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Thermodynamics vs Kinetics
Overview
A general Reaction Coordinate Diagram relating the energy of a system to its geometry along one possible reaction pathway is given in the figure below. In the figure below, the Activation Energy, Ea is that critical minimum energy in a chemical reaction required by reactants to be converted into products. the quantities, Ea; f and Ea; r are the activation energies for the forward and reverse reactions respectively. The Transition State is that point on the energy surface where the Activated Complex, an unstable species having the highest energy, crosses over from reactants to products.
Reactant
Transition state
Product
Reaction Coordinate
Energy
Ea,f Ea,r
∆EReaction = Ea,f –Ea,r
The rate constant k in a chemical reaction is a kinetic quantity related to the the activation energy through the Arrhenius Equation, k = Ae Ea=RT. The energy difference, ∆EReaction = Ea; f Ea; r, is a thermodynamic quantity related to the Free Energy (∆G), for a chemical reaction:
∆G = ∆EReaction = Ea; f Ea; r
Interpretation of Reaction Coordinate Diagram
The simple reaction coordinate diagram given on the previous page contains a great deal of useful information:
It defines the geometries of reactants, transition state, and products along the reaction coor- dinate.
It provides insight regarding the thermochemistry of the overall chemical reactions. For ex- ample, in the figure below on the left, the products are lower in energy than the reactants leading to an exothermic reaction (∆H < 0 ). On the other hand, if the reaction were en- dothermic (∆H > 0 ) as in the figure below on the right, the products would be higher in energy than the reactants.
Exothermic Reaction Endothermic Reaction
reactant
transition state
product
Exothermic Reaction
Energy
Reaction Coordinate
reactant
transition state
product
Endothermic Reaction
Energy
Reaction Coordinate
Finally, the diagram gives information about the rate of a reaction. The higher the energy of the transition state (corresponding to an increase in activation energy E a ) the slower the reaction is likely to proceed.
SN 2 Reactions
An SN 2 reaction involves the attack of a nucleophile X (e.g. F ; Cl ; OH ) at a tetrahedral carbon site opposite a leaving group Y which leads to inversion at the carbon center, similar to an umbrella that flips inside out as a result of a strong wind. A nucleophile is any species with a large concentration of electron density (e.g. a negatively charged ion) which has a strong affinity for a positively charged center. For example, the carbon–chlorine bond in H 3 C Cl is polarized (Cδ+^ Clδ ) which leads the nucleophile X to attack at the positively charged carbon atom: X ; Cδ+^ Clδ .
X + X - C Y
H
H
H (^) H
- (^) + - H
C - Y
H
The SN 2 reaction in which the attacking nucleophile and leaving group are both Cl can be written as:
Cl + CH 3 Cl! Cl CH 3 Cl! [Cl CH 3 Cl] ‡^! ClCH 3 Cl ! CH 3 Cl + Cl
This is known as a symmetrical or identity reaction since both the reactants (Cl + CH 3 Cl) and products (CH 3 Cl + Cl ) are identical. However, more general reactions involving different attacking and leaving groups form the basis of this reaction. The restriction of having identical attacking and leaving groups was purposefully chosen for one component of the present exercise in order to allow an easier analysis without any loss of the concepts inherent in more general SN 2 reactions. In this exercise we will examine both an identity SN 2 reaction as well as a more general SN 2 reaction. In the reaction above the two species: Cl CH 3 Cl; ClCH 3 Cl are called ion–molecule complexes. They are formed when the anion and the molecule approach each other at distances ( 2 : 5 3 : 5 A˚) where they can interact to produce a stable, weakly-bound aggregate, ion-molecule complex. The forces holding this complex together are mostly coulombic and are very similar to the ionic forces you have discussed in lecture. The geometry of the methyl chloride group in these complexes is similar to that of isolated methyl chloride, and though too weakly interacting to persist in solution, they do exist in the gas phase. The complex [Cl CH 3 Cl] ‡^ is defined as the transition state structure, the highest energy structure on the reaction energy surface, and has a trigonal-bipyramidal geometry similar to Cl PH 3 Cl. Of course, the transition state structure, [Cl CH 3 Cl] ‡^ , is much more unstable than Cl PH 3 Cl because the carbon atom has five bonds (two weak C-Cl bonds and three C-H bonds), but carbon likes to form four bonds. On the other hand, the phosphorus atom is capable of forming stable structures containing five bonds.
Reaction Profile for the Cl + CH3 Cl SN 2 Reaction
Initially, we will focus our attention on the symmetric or identity reaction discussed previously:
Cl + CH 3 Cl! Cl CH 3 Cl! [Cl CH 3 Cl] ‡^! ClCH 3 Cl ! ClCH 3 + Cl
Construct the gas phase Reaction Coordinate Diagram for the Cl + CH 3 Cl SN 2 reaction by
plotting the relative energy in kJ mol ^1 versus Cl| {z + C}
Distance
H 3 Cl. Place the Reaction Coordinate
Diagram on the graph provided below and plot the energies on a relative energy scale. Label the various species along the reaction pathway.
