The standard entropy of a substance is its entropy at 1 atm pressure. The values found in tables are normally those for 298K, and are expressed in units of J K–1 mol–1. This table below shows some typical values for gaseous substances.
Although the standard internal energies and enthalpies of these substances would be zero, the entropies are not. This is because there is no absolute scale of energy, so we conventionally set the energies of formation of elements in their standard states to zero. Entropy, however, measures not energy itself, but its dispersal amongst the various quantum states available to accept it, and these exist even in pure elements.
It is apparent that entropies generally increase with molecular weight. For the noble gases, this is of course 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. The entropies of the solid elements are strongly influenced by the manner in which the atoms are bound to one another. The contrast between diamond and graphite is particularly striking. Graphite, which is built up of loosely-bound stacks of hexagonal sheets, appears to be more than twice as good at soaking up thermal energy as diamond, in which the carbon atoms are tightly locked into a three-dimensional lattice, thus affording them less opportunity to vibrate around their equilibrium positions.
There is a general inverse correlation between the hardness of a solid and its entropy. Thus sodium, which can be cut with a knife, has almost twice the entropy of iron; the much greater entropy of lead reflects both its high atomic weight and the relative softness of this metal. These trends are consistent with the oft-expressed principle that the more disordered a substance, the greater its entropy.
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 owing to the multiplicity of ways in which the molecules can interact (that is, store energy.)
Let's briefly look at the entropy of gases. The standard molar entropy of a gas at STP includes contributions from:
- The heat capacity of one mole of the solid from 0 K to the melting point (including heat absorbed in any changes between different crystal structures),
- The latent heat of fusion of the solid,
- The heat capacity of the liquid from the melting point to the boiling point,
- The latent heat of vaporization of the liquid,
- The heat capacity of the gas from the boiling point to room temperature,
- Changes in entropy are associated with phase transitions and chemical reactions.
- Chemical equations make use of the standard molar entropy of reactants and products to find the standard entropy of reaction.
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: