Kaplan MCAT General Chemistry Review

The final state function that we will examine in this chapter is Gibbs free energy, G. Now, you can be sure that Josiah Gibbs isn’t giving it away for free. Actually, given that the man died way back in 1903, it’s unlikely that he’s got much more energy to give away, anyway. This state function is a combination of the two that we’ve just examined: enthalpy and entropy. The change in Gibbs free energy, G, is a measure of the change in the enthalpy and the change in entropy as a system undergoes a process, and it indicates whether a reaction is spontaneous or nonspontaneous. The change in the free energy is the maximum amount of energy released by a process, occurring at constant temperature and pressure, that is available to perform useful work. The change in Gibbs free energy is defined as follows:

G = H-

where T is the temperature in Kelvin and represents the total amount of energy that is absorbed by a system when its entropy increases reversibly.

Mnemonic

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A helpful visual aid for conceptualizing Gibbs free energy is to think of it as a valley between two hills. Just as a ball would tend to roll down the hill into the valley and eventually come to rest at the lowest point in the valley (as long as nothing prevents it from doing so), any system, including chemical reactions, will move in whatever direction results in a reduction of the free energy of the system. The bottom of the valley, the lowest point, represents equilibrium, and the sides of the hill represent the various points in the pathway toward or away from equilibrium. Movement toward the equilibrium position is associated with a decrease in Gibbs free energy (-G) and is spontaneous, while movement away from the equilibrium position is associated with an increase in Gibbs free energy (+G) and is nonspontaneous. You wouldn’t quite believe your eyes if, all of a sudden, the ball at the bottom of the valley began to roll up the hill with no assistance. Once at the energy minimum state, the position of equilibrium (the bottom of the valley), the system will resist any changes to its state, and the change in free energy is zero for all systems at equilibrium. To summarize:

1. If G is negative, the reaction is spontaneous.

2. If G is positive, the reaction is nonspontaneous.

3. If G is zero, the system is in a state of equilibrium; thus H = .

Key Concept

Recall that thermodynamics and kinetics are separate topics. When a reaction is thermodynamically spontaneous, it has no bearing on how fast it goes. It only means that it will proceed eventually without external energy input.

Because the temperature in Gibbs free energy is in units of Kelvin, it is always positive. Therefore, the effects of the signs on H and S and the effect of temperature on the spontaneity of a process can be summarized as follows:

HSOutcome-+spontaneous at all temperatures+-nonspontaneous at all temperatures++spontaneous only at high temperatures--spontaneous only at low temperatures

Key Concept

G is temperature-dependent when H and S have the same sign.

Phase changes are examples of temperature-dependent processes. The phase changes of water should be familiar to you. Have you ever wondered why water doesn’t boil at, say, 20°C instead of 100°C? Well, first of all, be thankful that it doesn’t because 20°C is room temperature. It’d be hard to keep a glass of water, not to mention you, around for very long. (Water makes up almost 99 percent of the total number of molecules in the human body. Excluding adipose tissue, the human body is about 75 percent water by mass!) So we all know that water boils at 100°C, but why? The answer lies in phase transformation:

H₂O (l) H₂O (g)       H_vap = 40.65 kJ/mol

When water boils, hydrogen bonds (H-bonds) are broken, and the water molecules gain sufficient potential energy to escape into the gas phase. Thus, boiling (vaporization) is an endothermic process, and H is positive. As thermal energy is transferred to the water molecules, energy is distributed through the molecules entering the gas phase, and entropy is positive and is positive. Both H and are positive, so the reaction will be spontaneous only if is greater than H, giving a negative G. These conditions are met only when the temperature of the system is greater than 373 K (100°C). Below 100°C, the free energy change is positive, and boiling is nonspontaneous; the water remains a liquid. At 100°C, H = and G = 0; equilibrium between the liquid and gas phases is established in such a way that the water’s vapor pressure equals the ambient pressure. This is the definition of the boiling point: the temperature at which the vapor pressure equals the ambient pressure.