Kaplan MCAT General Chemistry Review

So far, in our discussion of reaction rates, we have been assuming that the reactions were irreversible; that is, the reaction proceeds in one direction only, the reaction goes to completion, and the amount of product formed is the maximum as determined by the amount of limiting reactant present. Reversible reactions are those in which the reaction can proceed in one of two ways: forward and reverse. (From the perspective of the direction in which the overall reaction is written, the forward reaction is the one that goes from “reactants” on the left to “products” on the right.) Reversible reactions usually do not proceed to completion because (by definition) the products can react together to re-form the reactants. When the reaction system is closed and no products or reactants are removed or added, the system will eventually “settle” into a state in which the rate of the forward reaction equals the rate of the reverse reaction and the concentrations of the products and reactants are constant. In this dynamic equilibrium state, the forward and reverse reactions are occurring—they haven’t stopped, as would be the case in a static equilibrium—but they are going at the same rate; thus, there is no net change in the concentrations of the products or reactants. Consider the following generic reversible reaction:

A B

At equilibrium, the concentrations of A and B are constant (though not necessarily equal), and the reactions A B and B A continue to occur at equal rates.

Equilibrium can be thought of as a balance between the two reactions (forward and reverse). Better still, equilibrium should be understood on the basis of entropy, which is the measure of the distribution of energy throughout a system or between a system and its environment. For a reversible reaction at a given temperature, the reaction will reach equilibrium when the system’s entropy—or energy distribution—is at a maximum and the Gibbs free energy of the system is at a minimum.

LAW OF MASS ACTION

For a generic reversible reaction aA + bB cC + dD, the law of mass action states that if the system is at equilibrium at a given temperature, then the following ratio is constant:

The law of mass action is actually related to the expressions for the rates of the forward and reverse reactions. Consider the following one-step reversible reaction:

2A B + C

Because the reaction occurs in one step, the rates of the forward and reverse reactions are given by

rate_f = k_f[A]², and rate_r = k_r[B][C]

When rate_f = rate_r, the system is in equilibrium. Because the rates are equal, we can set the rate expressions for the forward and reverse reactions equal to each other:

Because k_f and k_r are both constants, we can define a new constant K_c, where K_c is called the equilibrium constant and the subscript c indicates that it is in terms of concentration. (When dealing with gases, the equilibrium constant is referred to a K_p, and the subscript p indicates that it is in terms of pressure.) For dilute solutions, K_c and K_eq are used interchangeably. The new equation can thus be written

Key Concept

For most purposes, you will not need to distinguish between different K values. For dilute solutions, K_eq K_c and both are calculated in units of concentration.

While the forward and the reverse reaction rates are equal at equilibrium, the concentrations of the reactants and products are not usually equal. This means that the forward and reverse reaction rate constants, k_f and k_r, are not usually equal. The ratio of k_f to k_r is K_c (K_eq).

When a reaction occurs by more than one step, the equilibrium constant for the overall reaction is found by multiplying together the equilibrium constants for each step of the reaction. When you do this, the equilibrium constant for the overall reaction is equal to the concentrations of the products divided by the concentrations of the reactants in the overall reaction, each concentration term raised to the stoichiometric coefficient for the respective species. The forward and reverse rate constants for the nth step are designated k_n and k_-n, respectively. For example, if the reaction

aA + bB cC + dD . . .

occurs in three steps, then

Example: What is the expression for the equilibrium constant for the following reaction?

3 H₂ (g) + N₂ (g) 2 NH₃ (g)

Solution: K_c =

MCAT Expertise

Remember our earlier warning about confusion between reaction coefficients and rate laws? Well, here the coefficients are equal to the exponents in the equilibrium expression. On Test Day, if the reaction is balanced, then the equilibrium expression should just about write itself on your scratch paper.

REACTION QUOTIENT