Breaking News

Thermodynamics in Organic Chemistry




For a reaction to be practical, the equilibrium must favor the products, and the reaction rate must be fast enough to form them in a reasonable time. These two conditions depend on the thermodynamics and the kinetics of a reaction, respectively.

Thermodynamics describes energy and equilibrium. How do the energies of the reactants and the products compare? What are the relative amounts of reactants and products at equilibrium?

Kinetics describes reaction rates. How fast are reactants converted to products?.

Equilibrium Constant and Free Energy Changes , ΔG°


The equilibrium constant, Keq , is a mathematical expression that relates the amount of starting material and product at equilibrium.

For example, when starting materials A and B react to form products C and D, the equilibrium constant is given by the following expression:


The size of Keq tells about the position of equilibrium; that is, it expresses whether the starting materials or products predominate once equilibrium has been reached.

(1) When Keq > 1, equilibrium favors the products (C and D) and the equilibrium lies to the right as the equation is written.

(2) When Keq < 1, equilibrium favors the starting materials (A and B) and the equilibrium lies to the left as the equation is written.

For a reaction to be useful, the equilibrium must favor the products, and Keq > 1.

What determines whether equilibrium favors the products in a given reaction?
The position of equilibrium is determined by the relative energies of the reactants and products. The free energy of a molecule, also called its Gibbs free energy, is symbolized by G°. The change in free energy between reactants and products, symbolized by ΔG°, determines whether the starting materials or products are favored at equilibrium.

ΔG°, Gibbs free energy,  is the overall energy difference between reactants and products.


Using this expression we can determine the relationship between the equilibrium constant and the free energy change between reactants and products.

(1) When Keq > 1, log Keq is positive, making ΔG° negative, and energy is released. Thus, equilibrium favors the products when the energy of the products is lower than the
energy of the reactants.

(2) When Keq < 1, log Keq is negative, making ΔG° positive, and energy is absorbed. Thus, equilibrium favors the reactants when the energy of the products is higher than the energy of the reactants.

Compounds that are lower in energy have increased stability. Thus, equilibrium favors the
products when they are more stable (lower in energy) than the starting materials of a reaction.


Because ΔG° depends on the logarithm of Keq, a small change in energy corresponds to a large difference in the relative amount of starting material and product at equilibrium. Several values of ΔG° and Keq are given in the following table:


For example, a difference in energy of only ~6 kJ/mol means that there is 10 times as much of the more stable species at equilibrium. A difference in energy of ~18 kJ/mol means that there is essentially only one compound, either starting material or product, at equilibrium.

Conclusion


Conditions Favoring Product Formation:

Energy Changes and Conformational Analysis


These equations can be used for any process with two states in equilibrium.

As an example, monosubstituted cyclohexanes exist as two different chair conformations that rapidly interconvert at room temperature, with the conformation having the substituent in the roomier equatorial position favored. Knowing the energy difference between the two conformations allows us to calculate the amount of each at equilibrium.

For example, the energy difference between the two chair conformations of phenylcyclohexane is –12.1 kJ/mol, as shown in the accompanying equation. Using the values in table above, this corresponds to an equilibrium constant of ~100, meaning that there is approximately 100 times more B (equatorial phenyl group) than A (axial phenyl group) at equilibrium.


Enthalpy and Entropy


The free energy change (ΔG°) depends on the enthalpy change (ΔH°) and the entropy change (ΔS°). ΔH° indicates relative bond strength, but what does ΔS° measure?

Entropy (S°) is a measure of the randomness in a system. The more freedom of motion or the more disorder present, the higher the entropy. Gas molecules move more freely than liquid molecules and are higher in entropy. Cyclic molecules have more restricted bond rotation than similar acyclic molecules and are lower in entropy.

The entropy change (ΔS°) is the change in the amount of disorder between reactants and products. ΔS° is positive (+) when the products are more disordered than the reactants. ΔS° is negative (–) when the products are less disordered (more ordered) than the reactants.

Reactions resulting in an increase in entropy are favored.

ΔG° is related to ΔH° and ΔS° by the following equation:


This equation tells us that the total energy change in a reaction is due to two factors:

(A) The change in the bonding energy


The change in bonding energy can be calculated from bond dissociation energies

(B) The change in disorder (Entropy).


Entropy changes are more difficult to access, but they are important in the following two cases:

(1) When the number of molecules of starting material differs from the number of molecules of product in the balanced chemical equation.

(2) When an acyclic molecule is cyclized to a cyclic one, or a cyclic molecule is converted to an acyclic one.

For example, when a single starting material forms two products, as in the homolytic cleavage of a bond to form two radicals, entropy increases and favors formation of the products. In contrast, entropy decreases when an acyclic compound forms a ring, because a ring has fewer degrees of freedom. In this case, therefore, entropy does not favor formation of the product.


In most other reactions that are not carried out at high temperature, the entropy term (TΔS°) is small compared to the enthalpy term (ΔH°) and it can be neglected. Thus, we will often approximate the overall free energy change of a reaction by the change in the bonding energy only. Keep in mind that this is an approximation, but it gives us a starting point from which to decide if the reaction is energetically favorable.


According to this approximation:

(1) The product is favored in reactions in which DH° is a negative value; that is, the bonds in the product are stronger than the bonds in the starting material.

(2) The starting material is favored in a reaction in which DH° is a positive value; that is, the bonds in the starting material are stronger than the bonds in the product.

Reference: Organic chemistry / T.W. Graham Solomons , Craig B.Fryhle , Scott A.snyder , / ( eleventh edition) / 2014.



No comments