Dependence of S on Molecular Structure
Since they all refer to the same temperatureA physical property that indicates whether one object can transfer thermal energy to another object. and pressureForce per unit area; in gases arising from the force exerted by collisions of gas molecules with the wall of the container., and also to 1 mol of substanceA material that is either an element or that has a fixed ratio of elements in its chemical formula., any differences in the entropyA thermodynamic state function, symbol S, that equals the reversible heat energy transfer divided by temperature; higher entropy corresponds to greater dispersal of energy on the molecular scale. See also standard entropy. values listed in the table of standard entropies must be due to differences in the molecular structure of the various substances listed. There are two aspects of the molecular structure of a substance which affect the value of its entropy: (1) The degree to which the movement of the atomsThe smallest particle of an element that can be involved in chemical combination with another element; an atom consists of protons and neutrons in a tiny, very dense nucleus, surrounded by electrons, which occupy most of its volume. and molecules in the structure is restricted—the less restricted this movement, the greater the entropy. (2) The massA measure of the force required to impart unit acceleration to an object; mass is proportional to chemical amount, which represents the quantity of matter in an object. of the atoms and molecules which are moving—the greater the mass, the larger the entropy. We will consider each of these factors in turn.
|Compound||Smo /J K-1mol-1||Compound||Smo /J K-1mol-1|
|Liquids||Polyatomic Gases( > 3)|
Restrictions on the Movement of Atoms and Molecules We have already encountered two examples of how the removal of a restriction on the motion of molecules allows an increase in the number of alternative ways in which the molecules can arrange themselves in space. The first of these is the case of the ring and chain forms of 1,4-butanediol discussed in the section on the molecular view of equilibrium, and displayed in figures 2 and 3 in that section. When the two ends of this molecule hydrogen bondAn attractive force, either intramolecular or intermolecular, between an electronegative atom and a hydrogen atom attached to another electronegative atom. to form a ring, the result is a fairly rigid structure. However, if the restricting influence of the hydrogen bond is removed, the more flexible chain form of the molecule is capable of many more alternative configurations. As a result, we find that W for a mole of molecules in the chain form is very much larger than W for a mole of molecules in the ring form. The chain form turns out to have a molar entropy which is 41 J K–1 mol–1 higher than that for the ring form.
A second example of the effect of relaxing a restriction on molecular motion is the expansion of a gas into a vacuum. When the molecules have more freedom of movement, many more alternative arrangements are possible, and hence W is larger. As we have already calculated, doubling the volume of a gas increases its molar entropy by 5.76 J K–1 mol–1.
Mass of the Atoms and Molecules We showed that when quantum mechanics is applied, the energies of a moving particle are confined to certain specific values and not those in between. The allowed energies, or energyA system's capacity to do work. levels, for a particle in a box were given by equation 4 in the section on wave mechanics:
From this equation we can see that the larger the mass m of a particle, the smaller the value of its energy Ek for a given value of the quantum numberOne of a set of numbers that specifies the state of an electron in an atom; the set of quantum numbers summarize results from quantum mechanics. n. Furthermore, the larger the value of m, the smaller the difference between Ek2 (for n = 2) and Ek1 (for n = 1). No matterAnything that occupies space and has mass; contrasted with energy. what kind of energy is involved—rotational, vibrational, or translational—this is always found to be true. The greater the mass of a particle, the closer together its energy levels.
The effect of closeness of energy levels on the entropy is shown in Fig. 1. The more closely spaced the levels, the more different ways the same quantity of energy can be distributed among them. This applies in general for any number of particles and any quantity of energy. Therefore, the heavier the molecules of a substance, the larger its molar entropy. This effect is quite obvious among the noble gases—their molar entropies increase steadily with molar (and hence molecular) mass.