Energy and Entropy

Many powerful calculations in thermodynamics are based on a few fundamental principles, which are called the laws of thermodynamics. Begin by reviewing the two main laws of the field.

The first law of thermodynamics asserts that energy is conserved during any process. The three major forms of energy for chemical purposes are the internal energy of each substance, the external work due to changes in pressure or volume, and the exchange of heat with the surroundings.

The internal energy is sometimes called chemical energy because it is the consequence of all the motions of particles and forces between particles: molecules, atoms, nucleons, and electrons.

If no heat flows in or out of a sample of matter, any external work done on or by the sample is precisely offset by the opposite change in internal energy. Expansion against a confining pressure reduces the internal energy, whereas external compression of the system increases the internal energy.

The first law of thermodynamics also tells you that if no work is done on or by the sample—that is, pressure and volume are held constant—any heat flow is counterbalanced by a change in internal energy. An exothermic reaction releasing heat to the surroundings, therefore, is accompanied by a decrease in internal energy, whereas an endothermic reaction has a concomitant increase in internal energy.

The second law of thermodynamics involves entropy, which for our purposes is a statistical measure of the degree of disorder in a chemical system. As an illustration, compare the arrangements of Na + and Cl ions in both solid and liquid sodium chloride.

Solid sodium chloride has a crystalline structure in which the cations and anions alternate in a repeating pattern. (See Figure 1.)

Figure 1. The crystal structure of NaCl.

figure 

If you examine the NaCl crystal structure closely, you will see that each Cl is surrounded by 6 Na +, and each Na + is surrounded by 6 Cl . The regular, repetitive structure has a high degree of order and low entropy or low disorder.

When solid NaCl is heated to 801°C, it melts, and the ions are no longer fixed in a simple geometric pattern. They will move relative to each other, subject only to the constraint of electrostatic attraction and repulsion. Each Na +, therefore, will be adjacent to as many Cl anions as possible, and each Cl will tend to be surrounded by Na + cations. No longer would each ion be surrounded by precisely 6 ions of the opposite charge. This looser arrangement of ions in molten sodium chloride shows that the liquid state displays an increased disorder than the solid state, so it is of higher entropy.

A gas has even greater disorder than a liquid because its constituent molecules or atoms are no longer constrained to be adjacent to each other. Each gas particle moves more or less independently of the other particles. This state is one of near maximum disorder and near maximum entropy.

The second law of thermodynamics states that the total entropy of a chemical system and that of its surroundings always increases if the chemical or physical change is spontaneous. The preferred direction in nature is toward maximum entropy. Moving in the direction of greater disorder in an isolated system is one of the two forces that drive change. The other is loss of heat energy, Δ H.

Chemists have found it possible to assign a numerical quantity for the entropy of each substance. When measured at 25°C and 1 atm, these are called standard entropies. Table 1 lists 12 such values, symbolized by S° where the superscript denotes the standard state.


Notice in Table 1 that the units for entropy, equation, require you to multiply each value by the temperature ( K) in order to obtain units of energy.

The point that solids have low entropies and gases have high entropies has already been made. An examination of the values in the table should convince you that this is indeed a valid generalization. Compare the pairs of values for the two states of H 2O and also the two states of lithium.

The symbol for entropy is S, so a change in entropy is shown as Δ S. The values in the preceding chart allow calculations of the entropy change when water evaporates at 25°C.

equation

The entropy of reaction is the difference in the entropy of the products and reactants:

Δ S = S productsS reactants = 189 – 70 = 119 J/deg

This positive entropy change means that there is greater disorder in the product (H 2O gas) than in the reactant (H 2O liquid). In terms of just entropy, the increase in entropy drives the reaction to the right, toward a condition of higher entropy.

As another example, the entropy change associated with the reaction 

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can be calculated from data in the chart of standard entropies: 

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This negative entropy of reaction would tend to inhibit this reaction from proceeding.

The entropy of reaction by itself, however, is not sufficient to predict the direction of a reaction. At 25°C, you know that H 2O ( l) is the stable phase, not H 2O ( g). Moreover, the second reaction

  equation

proceeds forward despite the negative entropy of reaction. You must consider both the enthalpy of reaction and the entropy of reaction in order to determine the direction of a chemical reaction with certainty.