Thermodynamics, reaction coordinate diagram, Gibbs free-energy change, exergonic reaction, endergonic reaction, exothermic reaction, endothermic reaction, enthalpy, Entropy, Solvation | Organic Chemistry
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Thermodynamics and Kinetics

Before we can understand the energy changes that take place in a reaction such as the addition of HBr to an alkene, we must have an understanding of thermodynamics, which describes a reaction at equilibrium, and an appreciation of kinetics, which deals with the rates of chemical reactions. If we consider a reaction in which Y is converted to Z, the thermodynamics of the reaction tells us the relative amounts of Y and Z that are present when the reaction has reached equilibrium, whereas the kinetics of the reaction tells us how fast Y is converted into Z.
Y is converted into Z

Reaction Coordinate Diagrams
The mechanism of a reaction describes the various steps that are believed to occur as reactants are converted into products. A reaction coordinate diagram shows the energy changes that take place in each of the steps of the mechanism. In a reaction coordinate diagram, the total energy of all species is plotted against the progress of the reaction. A reaction progresses from left to right as written in the chemical equation, so the energy of the reactants is plotted on the left-hand side of the x-axis and the energy of the products is plotted on the right-hand side. A typical reaction coordinate diagram is shown in Figure 3.2. The diagram describes the reaction of A—B with C to form A and B—C. Remember that the more stable the species, the lower is its energy.

As the reactants are converted into products, the reaction passes through a maximum energy state called a transition state. The structure of the transition state lies somewhere between the structure of the reactants and the structure of the products. Bonds that break and bonds that form, as reactants are converted to products, are partially broken and partially formed in the transition state. Dashed lines are used to show partially broken or partially formed bonds.
a reaction coordinate diagram

Thermodynamics
The field of chemistry that describes the properties of a system at equilibrium is called thermodynamics. The relative concentrations of reactants and products at equilibrium can be expressed numerically as an equilibrium constant, Keq (Section 1.17). For example, in a reaction in which m moles of A react with n moles of B to form s moles of C and t moles of D, Keq is equal to the relative concentrations of products and reactants at equilibrium.
relative concentrations of products and reactants at equilibrium
The relative concentrations of products and reactants at equilibrium depend on their relative stabilities: The more stable the compound, the greater is its concentration at equilibrium. Thus, if the products are more stable (have a lower free energy) than the reactants (Figure 3.3a), there will be a higher concentration of products than reactants at equilibrium, and Keq will be greater than 1. On the other hand, if the reactants are more stable than the products (Figure 3.3b), there will be a higher concentration of reactants than products at equilibrium, and Keq will be less than 1.
Several thermodynamic parameters are used to describe a reaction. The difference between the free energy of the products and the free energy of the reactants under standard conditions is called the Gibbs free-energy change ( ∆G° ) The symbol ° indicates standard conditions—all species at a concentration of 1 M, a temperature of 25 C°, and a pressure of 1 atm.
Gibbs free-energy change
From this equation, we can see that ∆G° will be negative if the products have a lower free energy—are more stable—than the reactants. In other words, the reaction will release more energy than it will consume. It will be an exergonic reaction (Figure 3.3a).
exergonic reaction

Figure 3.3 Reaction coordinate diagrams for (a) a reaction in which the products are more stable than the reactants (an exergonic reaction) and (b) a reaction in which the products are less stable than the reactants (an endergonic reaction).

If the products have a higher free energy—are less stable—than the reactants, ∆G°will be positive, and the reaction will consume more energy than it will release; it will be an endergonic reaction (Figure 3.3b). (Notice that the terms exergonic and endergonic refer to whether the reaction has a negative ∆G° or a positive ∆G°, respectively. Do not confuse these terms with exothermic and endothermic, which are defined later.) Therefore, whether reactants or products are favored at equilibrium can be indicated either by the equilibrium constant (Keq) or by the change in free energy (∆G°) These two quantities are related by the equation
equilibrium constant-change in free energy equation
Where R is the gas constant ( 1.986 x 10–3 kcal mol–1K–1 , or 8.314 x 10–3 kJ mal–1K–1 , because 1 kcal = 4.184 kJ ) and T is the temperature in degrees Kelvin ( K = °C+273 ; therefore, 25°C = 298 K). (By solving Problem 13, you will see that even a small difference in ∆G° gives rise to a large difference in the relative concentrations of products and reactants.)