0
5
10
15
20
25
30
35
40
45
50
55
4.0 3.5 3.0 2.5 2.0 1.8 2.0 2.5 3.0 3.5 4.
Relative Energy (kJ/mol)
Cl
+ C
| {z } Distance
H 3 Cl Cl H 3 C + Cl
| {z } Distance
Structure and Bonding in the Cl + CH 3 Cl SN 2 Reaction
Questions
Obtain values of charges for all the atoms in the ion-molecule species Cl CH 3 Cl and place them on the corresponding sketch given previously. Discuss the forces holding to- gether this weak complex. Compare the C Cl bond distance with C-Cl bond distance in CH 3 Cl, and comment on the relative strength of these two bonds.
Discuss the bonding around the central C atom in the [Cl CH 3 Cl] ‡^ transition state. Does the carbon atom prefer to have four or five bonds attached to it? Why doesn’t the carbon atom easily undergo valence-shell expansion similar to the P atom in PCl 5? Predict the structure of the [Cl CH 3 Cl] ‡^ transition state from VSEPR theory and give the Structure Number (SN) about the C atom.
Reaction Profiles for the Br + CH 3 Cl SN 2 Reaction
The following exercises now focus on a more general SN 2 reaction in which the attacking group (Br ) differs from the leaving group (Cl ):
Br + CH 3 Cl! Br CH 3 Cl! [Br CH 3 Cl] ‡^! BrCH 3 Cl ! BrCH 3 + Cl
Construct both gas and solution phase Reaction Coordinate Diagrams for the Br + CH 3 Cl SN 2
reaction by plotting the relative energy in kJ mol ^1 versus Br| {z + C}
Distance
H 3 Cl. Place both reaction
profiles on the same graph provided below, and plot the energies on a relative energy scale. Please be sure to label the various species along the reaction pathway.
0
5
10
15
20
25
30
35
40
45
50
5.0 4.0 3.0 2.0 1.
Relative Energy (kJ/mol)
Br
| {z^ + C}
Distance
H 3 Cl
Analysis of the Br + CH3 Cl SN 2 Reaction
Sketch the structure of the transition state species below providing geometrical parameters including bond distances and bond angles.
[Cl CH 3 Br] ‡ How does the above structure compare to the transition state structure for the identity or symmetric Cl + CH 3 Cl SN 2 reaction: [Cl CH 3 Cl] ‡^? Which structure corresponds more closely to the idealized trigonal bipyramid structure with a carbon atom at the center?
View the animation of the electrostatic potential map for the Br + CH 3 Cl SN 2 reaction by stepping through each frame. Specifically, observe the changes which occur in the elec- trostatic potential map of the iso-density surface from frame to frame and interpret the color shifts. Recall that colors toward red represent excess negative charge while colors toward blue represent excess positive charge. Describe your observations.
Analysis of the Br + CH3 Cl SN 2 Reaction
View the animation of the imaginary frequency for the [Cl CH 3 Br] ‡^ transi- tion state structure. Make a sketch of the movement of each atom by sketching the structure below and draw small vectors next to each atom to designate the direction of movement.
View the animation of the bond density for the Br + CH 3 Cl SN 2 reaction by stepping through each frame. Observe what electron density shifts are taking place, and describe your findings.
From the above observations provide a description of the chemical transformation taking place as the Br ion approaches the CH 3 Cl molecule.
Thermodynamics and Kinetics of the Br ^ + CH 3 Cl SN 2 Reaction
The equilibrium constant (K = (^) [[^ reactantsproducts ]] ) can be related to the Free Energy (∆G) between reactants and products by the equation:
∆G 0 = R T lnK
where R is the gas constant ( 8 :31451 J mol ^1 K ^1 ), and T is the temperature in degrees Kelvin. As was noted earlier, the Free Energy change for a reaction can be given by
∆G = ∆EReaction = Ea; f Ea; r
Calculate the equilibrium constant, K for the SN 2 reaction:
Br (aq) + CH 3 Cl(aq)! Br CH 3 (aq) + Cl (aq)
at 25 0 C and 60 0 C
Is the trend in K derived from your calculations above consistent with what should occur as the temperature is increased? Explain.
Thermodynamics and Kinetics of the Br ^ + CH 3 Cl SN 2 Reaction
The rate can be expressed as a second order equation for the SN 2 reaction:
Br (aq) + CH 3 Cl(aq)! Br CH 3 (aq) + Cl (aq)
rate = k
Br
[CH 3 Cl]
where the rate constant, k at 60^0 C is 6.2 x 10 ^4 L ^1 mol ^1 s ^1.
Calculate the rate constant at 25 0 C using the equation
ln
k 1 k 2
Ea R
T 1
T 2
For the SN 2 reaction in the gas phase
Br (g) + CH 3 Cl(g)! Br CH 3 (g) + Cl (g)
the identical second order rate law given above is followed. However the rate constant k is several orders of magnitude larger giving rise to significantly faster rates for the gas phase.
Give possible reasons why the gas phase reaction rate is faster than that for the solution phase.
Last Revised: 02/02/
