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680 Chapter 13 | Fundamental Equilibrium Concepts
3. Whether a process will be spontaneous, non-spontaneous, or what we have called an equilibrium process
Recall that when the value ∆G for a reaction is zero, we consider there to be no free energy change—that is, no free energy available to do useful work. Does this mean a reaction where ΔG = 0 comes to a complete halt? No, it does not. Just as a liquid exists in equilibrium with its vapor in a closed container, where the rates of evaporation and condensation are equal, there is a connection to the state of equilibrium for a phase change or a chemical reaction. That is, at equilibrium, the forward and reverse rates of reaction are equal. We will develop that concept and extend it to a relationship between equilibrium and free energy later in this chapter.
In the explanation that follows, we will use the term Q to refer to any reactant or product concentration or pressure. When the concentrations or pressure of reactants and products are at equilibrium, the term K will be used. This will be more clearly explained as we go along in this chapter.
Now we will consider the connection between the free energy change and the equilibrium constant. The fundamental relationship is:
—this can be for or (and we will see later, any equilibrium constant we encounter).
We also know that the form of K can be used in non-equilibrium conditions as the reaction quotient, Q. The defining
relationship here is
Without the superscript, the value of ∆G can be calculated for any set of concentrations.
Note that since Q is a mass-action reaction of productions/reactants, as a reaction proceeds from left to right, product concentrations increase as reactant concentrations decrease, until Q = K, and at which time ∆G becomes zero:
, a relationship that reduces to our defining connection between Q and K. Thus, we can see clearly that as a reaction moves toward equilibrium, the value of ∆G goes to zero. Now, think back to the connection between the signs of ∆G° and ∆H°
∆H° Negative Positive Positive Negative
∆S° Result
Positive Negative Positive Negative
Always spontaneous
Never spontaneous
Spontaneous at high temperatures Spontaneous at low temperatures

Only in the last two cases is there a point at which the process swings from spontaneous to non-spontaneous (or the reverse); in these cases, the process must pass through equilibrium when the change occurs. The concept of the connection between the free energy change and the equilibrium constant is an important one that we will expand upon in future sections. The fact that the change in free energy for an equilibrium process is zero, and that displacement of a process from that zero point results in a drive to re-establish equilibrium is fundamental to understanding the behavior of chemical reactions and phase changes.
13.1 Chemical Equilibria
By the end of this section, you will be able to:
• Describe the nature of equilibrium systems
• Explain the dynamic nature of a chemical equilibrium
A chemical reaction is usually written in a way that suggests it proceeds in one direction, the direction in which we read, but all chemical reactions are reversible, and both the forward and reverse reaction occur to one degree or another depending on conditions. In a chemical equilibrium, the forward and reverse reactions occur at equal rates, and the concentrations of products and reactants remain constant. If we run a reaction in a closed system so that the products cannot escape, we often find the reaction does not give a 100% yield of products. Instead, some reactants
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