRatesReaction rates are related to temperatureReaction rates are related to temperatureby the by the Arrhenius equationArrhenius equation::

kr = Ae-E /RTa Arrhenius equationArrhenius equation

A = Frequency FactorA = Frequency FactorEa = Activation EnergyEa = Activation Energyee-Ea/RT-Ea/RT = Fraction of collisions in which the = Fraction of collisions in which the particles have the minimum Eparticles have the minimum Eaa to react. to react.

Frequency Factor (A):Frequency Factor (A): fraction of collisions fraction of collisions with proper orientation for reaction to occur.with proper orientation for reaction to occur.

Activation Energy (EActivation Energy (Eaa):): minimum kinetic minimum kinetic

energy molecules must possess to energy molecules must possess to overcome repulsions between their electron overcome repulsions between their electron clouds when they collide.clouds when they collide.

4. Activation Energy and Temperature Dependence of Rates4. Activation Energy and Temperature Dependence of Rates

The Arrhenius equation implies that the reaction The Arrhenius equation implies that the reaction rate depends upon the fraction of molecules withrate depends upon the fraction of molecules withkinetic energy of at least Ekinetic energy of at least Eaa..

4. Activation Energy and Temperature Dependence of Rates4. Activation Energy and Temperature Dependence of Rates

The variation in the distribution of KE in a sampleThe variation in the distribution of KE in a sampledepends on temperature, and can be described bydepends on temperature, and can be described bythe the Boltzman Distribution:Boltzman Distribution:

Number of moleculesNumber of moleculeshaving a given Ehaving a given Eaa

decreases as Edecreases as Eaa

increases. At higher increases. At higher temperatures,more temperatures,more collisions have the collisions have the needed energy.needed energy.

In general, the reaction rate doubles for each 10 In general, the reaction rate doubles for each 10 00C rise in C rise in temperature.temperature.

Energy (E)

Fraction of moleculeshaving energy E

Room temp(300 K)

100 0C

(373 K)

1 kcal/mol

10 kcal/mol

19 kcal/mol

Energy Diagrams: Energy Diagrams: Graphical representation of Graphical representation of reaction energetics in proceeding from reactants to reaction energetics in proceeding from reactants to products.products.

Y Axis:Y Axis: Represents the total potential energy of all species Represents the total potential energy of all species involved in the reaction.involved in the reaction.

X Axis:X Axis: Described as the reaction coordinate or “progress Described as the reaction coordinate or “progress of reaction”. Symbolizes the progress of the reaction in of reaction”. Symbolizes the progress of the reaction in going from reactants to products.going from reactants to products.

Transition State:Transition State: highest point on graph. Represents the highest point on graph. Represents the highest energy state in a molecular collision that leads to highest energy state in a molecular collision that leads to a reaction. It is highly unstable and cannot be isolated. It a reaction. It is highly unstable and cannot be isolated. It is symbolized by a “double dagger” (‡).is symbolized by a “double dagger” (‡).

Ea:Ea: Energy difference between the reactants and the Energy difference between the reactants and the transition state.transition state.

H:H: The heat of the reaction. Represents the difference in The heat of the reaction. Represents the difference in energy between the reactants and the products.energy between the reactants and the products.

Reaction Energy Diagram for a One Reaction Energy Diagram for a One Step Exothermic ReactionStep Exothermic Reaction

5. Energy Diagrams5. Energy Diagrams

Ea

H0

Transition state

C + D (products)

A + B (reactants)

Reaction coordinate

Energy

A + B C + D

Reaction Energy Diagram for a Two Reaction Energy Diagram for a Two Step Exothermic ReactionStep Exothermic Reaction

5. Energy Diagrams5. Energy Diagrams

C + D (products)

A + B (reactants)

Energy

Reaction coordinate

Ea

rate determining transition state

reactive intermediate

In a multistep reaction,In a multistep reaction,each step has its owneach step has its ownrate, but there is onlyrate, but there is onlyone overall rate. Theone overall rate. The overall rate is overall rate is controlled by the rate-controlled by the rate-determining step. Indetermining step. Ingeneral, the highest general, the highest energy step of a multi-energy step of a multi-step reaction representsstep reaction representsthe rate-determining the rate-determining step.step.

State University of New York at Albany State University of New York at Albany

Introduction to Organic Introduction to Organic Reactions: Reactions: Reaction Reaction

MechanismsMechanisms

A A mechanismmechanism is a step by step description of is a step by step description of exactly which bonds break and which bonds exactly which bonds break and which bonds form in order to give observed products.form in order to give observed products.

Bond CleavageBond CleavageIn any chemical reaction, some bonds In any chemical reaction, some bonds are broken and other bonds are formed. are broken and other bonds are formed. Bond breakage or cleavage can be Bond breakage or cleavage can be homolytic (to give radicals) or homolytic (to give radicals) or heterolytic (to give ions).heterolytic (to give ions).

