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?

Information we want to know:

How much heat is generated?

How fast is the reaction?

Are any intermediates generated?

(What is the THERMODYNAMICS of the reaction?)

(What is the KINETICS of the reaction?)

(What is the reaction mechanism?)

CH3ONa CH3Cl CH3OCH3 NaCl

171  

All of this information is included in an Energy Diagram

Potential energy

Reaction Coordinate

Potential energy

Reaction Coordinate

Possible Mechanism 1 Possible Mechanism 2

Starting material

Starting material Products

Products

Transition states

Transition states

Intermediate

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

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

ΔG

Reaction Coordinate

A B C D

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)

Keq = e(-ΔG˚/RT)

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, But instead by the energy of activation

(Ea)

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

Ea

Reaction Coordinate

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

ΔG

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

Rate = kr [A]a[B]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

A B C D

178  

Arrhenius Equation

Referring back to our energy diagram the rate can be related to the energy of activation (Ea)

kr = Ae(-Ea/RT)

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)

1/T

ln kobs

Slope = -Ea/R Intercept = ln A

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‡

Reaction Coordinate

ΔG

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

A Bk1

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

K‡A‡

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

kr = Ae(-Ea/RT)

1/T

ln kobs

Slope = -Ea/R Intercept = ln A

k1 = (ĸT/h) e (-ΔH‡/RT) e (ΔS‡/R)

1/T

ln k/T Slope = -ΔH‡/R

Intercept = ln (ĸ/h) + ΔS‡/R

Arrhenius plot

Eyring plot

Due to differences: 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

NND

D

HH

!

HH

DD

HH

DD

HH

DD

inversion

retention

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

H3CCH3

H H

H H

For n-Butane:

Have two groups with a C-(C)(H)3

Have two groups with a C-(C)2(H)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    (kcal/mol)  

Group   ΔH˚298    (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

H3CCH3

H H

H H

For n-Butane: Have two groups with a C-(C)(H)3

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

CH3CH3

CH34 CB-(H) 2 CB-(C)

2 C-(CB)(H)3

4(3.30) 4(3.30) 2(5.51) 2(5.51)

2(-10.20) 2(-10.20)

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

0.57 4.39 3.82

ortho correction kcal/mol kcal/mol

188  

Thermochemistry

H H

H3C CH2CH3

2 C-(C)(H)3

2 Cd-(C)(H) 1 C-(C)2(H)2

2(-10.20) 2(8.59) -4.93 -8.15 1.00 cis correction -7.15

Value for trans 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

kcal/mol

kcal/mol Value for cis isomer

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

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

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”

Reaction Coordinate Reaction Coordinate

Endothermic reaction, transition state structure resembles product

Exothermic reaction, transition state structure resembles starting material 191  

Hammond Postulate

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

H3C CH3

CH3H3C CH3

H3CCH2

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)

Increasing 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

state 1 state 2

1‡"

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

Reaction Coordinate

Consider an E2 reaction with a 2˚ alkyl bromide

PhBr

CH3 base

HPh

CH3H

PhH

CH3H

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

Br

H CH3H

PhHBr

H CH3H

HPh

Br

H CH3

H

PhH

Br

H CH3

H

HPh

Difference in energy of reactive conformers is

not important

Difference in energy for transition states is

important

More sterics

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Kinetic versus Thermodynamic Control What forms faster (kinetic product) and what is more stable (thermodynamic product)

need not be the same

H+

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

Generate allylic cation in first step Allylic cation can have water react at two sites

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

!+

!+H2O

H2O

!+

!+

Thus the kinetic product has water reacting at 2˚ site

OH

OH

Reaction a 1˚ site, though, generates more stable product

(more substituted double bond)

The thermodynamic product has water reacting at 1˚ site

E

Reaction at 2˚ site Reaction at 1˚ site

195