Thermochemistry

Studying an Organic Reaction

How do we know if a reaction can occur?

And – if a reaction can occur what do we know about the reaction?

CH3ONa CH3Cl CH3OCH3 NaCl

Information we want to know:

How much heat is generated? (What is the THERMODYNAMICS of the reaction?)

How fast is the reaction? (What is the KINETICS of the reaction?)

Are any intermediates generated? (What is the reaction mechanism?) 171 All of this information is included in an Energy Diagram

Possible Mechanism 1 Possible Mechanism 2

Transition Transition states states

Potential Potential Intermediate energy energy Starting material

Starting Products material Products

Reaction Coordinate Reaction Coordinate

If we know the “shape” of the reaction coordinate, then all questions about the mechanism

can be answered (thermodynamics and kinetics) 172 Equilibrium Constants

Equilibrium constants (Keq) indicate thermodynamically whether the reaction is favored in the forward or reverse direction and the magnitude of this preference

A B C D ΔG

Keq = ([C][D]) / ([A][B]) = ([products]) /([starting material])

Reaction Coordinate

173 Gibb’s Free Energy

The Keq is used to determine the Gibb’s free energy

ΔG = (free energy of products) – (free energy of starting materials)

If we use standard free energy then ΔG˚ (25˚C and 1 atm)

(-ΔG˚/RT) Keq = e

or

ΔG˚ = -RT(ln Keq) = -2.303 RT(log10 Keq)

A favored reaction thus has a negative value of ΔG˚ (energy is released)

174 Contributions to Free Energy

ΔG˚ = ΔH˚ -TΔS˚

The free energy term has two contributions: enthalpy and entropy

Enthalpy (ΔH˚): heat of a reaction (due to bond strength) Exothermic reaction: heat is given off by the reaction (-ΔG˚) Endothermic reaction: heat is consumed by the reaction (+ΔG˚)

Entropy (ΔS˚): a measure of the freedom of motion - Reactions (and nature) always prefer more freedom of motion

Organic reactions are usually controlled by the enthalpy

175 Bond Dissociation Energies

The free energy of organic reactions is often controlled by the enthalpic term

-The enthalpic term in organic reactions is often controlled by the energy of the bonds being formed minus the energy of the bonds being broken

The energies of bonds is called the Bond Dissociation Energy

Many types of bonds have been recorded (both experimentally and computationally) we can therefore predict the equilibrium of a reaction by knowing these BDE’s

176 Kinetics

A second important feature is the RATE of a reaction

The rate is not determined by Keq, Ea But instead by the energy of activation (Ea)

ΔG

Knowing the Ea of a reaction tells us how fast a reaction will occur

Rate therefore depends on the structure of the transition state along the rate determining step Reaction Coordinate

While both the thermodynamics and kinetics depend on the structure of the starting material, the thermodynamics depends on product structure while rate depends on transition state structure 177 Rate Equation

The rate of a reaction can be written in an equation that relates the rate to the concentration of various reactants

A B C D

a b Rate = kr [A] [B]

The exponents are determined by the number of species involved for the reaction step - The exponents also indicate the “order” of the reaction with respect to A and B

Overall order of the reaction is a summation of the order for each individual reactant

178 Arrhenius Equation

Referring back to our energy diagram the rate can be related

to the energy of activation (Ea)

(-Ea/RT) kr = Ae

Intercept = ln A Slope = -Ea/R

ln kobs

1/T A is the Arrhenius “preexponential” factor

Ea is the minimum kinetic energy required to cause the reaction to proceed As a general guide, the rate of a reaction generally will double every ~10˚C increase in temperature (as the temperature of a reaction increases, there are more molecules with the minimum energy required to cause a reaction to occur) 179 Transition State Theory

The Arrhenius equation is an empirical fit to observed data

In an attempt to correlate the rate characteristics (which are not known exactly, primarily due to the structure of the transition state is not determined exactly) to the well established thermodynamic equations (Gibb’s equation is an exact equation) transition state theory was developed

ΔG‡

ΔG

Reaction Coordinate

Instead of calling the energy barrier as an “energy of activation” (Ea), the barrier will be called the ΔG‡ 180 Transition State Theory

Consider a reversible unimolecular reaction

k1 A B k-1

If A goes to B it passes a transition state A‡, once reaction reaches A‡ it can either return to A or proceed to product B

