Thermodynamic and Kinetic Control

Difference between Thermodynamics and Kinetics

What is the difference between kinetics and thermodynamics?1. Kinetics relates to the rate of a given reaction.2. Thermodynamics is concerned with the stability of reactants and products.Now we may ask, "Are kinetics and thermodynamics related?" Yes, in many ways, kinetics is related to thermodynamics and vice-versa. To give a brief example, let's consider the following reaction:

$$aA+bB \rightarrow cAB$$

where reactant, A, has stoichiometric constant, a, reactant, B, has stoichiometric constant, b, and product, AB, has stoichiometric constant, c. The stoichiometric coefficient (constant) is the number in front of a chemical species in a balanced equation.

The chemical equilibrium constant, K_eq, is a thermodynamic quantity that is the ratio of the products, raised to the power of the stoichiometric coefficients of the balanced equation, divided by the reactants, raised to the power of the stoichiometric coefficients. Then for the above reaction, the equilibrium constant would be:

On the other hand, the instantaneous rate law for this reaction can be initially modeled by the following kinetic rate law:

$$Rate=\frac{-1}{a}\frac{d[A]}{dt}=\frac{-1}{b}\frac{d[B]}{dt}=\frac{1}{c}\frac{d[AB]}{dt}$$

where the negative sign denotes a decrease in the concentrations of the reactants ([A] and [B]). The changes in the concentrations with time of all components are denoted by the symbol: \(\frac{d[...]}{dt}\).

Thus, we see that formulas for the instantaneous rate law and the equilibrium constant are calculated in terms of the concentrations of the reactants and products and their respective stoichiometric coefficients. However, there is no mathematical formula that directly relates the equilibrium constant, K_eq, for a given reaction and its power rate law.

1. Thermodynamic control versus kinetic control in chemical reactions:

• Kinetic control favors the product in a reaction that has the lowest activation energy, E_a, and that is formed fastest.
• Thermodynamic control favors the most stable product.

Typically, a given chemical reaction will be far from chemical equilibrium over an extended period of time. As a result, the outcome of chemical reactions in the laboratory will be determined by three factors:

• The rate of formation of products.
• The relative stability of the products.
• The reaction conditions (temperature, pressure, concentration, and solvent).

The product mixture for a given experiment can be controlled by adjusting the reaction conditions and manipulating the Gibbs free energy difference, ΔG, as will be discussed in greater detail in the "Transition State Theory" section below.

Dynamic Chemical Equilibrium

• When the rate of the reaction leading to products, the forward reaction, is equal to the rate of reaction leading back to reactants, the reverse reaction, we have a system at chemical equilibrium.
• The rates of reaction for a system at equilibrium are not zero.
• The reaction rates correspond to how fast components change in a dynamic system.

As will be discussed below, although the rates of reaction are not zero for a system at equilibrium, the fact that the concentrations of products and reactants do not change at dynamic chemical equilibrium leads to the notion that the Gibbs free energy difference is equal to zero at equilibrium. Please continue reading for more details about this point.

Transition State Theory

The composition of products and the ratio of products to reactants can vary widely for chemical reactions that have not yet reached equilibrium. The possible outcomes of a given reaction that has not yet reached equilibrium are determined by two main factors:

• The rate of the formation of products (kinetics).
• The relative stability of products (thermodynamics).

Chemists can control the reaction mechanism (thermodynamic versus kinetic) to increase the yield of the desired product. Engineering the mechanism of control (thermodynamic versus kinetic control) for a chemical reaction is essential. The control mechanism will not only affect the desired product yield for a given reaction mixture but will also determine which reaction pathway is taken.

The reaction pathway taken by a chemical reaction is determined by selectivity. In turn, reaction selectivity is determined by the control mechanism through manipulation of the Gibbs free energy difference, ΔG. The reaction selectivity is an effect determined by the molecular mechanism of the reaction.

The Gibbs Free Energy Difference, ΔG, is given by:

Let's consider, for example, a reversible reaction in which we have reactant, A, and product, B.

$$A \leftrightarrows B$$

Calculating the Gibbs free energy difference for this reversible reaction, we might find that the free energy difference is less than zero, ΔG < 0. In this case, we shall say that the reaction will occur "spontaneously." On the other hand, if we find that the free energy difference for this reaction is greater than zero, ΔG > 0, we shall say that the reaction is "non-spontaneous." This characterization of a reversible reaction as either spontaneous or non-spontaneous is relevant in the following ways:

1. A spontaneous reaction is when the reactants are at a higher free energy level than the products. A spontaneous (thermodynamically favorable) reaction will eventually occur without the input of external energy from the surroundings.