A B A B A B+

A B A B A B+Heterolytic Bond Cleavage:Heterolytic Bond Cleavage:

Homolytic Bond Cleavage:Homolytic Bond Cleavage:

ionsions

radicalsradicals

RadicalsRadicals are electron deficient because they are electron deficient because they lack an octet. They readily combine with a lack an octet. They readily combine with a single electron from another atom to complete single electron from another atom to complete the octet and form a bond. the octet and form a bond. Radicals are Radicals are usually represented by a structure with a usually represented by a structure with a single dot representing the unpaired electron.single dot representing the unpaired electron.

Cl Br H O H C H C CH

H

H

H

H

H

Cl Br HO CH3 CH3CH2

Lewis Structures:Lewis Structures:

Written:Written:

Free Radical Halogenation of Free Radical Halogenation of AlkanesAlkanes

Alkanes react with molecular halogens (typically Alkanes react with molecular halogens (typically ClCl22 and Br and Br22) to form alkyl halides. ) to form alkyl halides. Alkyl halides Alkyl halides

are hydrocarbons that contain at least one are hydrocarbons that contain at least one halogen atom.halogen atom. These reactions take place at These reactions take place at high temperatures or in the presence of UV light high temperatures or in the presence of UV light (symbolized by h(symbolized by h).).

CH3Cl + HClCH4 + Cl2heat () or light (h)

CH3CH2Br + HBrCH3CH3 + Br2heat () or light (h)

Methyl chlorideMethyl chloride

ethyl bromideethyl bromide

Free Radical Halogenation of AlkanesFree Radical Halogenation of Alkanes

The Mechanism of the reaction of CHThe Mechanism of the reaction of CH44 with Cl with Cl22 is as is as

follows:follows:Cl Cl

+

2 Cl

Cl H CH3 HCl +

CH3 Cl Cl

+

Cl CH3 Cl+

Cl Cl Cl2

CH3 + CH3 CH3 CH3

Cl + CH3 CH3 Cl

CH3

+PropagationPropagation

stepssteps

TerminationTerminationstepssteps

InitiationInitiationstepstep

In Free Radical Reactions:In Free Radical Reactions: The The initiation stepsinitiation steps generally create new generally create new

free radicalsfree radicals The The propagation stepspropagation steps usually combine a usually combine a

free radical and a reactant to form a free radical and a reactant to form a product and another free radical.product and another free radical.

Termination stepsTermination steps generally decrease the generally decrease the number of free radicals, and involve the number of free radicals, and involve the combination of two radicals to give a combination of two radicals to give a product.product.


Halogenation of Higher AlkanesHalogenation of Higher Alkanes


In higher alkanes, the replacement of In higher alkanes, the replacement of different hydrogen atoms leads to different hydrogen atoms leads to different products:different products:

CH3CH2CH3 + Cl2 Cl-CH2CH2CH3 CH3CHCH3

Cl

+h, 25 0C

1-chloropropane 2-chloropropane

40% 60%

The minor product was formed from substitution of a 1The minor product was formed from substitution of a 100 hydrogen. hydrogen.The major product was formed from substitution of a 2The major product was formed from substitution of a 200 hydrogen. hydrogen.

Relative radical stabilities control product Relative radical stabilities control product distribution.distribution.


Methyl radical < 1Methyl radical < 100 < 2 < 200 < 3 < 300

Increasing radical stabilityIncreasing radical stability

The more highly substituted the radical,The more highly substituted the radical,the greater its stability.the greater its stability.

In the analogous reaction using bromine,In the analogous reaction using bromine,the product ratios are different, even the product ratios are different, even though the mechanism is exactly the same.though the mechanism is exactly the same.


CH3CH2CH3 + Br2 Br-CH2CH2CH3 CH3CHCH3

Br

+h, 25 0C

1-chloropropane 2-chloropropane

3% 97%

The 97:3 product ratio shows that Br abstractsThe 97:3 product ratio shows that Br abstractsa 2a 200 hydrogen 97 times as fast as a 1 hydrogen 97 times as fast as a 100 hydrogen. hydrogen.We say that bromine is much more selective thanWe say that bromine is much more selective thanchlorine, and chlorine is much more reactive thanchlorine, and chlorine is much more reactive thanbromine.bromine.

Hammond PostulateHammond PostulateThe difference in reactivity/selectivity of bromine The difference in reactivity/selectivity of bromine relative to chlorine can be rationalized by the relative to chlorine can be rationalized by the Hammond Postulate Hammond Postulate which states:which states:

Related species that are similar in energy are alsoRelated species that are similar in energy are also

similar in structure. The structure of a transition similar in structure. The structure of a transition state resembles the structure of the closest stable state resembles the structure of the closest stable species.species.