A A‡ B

An equilibrium constant for the transition state versus the starting material can be written

A‡ K‡ = A

The equations can be solved in a similar method as Gibb’s for the equilibrium to obtain:

‡ k1 = (ĸT/h) e (-ΔG /RT) Eyring equation

‡ ‡ k1 = (ĸT/h) e (-ΔH /RT) e (ΔS /R) 181 Thermochemistry

The Arrhenius and Eyring equations appear quite similar

(-Ea/RT) kr = Ae ‡ ‡ k1 = (ĸT/h) e (-ΔH /RT) e (ΔS /R)

Intercept = ln A Slope = -E /R a Arrhenius plot ln kobs

1/T Intercept = ln (ĸ/h) + ΔS‡/R Slope = -ΔH‡/R Eyring plot ln k/T

Due to differences: ‡ 1/T Ea = ΔH + RT

182 Thermochemistry

While the Arrhenius and Eyring equations are widely used to determine ‡ either energy of activation (Ea) or ΔH for reactions, they are both merely empirical equations that are not quantum mechanically correct

Main problem is that unlike Gibb’s equation where the points of the starting materials and products along the reaction coordinate are stable structures, the transition state is a high energy point along the coordinate

The equations consider the pathway to the transition state as isolated from other pathways (and the subsequent pathway to the product) while in reality the pathways are linked

While it is convenient to draw a reaction coordinate as a one-dimensional curve, the actual surface is multidimensional

Reaction Coordinate Reaction Coordinate 183 Thermochemistry

One consequence of this trajectory along a multidimensional surface has been proposed by Carpenter as a “conservation of momentum”

Consider a reaction that generates a diradical intermediate that can continue to generate two equal energy products

D D retention D D H D N ! D H H N H D H H D H inversion H

By symmetry these two potential energy barriers are identical, therefore the rate of inversion product must be identical to rate of retention product

Experimentally determine that ki/kr = 5.0

T.H. Peterson, B.K. Carpenter, J. Am. Chem. Soc., 1992, 114, 766-767 184 Thermochemistry

In order to predict the equilibrium for a reaction need to know the relative energies of starting material and product

Since starting materials and products are stable structures, the energies can be accurately determined either experimentally or computationally

In a molecular mechanics calculation, the energy is predicted by comparison to known compounds already included in the database

Another way to determine the energy is similar to a molecular mechanics calculation, but use group additives to estimate the energy

In this approach, a group in one molecule will be identical in energy to the same group in another molecule For n-Butane: H H CH Have two groups with a C-(C)(H)3 H C 3 3 Have two groups with a C-(C) (H) H H 2 2 Add the value of these groups to determine enthalpy of butane 185 Thermochemistry

These groups values were initially tabulated by a chemist, Sidney William Benson (and are called Benson group equivalents)

Group ΔH˚298 Group ΔH˚298 (kcal/mol) (kcal/mol)

C-(C)(H)3 -10.20 Cd-(CB)(C) 8.64

C-(C)2(H)2 -4.93 C-(CB)(C)(H)2 -4.86

C-(C)3(H)1 -1.90 C-(CB)(C)2(H) -0.98

C-(C)4 0.50 Ct-(H) 26.93

Cd-(H)2 6.26 Ct-(C) 27.55

Cd-(C)(H) 8.59 Ct-(Cd) 29.20

Cd-(C)2 10.34 CB-(H) 3.30

Cd-(Cd)(H) 6.78 CB-(C) 5.51

Cd-(Cd)(C) 8.88 CB-(Cd) 5.68

Cd-(CB)(H) 6.78

S.W. Benson, F.R. Cruickshank, D.. Golden, G.R. Haugen, H.E. O’Neal, A.S. Rodgers, R. Shaw, R. Walsh, Chem. Rev., 1969, 69, 279-324 186 Thermochemistry

Using these values, the enthalpy for any hydrocarbon can be determined

For n-Butane: H H CH3 Have two groups with a C-(C)(H)3 H3C H H Have two groups with a C-(C)2(H)2 Add the value of these groups to determine enthalpy of butane

ΔH˚ = 2(-10.20) + 2(-4.93) = -30.26 kcal/mol Experimentally determined value is -30.15 kcal/mol

For Benzene:

Have six groups of CB-(H)

ΔH˚ = 6(3.30) = 19.80 kcal/mol Experimentally determined value is 19.82 kcal/mol 187 Thermochemistry Compare the energy calculated for two structural isomers CH3 CH3 CH3