The Gibbs standard free-energy change (∆G°) has an enthalpy (∆H°) component and an entropy (∆S°) component:

The enthalpy term (∆H°)is the heat given off or the heat consumed during the course of a reaction. Atoms are held together by bonds. Heat is given off when bonds are formed, and heat is consumed when bonds are broken. Thus, ∆H°is a measure of the bond-making and bond-breaking processes that occur as reactants are converted into products.

If the bonds that are formed in a reaction are stronger than the bonds that are broken, more energy will be released as a result of bond formation than will be consumed in the bond-breaking process, and ∆H° will be negative. A reaction with a negative ∆H° is called an exothermic reaction. If the bonds that are formed are weaker than those that are broken, ∆H° will be positive. A reaction with a positive ∆H° is called an endothermic reaction.
Entropy (∆S°) is defined as the degree of disorder. It is a measure of the freedom of motion of the system. Restricting the freedom of motion of a molecule decreases its entropy. For example, in a reaction in which two molecules come together to form a single molecule, the entropy in the product will be less than the entropy in the reactants because two individual molecules can move in ways that are not possible when the two are bound together in a single molecule. In such a reaction, ∆S° will be negative. In a reaction in which a single molecule is cleaved into two separate molecules, the products will have greater freedom of motion than the reactant, and ∆S° will be positive.


A reaction with a negative ∆G° has a favourable (Keq >1 ) equilibrium constant; that is, the reaction is favored as written from left to right because the products are more stable than the reactants. If you examine the expression for the Gibbs standard free-energy change, you will find that negative values of ∆H° and positive values of ∆S° contribute to make ∆G°negative. In other words, the formation of products with stronger bonds and with greater freedom of motion causes ∆G° to be negative.



Values of ∆H° are relatively easy to calculate, so organic chemists frequently evaluate reactions only in terms of that quantity. However, you can ignore the entropy term only if the reaction involves only a small change in entropy, because then the T∆S° term will be small and the value of ∆H° will be very close to the value of ∆G°. Ignoring the entropy term can be a dangerous practice, however, because many organic reactions occur with a significant change in entropy or occur at high temperatures and so have significant T∆S° terms. It is permissible to use ∆H° values to approximate whether a reaction occurs with a favorable equilibrium constant, but if a precise answer is needed, ∆G° values must be used. When ∆G° values are used to construct reaction coordinate diagrams, the y-axis is free energy; when ∆H° values are used, the y-axis is potential energy.

Values of ∆H° can be calculated from bond dissociation energies (Table 3.1). For example, the ∆H° for the addition of HBr to ethene is calculated as shown here:


Homolytic Bond Dissociation Energies

The bond dissociation energy is indicated by the special term DH° Recall from Section 2.3 that the barrier to rotation about the π bond of ethene is 63 kcal/mol .In other words, it takes 63 kcal/mol to break the π bond.
The value of –20 kcal/mol for ∆H° calculated by subtracting the ∆H° for the bonds being formed from the ∆H° for the bonds being broken—indicates that the addition of HBr to ethene is an exothermic reaction. But does this mean that the ∆G° for the reaction is also negative? In other words, is the reaction exergonic as well as exothermic? Because ∆H° has a significant negative value (–20 kcal/mol), you can assume that ∆G° is also negative. If the value of ∆H° were close to zero, you could no longer assume that ∆H° has the same sign as ∆G°.
Keep in mind that two assumptions are being made when using ∆H° values to predict values of ∆G°. The first is that the entropy change in the reaction is small, causing T∆S° to be close to zero and, therefore, the value of ∆H° to be very close to the value of ∆G°; the second is that the reaction is taking place in the gas phase.
When reactions are carried out in solution, which is the case for the vast majority of organic reactions, the solvent molecules can interact with the reagents and with the products. Polar solvent molecules cluster around a charge (either a full charge or a partial charge) on a reactant or product, so that the negative poles of the solvent molecules surround the positive charge and the positive poles of the solvent molecules surround the negative charge. The interaction between a solvent and a species (a molecule or ion) in solution is called solvation.
Solvation by water
Solvation can have a large effect on both the ∆H° and the ∆S° of a reaction. For example, in a reaction in which a polar reagent is solvated, the ∆H° for breaking the dipole–dipole interactions between the solvent and the reagent has to be taken into account, and in a reaction in which a polar product is solvated, the ∆H° for forming the dipole–dipole interactions between the solvent and the product has to be taken into account. In addition, solvation of a polar reagent or a polar product by a polar solvent can greatly reduce the freedom of motion of the solvent molecules, and this will affect the value of ∆S°.

Next Topic : Kinetics
Next Chapter : Reactions of Alkenes
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