Entropy and Molecular structure: How are the two related?

Summary

There are two aspects of the molecular structure of a substance that affect the value of its entropy: (1) The degree to which the movement of the atoms and molecules in the structure is restricted—the less restricted this movement, the greater the entropy. (2) The mass 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.

Among crystalline materials, those with the lowest entropies tend to be rigid crystals composed of small atoms linked by strong, highly directional bonds, such as diamond.

In contrast, graphite, the softer, less rigid allotrope of carbon, has a higher entropy due to more disorder in the crystal.

?Soft crystalline substances and those with larger atoms tend to have higher entropies because of increased molecular motion and disorder.

Similarly, the absolute entropy of a substance tends to increase with increasing molecular complexity because the number of available microstates increases with molecular complexity.

?Entropy is a measure of the unavailability of a system’s energy to do work. It is a measure of disorder. In thermodynamics, a parameter representing the state of disorder of a system at the atomic, ionic, or molecular level; the greater the disorder the higher the entropy. At the molecular level, the value of the entropy of the distribution of atoms and molecules in a thermodynamic system is a measure of the disorder in the arrangements of its particles.?

In a stretched-out piece of rubber, for example, the arrangement of the molecules of its structure has an “ordered” distribution and has zero entropy, while the “disordered” kinky distribution of the atoms and molecules in the rubber in the non-stretched state has positive entropy. Similarly, in a gas, the order is perfect and the measure of the entropy of the system has its lowest value when all the molecules are in one place, whereas when more points are occupied, the gas is all the more disorderly and the measure of the entropy of the system has its largest value.

General understanding of entropy

Following processes increase entropy

-Increasing the volume that gas can occupy will increase the disorder of a gas

-Dissolving a solute into a solution will increase the entropy of the solute - typically resulting in an increase in the entropy of the system. (Note: the solvation of a solute can sometimes result in a significant decrease in the solvent entropy - leading to a net decrease in entropy of the system)

-Phase changes from solid to liquid, or liquid to gas, lead to an increase in the entropy of the system

Following processes decrease the entropy

ΔS<0 :

-A gas molecule dissolved in a liquid is much more confined by neighboring molecules than when it’s in the gaseous state. Thus, the entropy of the gas molecule will decrease when it is dissolved in a liquid

-A phase change from a liquid to a solid (i.e. freezing), or from a gas to a liquid (i.e. condensation) results in a decrease in the disorder of the substance, and a decrease in the entropy

-A chemical reaction between gas molecules that results in a net decrease in the overall number of gas molecules will decrease the disorder of the system, and result in a decrease in the entropy

2NO(g)+O2(g)→2NO2(g), ΔS<0

What is the molecular basis for the above observations for the change in entropy?

Let's first consider the reaction below. The decrease in entropy is associated with a decrease in the number of gas molecules in the reaction below.

2NO(g)+O2(g)→2NO2(g), ΔS<0

The product of this reaction (NO2) involves the formation of a new N-O bond and the O atoms, originally in a separate O2 molecule, are now connected to the NO molecule via a new N?O bond.

?Since they are now physically bonded to the other molecule (forming a new, larger, single-molecule) the O atoms have less freedom to move around

The reaction has resulted in a loss of freedom of the atoms (O atoms)

There is a reduction in the disorder of the system (i.e., due to the reduction in the degrees of freedom, the system is more ordered after the reaction).?ΔS<0.

Molecular Degrees of Freedom

The atoms, molecules, or ions that compose a chemical system can undergo several types of molecular motion, including translation, rotation, and vibration

Molecular Motions:. The vibrational, rotational, and translational motions of a carbon dioxide molecule are illustrated here. Only a perfectly ordered, crystalline substance at absolute zero would exhibit no molecular motion and have zero entropy. In practice, this is an unattainable ideal.

?-Translational motion: The entire molecule can move in some direction in three dimensions

-Rotational motion: The entire molecule can rotate around any axis, (even though it may not actually change its position translationally)

-Vibrational motion: The atoms within a molecule have certain freedom of movement relative to each other; this displacement can be periodic motion like the vibration of a tuning fork

These forms of molecular motion are ways in which molecules can store energy. The greater the molecular motion of a system, the greater the number of possible microstates and the higher the entropy.

The Third Law of Thermodynamics

These forms of motion are ways in which the molecule can store energy. The greater the molecular motion of a system, the greater the number of possible microstates and the higher the entropy. A perfectly ordered system with only a single microstate available to it would have an entropy of zero. 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. Such a state of perfect order (or, conversely, zero disorder) corresponds to zero entropy. In practice, absolute zero is an ideal temperature that is unobtainable, and a perfect single crystal is also an ideal that cannot be achieved. 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.

Since S = 0 corresponds to perfect order. The position of the atoms or molecules in the crystal would be perfectly defined

As the temperature increases, the entropy of the atoms in the lattice [ lattice is the symmetrical three-dimensional structural arrangements of atoms, ions or molecules inside a crystalline solid] increase

Vibrational motions cause the atoms and molecules in the lattice to be less well ordered

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, the absolute entropy of a substance is determined by measuring the molar heat capacity (Cp) as a function of temperature and then plotting the quantity Cp/T versus T. The area under the curve between 0 K and any temperature T is the absolute entropy of the substance at T. In contrast, other thermodynamic properties, such as internal energy and enthalpy, can be evaluated in only relative terms, not absolute terms.

Please refer to the table below.

As shown in the table below, for substances with approximately the same molar mass and a number of atoms, S° values fall in the order S°(gas) > S°(liquid) > S°(solid). For instance, S° for liquid water is 70.0 J/(mol·K), whereas S° for water vapor is 188.8 J/(mol·K). Likewise, S° is 260.7 J/(mol·K) for gaseous I2 and 116.1 J/(mol·K) for solid I2. This order makes qualitative sense based on the kinds and extents of motion available to atoms and molecules in the three phases.

Entropy increases with softer, less rigid solids, solids that contain larger atoms, and solids with complex molecular structures.

A closer examination of LHS table also reveals that substances with similar molecular structures tend to have similar S° values. Among crystalline materials, those with the lowest entropies tend to be rigid crystals composed of small atoms linked by strong, highly directional bonds, such as diamond [S° = 2.4 J/(mol·K)]. In contrast, graphite, the softer, less rigid allotrope of carbon, has a higher S° [5.7 J/(mol·K)] due to more disorder in the crystal. Soft crystalline substances and those with larger atoms tend to have higher entropies because of increased molecular motion and disorder. Similarly, the absolute entropy of a substance tends to increase with increasing molecular complexity because the number of available microstates increases with molecular complexity. For example, compare the S° values for CH3OH(l) and CH3CH2OH(l). Finally, substances with strong hydrogen bonds have lower values of S°, which reflects a more ordered structure.

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References:

Mike Blaber (Florida State University)

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