Thermodynamics of Organic Compounds

– In this subject, we will discuss the Thermodynamics of Organic Compounds

Thermodynamics of Organic Compounds

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

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

(2) When K_eq < 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 K_eq > 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 K_eq > 1, log K_eq 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 K_eq < 1, log K_eq 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 K_eq, 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 K_eq 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: Thermodynamics of Organic Compounds

– 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 the 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.

Thermodynamics of Organic Compounds: 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.

The relationship between ΔG° is related to ΔH°

– 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.

– 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 the formation of the product.

– In most other reactions that are not carried out at high temperatures, 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 ΔH° 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 ΔH° 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.