The Hammond Postulate tells us whether theThe Hammond Postulate tells us whether thetransition state is more like the reactant(s) or the transition state is more like the reactant(s) or the product(s). When the reaction is endothermic, the product(s). When the reaction is endothermic, the transition state is reached relatively late on the transition state is reached relatively late on the reaction coordinate. reaction coordinate.

A B C

A B

B C

reaction coordinate

endothermic, +Ho

energy

Bond breaking (in the Bond breaking (in the reactant) and bondreactant) and bondformation (in the formation (in the product) has occurred to product) has occurred to a large extent and the a large extent and the structure of the transitionstructure of the transitionstate is more like that ofstate is more like that ofthe product than the reactant.the product than the reactant.


If the reaction is exothermic,If the reaction is exothermic,the transition state is the transition state is reached relatively early onreached relatively early onthe reaction the reaction coordinate. Bond coordinate. Bond breaking and bondbreaking and bondforming has not occurred forming has not occurred to a large extent, and theto a large extent, and thestructure of the transitionstructure of the transitionstate resembles the state resembles the reactant more than the reactant more than the product.product.


reaction coordinate

exothermic, - Ho

A B C

A B

B C

energy

The first propagation step is endothermic for bromine The first propagation step is endothermic for bromine but exothermic for chlorine. The product like but exothermic for chlorine. The product like transition state for bromination has the C--H bond transition state for bromination has the C--H bond nearly broken and a great deal of radical character on nearly broken and a great deal of radical character on the carbon atom. The energy of this transition state the carbon atom. The energy of this transition state reflects the energy difference of the radical products. reflects the energy difference of the radical products. Therefore bromination is more selective.Therefore bromination is more selective.

The reactant like transition state for the chlorination The reactant like transition state for the chlorination has the C--H bond just beginning to break, with littlehas the C--H bond just beginning to break, with littleradical character on the C atom. This transition stateradical character on the C atom. This transition statereflects only a small part of the energy difference of reflects only a small part of the energy difference of the radical products. the radical products. Therefore, chlorination is less Therefore, chlorination is less selective.selective.


Reactive IntermediatesReactive Intermediates Carbocations:Carbocations: contain carbon bearing a positive charge. contain carbon bearing a positive charge.

They are spThey are sp22 hybridized. Carbocations are electron hybridized. Carbocations are electron deficient, so they are strong electrophiles (Lewis acids). deficient, so they are strong electrophiles (Lewis acids). Like radicals, they are stabilized by alkyl substituents Like radicals, they are stabilized by alkyl substituents through (a) the inductive effect, and (b) through (a) the inductive effect, and (b) hyperconjugation. hyperconjugation. The inductive effect is donation of The inductive effect is donation of electron density through the sigma bonds of the electron density through the sigma bonds of the molecule.molecule. The positively charged carbon atom withdraws The positively charged carbon atom withdraws some electron density from the alkyl groups bonded to some electron density from the alkyl groups bonded to it. it. Hyperconjugation refers to the weak partial overlap of Hyperconjugation refers to the weak partial overlap of filled p orbitals with empty ones. filled p orbitals with empty ones. Cations are also Cations are also stabilized by resonance.stabilized by resonance.

Methyl cation < 1Methyl cation < 100 < 2 < 200 < 3 < 300

Increasing carbocation stabilityIncreasing carbocation stability

Free Radicals:Free Radicals: Like carbocations, radicals are sp Like carbocations, radicals are sp22 hybridized and planar. Unlike carbocations, the p orbital hybridized and planar. Unlike carbocations, the p orbital perpendicular to the plane of the molecule is not empty, perpendicular to the plane of the molecule is not empty, but contains one unpaired electron. Radicals are also but contains one unpaired electron. Radicals are also stabilized by alkyl groups as well as resonance. stabilized by alkyl groups as well as resonance.

Carbanions:Carbanions: Are not electron deficient since they have Are not electron deficient since they have an octet. They have tetrahedral geometry. Carbanions an octet. They have tetrahedral geometry. Carbanions are nucleophilic and basic. They are destabilized by alkyl are nucleophilic and basic. They are destabilized by alkyl groups but stabilized by resonance.groups but stabilized by resonance.

Carbenes:Carbenes: Uncharged reactive intermediates containing Uncharged reactive intermediates containing a divalent carbon atom. The simplest carbene has the a divalent carbon atom. The simplest carbene has the formula :CHformula :CH22. The carbon atom is sp. The carbon atom is sp22 hybridized. An hybridized. An

unshared electron pair occupies one of the spunshared electron pair occupies one of the sp22 orbitals, orbitals, and there is an empty p orbital extending above and and there is an empty p orbital extending above and below the plane of the molecule. Carbenes can act as below the plane of the molecule. Carbenes can act as electrophiles or nucleophiles since they have both a lone electrophiles or nucleophiles since they have both a lone pair and an empty p orbital.pair and an empty p orbital.

the study of chemical reactions

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