5. The Molar Entropy -
a Thermal Property of Matter

Physical properties are called phenomena, which are characteristic of particular substances. If, in the case of a certain phenomenon measurements of large amounts of substance yield values different from those of small amounts, then this indicates this phenomnon is not a physical property of the investigated substance: The mass of a certain amount of a substance is not a physical property of the substance, but merely a property of the investigated amount of the substance. If, however, the mass is referred to the volume of this amount of substance we obtain the physical property "density" of the substance, independently of the amount.

The same is true with entropy. In the case of a larger amount of substance, a larger entropy value is measured. If the measured entropy is referenced to the mass, the volume or the number of particles, generally the size of the investigated object, then a corresponding property is obtained with the corresponding quotient (measured value per size of the object). It is most common to refer the entropy to the amount of substance. These values are listed as molar standard entropies under defined conditions in thermodynamic tables.

Contrary to many physical properties, it does not exist an intuitive idea about entropy generally accepted by scientists. In this chapter, the molar entropy is interpreted as a physical property of matter and its thermal quality is made comprehensible.

5.1. Entropy is Absolute

With the help of the shelf-model it is possible to understand that entropy is a measure of the number of occupied energy levels in a system, in a substance. Molar entropies belong to the thermodynamic quantities, which are given as absolute values and not relative to an arbitrarily selected zero level. Only the unit of entropy we are able to elect freely, because each phenomenon is invariant in relation to the used unit.
For this reason molar entropy is a physical property*, which depends - similar to the density of a substance - on temperature. The way a substance reacts to thermal work or volume work carried out on it is characteristic of the thermal properties of this substance and expresses itself in the value of its standard entropy. A large value of entropy indicates an extended store system for thermal energy. You can take this for a more generalizing definition of entropy:

Entropy is a measure of the extent of the storage system for thermal energy
formed by the particles of a substance

The absolute character of entropy is very much shaping and we should take this as a hint to omit all kinds of arbitrary handling while approaching this phenomenon. Usually molar entropies refer to the amount of substance in multiples of the used formula unit. In the choice of the formula unit however we proceed very often arbitrarily instead of systematically. Thus for gases such as chlorine, hydrogen, oxygen etc. it is always indicated that the smallest particles of these materials consist of two atoms. With regard to sulfur and phosphorus the formulas are inconsequentially given without the indication of the molecule size S8 and/or P4 . It is known that water consists out of Clusters, but no one indicates it in the formula unit. For crystalline sodium chloride as well we do not use the smallest unit of the crystal, the elementary cell. This contains 4 formula units NaCl. This arbitrariness prevents ud from understanding entropy values, especially if you want to compare entropy of different substances. One mole sulfur S8 consist out twice as many atoms as there are in a mole phosphorus P4 . It is obvious that a larger amount of atoms will occupy a greater number of energy levels and thus will store more energy. Therefore for the following statements the molar entropies were converted and referred to the number of atoms. For these values the designation atomic entropy and the symbol Sat are used here. Atomic entropies are rather more meaningful than the molar entropies especially if you intend to compare substances with different stoichiometry.

* An article about "Entropy and the Shelf Model" has been published in the Journal of Chemical Education.