The second, based on the fact that entropy is a state function, uses a thermodynamic cycle similar to those we first encountered in Chapter 5 'Energy Changes in Chemical Reactions'.Ĭalculating Δ S from Standard Molar Entropy Values The first, based on the definition of absolute entropy provided by the third law of thermodynamics, uses tabulated values of absolute entropies of substances. In this section, we examine two different ways to calculate Δ S for a reaction or a physical change. In contrast, other thermodynamic properties, such as internal energy and enthalpy, can be evaluated in only relative terms, not absolute terms. The area under the curve between 0 K and any temperature T is the absolute entropy of the substance at T. In practice, chemists determine the absolute entropy of a substance by measuring the molar heat capacity ( C p) as a function of temperature and then plotting the quantity C p/ T versus T. The third law of thermodynamics has two important consequences: it defines the sign of the entropy of any substance at temperatures above absolute zero as positive, and it provides a fixed reference point that allows us to measure the absolute entropy of any substance at any temperature. In practice, this is an unattainable ideal. Only a perfectly ordered, crystalline substance at absolute zero would exhibit no molecular motion and have zero entropy.

Vibrational, rotational, and translational motions of a carbon dioxide molecule are illustrated here. Nonetheless, the combination of these two ideals constitutes the basis for the third law of thermodynamics The entropy of any perfectly ordered, crystalline substance at absolute zero is zero.: the entropy of any perfectly ordered, crystalline substance at absolute zero is zero. In practice, absolute zero is an ideal temperature that is unobtainable, and a perfect single crystal is also an ideal that cannot be achieved. Such a state of perfect order (or, conversely, zero disorder) corresponds to zero entropy. The only system that meets this criterion is a perfect crystal at a temperature of absolute zero (0 K), in which each component atom, molecule, or ion is fixed in place within a crystal lattice and exhibits no motion. A perfectly ordered system with only a single microstate available to it would have an entropy of zero. The greater the molecular motion of a system, the greater the number of possible microstates and the higher the entropy. The atoms, molecules, or ions that compose a chemical system can undergo several types of molecular motion, including translation, rotation, and vibration ( Figure 18.13 'Molecular Motions'). To use thermodynamic cycles to calculate changes in entropy.

Entropy change