2. A non-spontaneous reaction is when the reactants are at a lower free energy level than the products. A non-spontaneous (thermodynamically unfavorable) reaction can occur only with the input of external energy from the surroundings.

Graphically, this situation for a spontaneous reversible reaction can be depicted in the following way:

Figure 1: Gibbs free energy difference graph. Note that the energy of activation is E_a.

From the above pair of graphs, we notice that the forward reaction, in this case, has a free energy difference that is negative, -ΔG, and thus spontaneous (thermodynamically favored). Also, we note that the free energy for the reactants is greater than the free energy for the products. For the reverse reaction, the free energy difference is positive, +ΔG, and thus is non-spontaneous (not thermodynamically favored) and would need energy input from the surroundings to proceed. In both cases, the absolute value of the Gibbs free energy difference has the same magnitude.

The kinetic barrier for a spontaneous or non-spontaneous reaction is the energy of activation, E_a :

• The activation energy is the minimum quantity of energy that the reactants must have to go to products, E_a.
• Most reactions require the input of energy from the surroundings to form an unstable, high-energy intermediate chemical species called the transition state.
• A reaction pathway with lower activation energy will yield a thermodynamically favorable kinetic product.

For example, consider a reaction in which two products, B + C, form from one reactant, A.

$$A \leftrightarrows B+C$$

Furthermore, let's assume that product, C, is more thermodynamically stable than product, B. In addition, let's assume that product, B, forms faster than product, C, making product, B, the kinetically favored product. This situation can be depicted graphically as follows:

From the graph, we can see that:

Figure 2: Thermodynamic versus kinetic control.

• Product, B, is the kinetic product and has lower activation energy, E_{a, B}. Product, B, is under kinetic control.
• Product, B, is the non-spontaneous product (thermodynamically unfavored) and requires an input of external energy from the surroundings for its formation.
• Product, C, is the thermodynamic product with higher activation energy, E_{a, C}. Product, C, is under thermodynamic control.
• Product, C, is the spontaneous product (thermodynamically favored) and requires no external energy input from the surroundings for its eventual formation.

Thus, product, C, is the thermodynamic product and is favored when the reaction system is under thermodynamic control ( i.e., the reaction is given enough time to reach thermodynamic equilibrium).

On the other hand, product, B, is the kinetic product. It is favored when the reaction is under kinetic control, i.e., adjustments to the reaction conditions (temperature, pressure, concentration, and solvent) can be utilized to affect the formation of product, B.

Note that the engineering of the control mechanism (thermodynamic versus kinetic control) will only be possible for those reactions that display differences in the activation energy, E_a, for different reaction pathways leading to different products.

Lastly, we note that when a system has reached equilibrium, the products have the greatest thermodynamic stability and the Gibbs free energy difference is zero, ΔG = 0.

Thermodynamic and Kinetics Requirements of a Reaction

What are kinetic and thermodynamic factors?

• The relative stability of the final products is the main thermodynamic factor in a chemical reaction.
• The reaction rate is the main kinetic factor and strongly affects the reaction conditions (temperature, pressure, concentration, and solvent).

Kinetic and Thermodynamic Products

Is the thermodynamic or kinetic product more stable?

• The thermodynamic product is usually more stable than a given kinetic product. However, if the stability of the kinetic product is equivalent to the thermodynamic product, then both products are the same.

Thermodynamic and Kinetic Stability

What is thermodynamic and kinetic stability?

• Thermodynamic stability is the stability of the lowest energy product, also called the thermodynamic product.
• Kinetic stability refers to the energy, or stability, of the highest energy state, or transition state, for a chemical reaction.

Kinetic Control and Thermodynamic Control

Finally, we note that thermodynamic control versus kinetic control in chemical reactions is characterized by the following:

• Kinetic control favors the product in a reaction that has the lowest activation energy, E_a, and that is formed fastest.
• Thermodynamic control favors the most stable product.