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Thermodynamic and Kinetic Control

Have you ever wondered how energy is used by your body to maintain its living state? It turns out that energy in your body is converted to useful work. This form of useful work is called Gibbs Free Energy.

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# Thermodynamic and Kinetic Control

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Nie wieder prokastinieren mit unseren Lernerinnerungen. Have you ever wondered how energy is used by your body to maintain its living state? It turns out that energy in your body is converted to useful work. This form of useful work is called Gibbs Free Energy.

The second law of thermodynamics measures the ability of a thermodynamic system to do useful work. We will discuss applications of the Gibbs Free Energy difference equation, which measures a system's Free Energy or ability to do useful work. We will also concentrate on applying the Gibbs Free Energy difference to the engineering of thermodynamic and kinetic control over Chemical Reactions.

• First, we will see the difference between Thermodynamics and Kinetics - Here we will go over reaction rate dynamic Chemical Equilibrium, and transition state theory.
• Then, the thermodynamics and Kinetic requirements of a Reaction - Here we go over the kinetic product and the thermodynamics product.
• After that, we will study the kinetic and Thermodynamic Products - Here we ask when both products are equivalent.
• Next, we will analyse the thermodynamic and Kinetic Stability - Here we discuss which is the more stable.
• We will finish with the kinetic Control and Thermodynamic Control - Here we review the results of the previous sections.

## 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, Keq, 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:

$$K_{eq}=\frac{[AB]^c}{[A]^a[B]^b}$$

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, Keq, for a given reaction and its power rate law.

Power Rate Law - a rate law whose mathematical formulation contains only the concentrations of reactants raised to numerical power (exponent). The power to which the reactant Concentration is raised is called the reaction order. For example, consider the following hypothetical reaction:

$$a[A]+b[B] \rightarrow c[AB]$$

The power rate law might then be given by:

$$rate=k[A]^x[B]^y$$

where the Rate Constant is, k, and the reaction orders, x and y, may have no relation to the stoichiometric coefficients, a and b, of the balanced equation.

In order to demonstrate further the above idea, let's consider a chemical reaction for which the power rate law is known. The reaction of Nitrogen dioxide with Carbon monoxide is:$$1NO_2\,(g)+1CO\,(g) \rightarrow 1NO\,(g)+1CO_2\,(g)$$The corresponding power rate law for this reaction is:$$rate=k[NO_2]^2[CO]^0$$
Notice, the stoichiometric coefficients, a = 1 and b = 1, are not related to the reaction orders, x = 2 and y = 0.

Thermodynamic Control is the product's relative stability determines the reaction's product ratio.

Kinetic Control is the rate at which products are produced determines the product ratio for the reaction.

Activation Energy is the minimum amount of energy, Ea, the reactants must have to go to products.

1. Thermodynamic control versus kinetic control in Chemical Reactions:

• Kinetic control favors the product in a reaction that has the lowest Activation Energy, Ea, 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

A reversible Reaction is a reaction in which products turn back into reactants at an appreciable rate

In what follows, we will refer to dynamic chemical equilibrium as just equilibrium. When a reaction is reversible, and there is no change in the concentrations of reactants and products, we have reached the equilibrium state.
• 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.
Ultimately, when the reaction system reaches chemical equilibrium, there is no change in the concentrations of products and reactants. However, one must remember that chemical bonds in the molecules of a system at equilibrium are dynamic and will be continuously forming, breaking, and reforming.

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

A kinetic Barrier is the height of the potential barrier (also known as the energy barrier) that separates the initial (reactant) and final (product) states in a Potential Energy Diagram.

Transition State - as we move along the reaction coordinate, it's the state that corresponds to the coordinate with the maximum potential energy.

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:

$$\Delta{G}=\Delta{H}-T\Delta{S}$$

Where ΔH is the enthalpy difference, T is the temperature, and ΔS is the entropy difference.

• The enthalpy, H, is the potential energy contained within a chemical bond. The enthalpy difference, ΔH, is the difference in potential bond energy between reactants and products.
• Entropy, S, is associated with the disorder of a chemical state.

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 Ea.

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, Ea :

• The activation energy is the minimum quantity of energy that the reactants must have to go to products, Ea.
• 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, Ea, 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, Ea, 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, Ea, 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, Ea, and that is formed fastest.
• Thermodynamic control favors the most stable product.

## Thermodynamic and Kinetic Control - Key takeaways

• Kinetic control favors the product in a reaction that has the lowest activation energy, Ea, and that is formed fastest.
• Thermodynamic control favors the most stable product.
• 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).
• If the free energy difference is negative, -ΔG, the reaction is thermodynamically favored.
• If the free energy difference is positive, +ΔG, the reaction is not thermodynamically favored and would need energy input from the surroundings to proceed.
• When a system has reached chemical equilibrium, the products have the greatest thermodynamic stability, and the Gibbs free energy difference is equal to zero, ΔG = 0.

## Thermodynamic and Kinetic Control Quiz - Teste dein Wissen

Question

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.

Show question

Question

Are kinetics and thermodynamics related?

Yes, he rate law of a reaction and the equilibrium constant for a reaction are both calculated in terms of the concentrations of the reactants and products and their respective stoichiometric coefficients.

Show question

Question

What is Thermodynamic Control?

The relative stability of the products determines the product ratio for the reaction.

Show question

Question

What is Kinetic Control?

The rate at which products are produced determines the product ratio for the reaction.

Show question

Question

What is the Equilibrium Constant?

The ratio of the concentration of products over reactants in a reaction mixture that has reached chemical equilibrium.

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Question

What is the reaction rate?

The reaction rate is the speed at which a chemical reaction occurs.

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Question

What is a reversible reaction?

A reaction in which products turn back into reactants at an appreciable rate

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Question

What is 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

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Question

What is the kinetic barrier?

The height of the potential barrier (also known as the energy barrier) that separates the initial (reactant) and final (product) states in a graph of the potential energy surface.

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Question

What is the activation energy?

the minimum quantity of energy, Ea , that the reactants must have in order to go to products.

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Question

What is the transition state?

As we move along the reaction coordinate, it's the state that corresponds to the coordinate with the maximum potential energy.

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Question

What is the kinetic product?

In a chemical reaction, it is the product that forms fastest.

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Question

What is the thermodynamic product?

In a chemical reaction, it is the most stable product formed.

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Question

The possible outcomes of a given reaction that has not yet reached equilibrium is determined by what two main factors?

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

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Flashcards in Thermodynamic and Kinetic Control14

Start learning

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.

Are kinetics and thermodynamics related?

Yes, he rate law of a reaction and the equilibrium constant for a reaction are both calculated in terms of the concentrations of the reactants and products and their respective stoichiometric coefficients.

What is Thermodynamic Control?

The relative stability of the products determines the product ratio for the reaction.

What is Kinetic Control?

The rate at which products are produced determines the product ratio for the reaction.

What is the Equilibrium Constant?

The ratio of the concentration of products over reactants in a reaction mixture that has reached chemical equilibrium.

What is the reaction rate?

The reaction rate is the speed at which a chemical reaction occurs.

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