#### Learning Objective

- Define standard entropy.

#### Key Points

- Entropies generally increase with molecular weight; for noble gases this is a direct reflection of the principle that translational quantum states are more closely packed in heavier molecules.
- Entropies can also show the additional effects of rotational quantum levels (in diatomic molecules) as well as the manner in which the atoms are bound to one another (solids).
- There is a general inverse correlation between the hardness of a solid and its entropy.
- The entropy of a solid is less than the entropy of a liquid which is much less than the entropy of a gas.

#### Term

- standard entropyEntropy of a substance at 1 atm pressure.

## Defining Standard Entropy

The standard entropy of a substance is its entropy at 1 atm pressure. The values found in the table are normally those for 298K, and are expressed in units of [latex]\frac {\text{J}}{\text{K} \cdot \text{mole}}[/latex]. Some typical standard entropy values for gaseous substances include:

- He: 126 [latex]\frac {\text{J}}{\text{K} \cdot \text{mole}}[/latex]
- Xe: 170 [latex]\frac {\text{J}}{\text{K} \cdot \text{mole}}[/latex]
- O
_{2}: 205 [latex]\frac {\text{J}}{\text{K} \cdot \text{mole}}[/latex] - CO
_{2}: 213 [latex]\frac {\text{J}}{\text{K} \cdot \text{mole}}[/latex] - H
_{2}O(g): 187 [latex]\frac {\text{J}}{\text{K} \cdot \text{mole}}[/latex]

Scientists conventionally set the energies of formation of elements in their standard states to zero. Entropy, however, measures not energy itself, but its dispersal among the various quantum states available to accept it, and these exist even in pure elements.

## Comparing Entropy

It is apparent that entropies generally *increase* with molecular weight. For the noble gases, this is a direct reflection of the principle that translational quantum states are more closely packed in heavier molecules, allowing them to be occupied. The entropies of the diatomic and polyatomic molecules show the additional effects of rotational quantum levels.

## Entropy in Solids

The entropies of solid elements are strongly influenced by the type of atom packing in the solid. Although both diamond and graphite are types of carbon, their entropies differ significantly. Graphite, which is built up of loosely-bound stacks of hexagonal sheets, soaks up thermal energy twice as well as diamond. The carbon atoms in diamond are tightly locked in a three-dimensional lattice, preventing them from vibrating around their equilibrium positions.

There is an inverse correlation between the hardness of a solid and its entropy. For example, sodium, which can be cut with a knife, has almost twice the entropy of iron, which cannot be easily cut. These trends are consistent with the principle that the more disordered a substance, the greater its entropy.

## Entropy in Gases and Liquids

Gases, which serve as efficient vehicles for spreading thermal energy over a large volume of space, have much higher entropies than condensed phases. Similarly, liquids have higher entropies than solids because molecules in a liquid can interact in many different ways.

The standard entropy of reaction helps determine whether the reaction will take place spontaneously. According to the second law of thermodynamics, a spontaneous reaction always results in an increase in total entropy of the system and its surroundings:

[latex]\Delta {S}_{\text{total}} = \Delta {S}_{\text{system}}+ \Delta {S}_{\text{surroundings}}[/latex]