The study of reactions is the essence of much of organic chemistry. To understand reactions, you need to know how they occur, and knowing how they occur involves the study of reaction equilibrium and rate. An equilibrium equation has the following form:
The term equilibrium refers to reversible reactions.
The rate of a reaction is the speed that the concentrations of the reactants change per unit of time—usually stated as moles per liter per second.
A + B C + D
In this reaction, the reactants, A and B, react to form the products, C and D; and, at the same time, the products, C and D, react to form the reactants, A and B. Equilibrium occurs when the rates of these two reactions are equal. An equilibrium is a state in which the forward and reverse reactions are continuous and simultaneous. The thermodynamics of the system determines whether the reactants or products are favored at equilibrium. The position of equilibrium favors the lowest energy state for the system.
Note that equilibrium does not imply an equality of
concentrations of A and B relative to C and D but an equality of rates for the forward and reverse reactions.
A number of factors affect the probability and the rate at which a reaction reaches a favorable equilibrium. The major factor is the mechanism that the reaction follows on its way from the reactants to the products. If the reaction pathway is thermodynamically favorable and if the products have less energy than the reactants, then the reaction can establish a favorable equilibrium. A secondary factor is the structure of the reactants. Other secondary factors are the reaction conditions, such as temperature and reactant concentrations.
These secondary factors affect the rate at which a favorable equilibrium is established.
Organic chemists view an equilibrium as favorable if a
reasonable amount of product is present.
A mechanism is the step-by-step pathway that the reaction follows on its way from reactants to products.
Section 6.5, page 000, begins the discussion of reaction mechanisms.
Chapters 3 and 11 provide the background for predicting reaction rates on the basis of structure.
For a brief look at the effect of reaction conditions, consider the reaction of methane with chlorine:
CH4 + Cl2 CH3Cl + HCl
Although this reaction moves toward a favorable equilibrium, its rate is easily controlled through regulating the reaction conditions. Mixed methane and chlorine gases, stored in the dark at room temperature, have no appreciable reaction even for extended time periods. However, if you either illuminate or heat the flask containing the mixture, a very rapid reaction immediately occurs. With other reactions, the rates at which the reactants attain a favorable equilibrium vary from imperceptibly slow to virtually instantaneous. By understanding these factors, not only can you control the rate of reaction, but you can also gain a better understanding of what happens—that is, what steps a reaction takes as it goes from reactants to products.
Writing an equilibrium equation in the form shown below indicates the specific rates at which the forward and reverse reactions proceed.
+ +
A B C
k1
k2
D
If the rate at which A and B react to produce C and D is proportional to the concentrations of both A and B, then the following equation expresses the rate law for this reaction:
The rate law correlates the rate of the reaction with the concentrations
of the reactants. rate1 = k1[A][B]
But, if the concentration of A, for example, is doubled, then the rate of the reaction also doubles. The proportionality constant, k, also called the rate constant, is the measure of the actual rate of the reaction when all the reactants are at 1 mole/liter (1 M) concentrations at a given temperature. The rate constant has a definite value for each temperature. Large values of k indicate fast reaction rates, and small values of k indicate slow reaction rates.
The rate constant is the measure of the rate of the reaction when the reactants are present in solution at a
concentration of 1 M.
To obtain the rate law for a reaction, chemists first measure the rate of that reaction experimentally for a number of concentrations. Then, using the data collected, they calculate the rate constant k1. As you will see in Chapter 7 and later, if there is more than one possible pathway for the reaction to take, the rate law helps determine the correct steps by showing which reactants are involved in the rate-limiting step of that reaction. Reactants that appear in the rate law are those that react in the slowest step of the mechanism for the reaction system. These reactants are the rate-limiting reactants. For example, in the reaction of A and B, if the rate depends only on the concentration of B, you look for the step in the possible mechanism that is a reaction of B. Another possibility for a reaction where the rate depends only on the concentration of B is where the concentration of A is so much larger than the concentration of B that no dependence of rate on the concentration of A can be observed. If the reaction depends on the concentrations of both A and B, then you look for a mechanism where the rate-limiting step involves a reaction of both A and B.
The rate-limiting step of a reaction is the slowest, or highest energy, step in the reaction mechanism.
Just as the previous equation describes the rate law for the reaction of A and B, the following equation describes the rate law for the reaction of C and D:
rate2 = k2[C][D]
When rate1 is equal to rate2, the system is in equilibrium. In equilibrium, the concentrations of A, B, C, and D do not change with time. Molecules of A and B still react to produce C and D, and at the same time molecules of C and D react to form molecules of A and B.
However, because the rates of the forward and reverse reactions are the same, there is no net increase or decrease in the concentration of either set of molecules. Chemists state the relationship between the two rate laws for the forward and reverse reactions for the example equilibrium you’ve been considering in the following way:
k1[A][B] = k2[C][D]
The equilibrium constant, K, is a property of a particular reaction at a specific temperature. K is independent of the initial concentrations of the reactants and products, although it does vary with temperature. To determine the equilibrium constant, calculate the quotient of the concentrations of the products and reactants at equilibrium using the following formula:
The equilibrium constant is a
mathematical quantity that describes the ratio of products to starting materials at
equilibrium.
K = [C]eq[D]eq [A]eq[B]eq = k1
k2
When a particular reaction reaches equilibrium, the actual concentrations of the reactants and products depend on their relative stabilities. The more stable one set is in comparison to the other, the higher is its concentration. That is, if the products are more stable than the reactants, then the reaction favors chemical compounds on the right and, at equilibrium, there is a higher concentration of products than reactants. Likewise, if the reactants are more stable than the products, the reaction favors the chemical compounds on the left, and there is a higher concentration of reactants than products.
An example of an equilibrium is the reaction of methyl chloride with hydroxide ion in water to produce methanol. Methyl chloride is a gas that is slightly soluble in water, forming solutions of about 0.1 M.
+ CH3Cl CH3OH + Cl
OH H2O
By substituting the concentrations of the reactants and products at equilibrium into the formula for the equilibrium constant and calculating, you get 1016 as the value of K.
K = [CH3OH][Clc- ]
[c- OH][CH3Cl] = 1016
This large value of K indicates that the amount of methyl chloride present at equilibrium is very small and the reaction has gone to completion. That is, it proceeds almost completely to the right.