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
states
Transition
states
Potential
energy
Intermediate
Potential
energy
Starting
material
Products
Reaction Coordinate
Starting
material
Products
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)
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)
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 177 while rate depends on transition state structure
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
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
178 Arrhenius Equation
Referring back to our energy diagram the rate can be related
to the energy of activation (Ea)
kr = Ae(-Ea/RT)
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
k-1
B
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)
k1 = (ĸT/h) e (-ΔH‡/RT) e (ΔS‡/R)
Eyring equation
181 Thermochemistry
The Arrhenius and Eyring equations appear quite similar
kr = Ae(-Ea/RT)
k1 = (ĸT/h) e (-ΔH‡/RT) e (ΔS‡/R)
Intercept = ln A
Slope = -Ea/R
ln kobs
Arrhenius plot
1/T
Intercept = ln (ĸ/h) + ΔS‡/R
Slope = -ΔH‡/R
ln k/T
1/T
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
D
D
D
D
H
H
N
N
!
H
D
D
H
H
retention
H
D
D
H
H
inversion
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
H3C
CH3
H H
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
For n-Butane:
H H
H3C
CH3
H H
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
CH3
CH3
CH3
4 CB-(H)
4(3.30)
2 CB-(C)
4(3.30)
2(5.51)
2 C-(CB)(H)3
2(-10.20)
2(-10.20)
ortho correction
0.57
2(5.51)
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
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
ΔH˚298
188 Thermochemistry
H
H3 C
H
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
Endothermic reaction, transition state
structure resembles product
Reaction Coordinate
Exothermic reaction, transition state
structure resembles starting material
191 Hammond Postulate
Increasing radical character
H3 C
CH2
H3 C
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
product 1
state 2
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
CH3
Ph
base
Br
H
Ph
CH3
H
CH3
H
H
Ph
Whether the E or Z isomer is favored is not due to energy difference of conformers
H
H
More sterics
CH3
Ph
H
H
CH3
H
H
Ph
Br
Br
H
H
H
CH3 H
CH3
H
Ph Ph
H
Br
Difference in energy for
transition states is
important
Br
Reaction Coordinate
Difference in energy of
reactive conformers is
not important
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+
!+
Generate allylic cation in first step
Allylic cation can have water react at two sites
Reaction at 2˚ site
Reaction at 1˚ site
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
195