CH3

4 CB-(H) 4(3.30) 4(3.30)

2 CB-(C) 2(5.51) 2(5.51)

2 C-(CB)(H)3 2(-10.20) 2(-10.20) ortho correction 0.57 4.39 kcal/mol 3.82 kcal/mol Values would be identical, how to account for steric strain? Need to apply corrections

Group ΔH˚298 Ring ΔH˚298 gauche 0.80 cyclopropane 27.6 cis 1.00 cyclobutane 26.2 ortho 0.57 cyclopentane 6.3 cis (1=tbutyl) 4.00 cyclohexane 0 cycloheptane 6.4 188 Thermochemistry

H H

H3C CH2CH3

2 C-(C)(H)3 2(-10.20)

2 Cd-(C)(H) 2(8.59)

1 C-(C)2(H)2 -4.93 -8.15 kcal/mol Value for trans isomer cis correction 1.00 -7.15 kcal/mol Value for cis isomer

Can therefore calculate the ΔH value for any hydrocarbon by adding the appropriate steric corrections (E/Z, ortho in aromatic, or ring effects)

There are also Benson group tables for oxygen, sulfur, nitrogen, and halogen containing compounds

189 Thermochemistry

We can therefore determine, or predict, energy of stable compounds (and thus predict the thermodynamics of a reaction) *How do we determine energy of transition states?

Transition state energies are directly related to the rates of reactions

Transition states only have a transitory existance and by definition they cannot be isolated

Reaction Coordinate 190 Hammond Postulate

The rate of a reaction is dependent upon the energy difference between the starting material and transition state in the rate determining step

While the structure of the starting material and products can be determined, the structure of the transition state is difficult to determine experimentally because it is at an energy maximum and cannot be isolated

As an aide in predicting rates, a generalization was made that is now referred to as the “Hammond Postulate” In an ENDOTHERMIC reaction, the transition state is closer to the PRODUCTS in energy and structure. In an EXOTHERMIC reaction, the transition state is closer to the REACTANTS in energy and structure

Reaction Coordinate Reaction Coordinate Endothermic reaction, transition state Exothermic reaction, transition state structure resembles product structure resembles starting material 191 Hammond Postulate

Increasing radical character

CH2 H3C

H3C CH3 CH3

H3C CH3

Reaction Coordinate

Another consequence of the Hammond postulate is how the transition state character changes when modifications of a reaction occur

Consider a reaction that generates a radical intermediate during the reaction

A 3˚ radical is more stable than a 2˚ radical which is more stable than a 1˚ radical Due to the 1˚ radical intermediate being more endothermic than the 2˚ or 3˚ radical, the transition state will more closely resemble the intermediate (therefore more radical character) 192 Curtin-Hammett Principle

Consider a reaction that equilibrates between two low energy states (often two conformers), and each can react to a different product

1‡ 2‡

state 1 state 2 product 1 Product 2

Reaction Coordinate

The Curtin-Hammett principle states that the only thing that determines the ratio of products 1 & 2 is the energy of activation difference (1‡ versus 2‡)

The ratio of states 1 and 2 do not influence formation of P1 or P2 (which is more stable does not affect which product is obtained, the more stable transition state is important) 193 Curtin-Hammett Principle

Consider an E2 reaction with a 2˚ alkyl bromide H CH H CH CH base 3 3 Ph 3 Br Ph H H Ph

Whether the E or Z isomer is favored is not due to energy difference of conformers H More sterics H

H CH3 H Ph H CH3 Ph H Difference in energy for Br transition states is Br important

H H H CH H CH 3 3 Difference in energy of H Ph Ph H reactive conformers is Br Br not important

Reaction Coordinate 194 Kinetic versus Thermodynamic Control What forms faster (kinetic product) and what is more stable (thermodynamic product) need not be the same

Consider the addition to conjugated dienes (as example react with H+/H2O)

H2O!+ Reaction at 2˚ cation site has a more stable transition state !+

H2O!+ E

H+ !+ OH

Generate allylic cation in first step Allylic cation can have water react at two sites OH Reaction at 2˚ site Reaction a 1˚ site, though, Reaction at 1˚ site generates more stable product (more substituted double bond) Thus the kinetic product has The thermodynamic product has water reacting at 2˚ site water reacting at 1˚ site 195