Thermodynamics:
Entropy
Thermodynamics Gateway Page
In this module:
Introduction
Disorder in Atoms
Disorder in Energy
Measuring Entropy
Entropy of Phase Changes
Patterns in the Entropies of Substances
Entropy in Thermochemical Equations
The Second Law of Thermodynamics
The Effect of Temperature
Predicting How Reactions will Go
Two Examples

Patterns in the entropies of substances

In the table below are some excerpts from the Thermodynamics Table.

Substance Sº (25 ºC) Substance Sº (25 ºC) Substance Sº (25 ºC) Substance Sº (25 ºC)
F2 (g) 202.7 CH4 (g) 186.15 NaF (s) 51.46 NaF (s) 51.46
Cl2 (g) 222.96 C2H6 (g) 229.5 MgO (s) 26.9 NaCl (s) 72.13
Br2 (l) 152.23 C3H8 (g) 269.9 AlN (s) 20.2 NaBr (s) 86.82
I2 (s) 116.14 C4H10 (g) 310.0 -- -- NaI (s) 98.53

Some patterns emerge when these values are compared.

  • The entropies of gases are much larger than those of liquids, which are larger than those of solids (columns 1, 3, and 4).

This can be predicted from equation (1): heat must be put into substances to convert them from solid to liquid or liquid to gas. Therefore, q and DS are both positive and the liquid or gas has more entropy than the solid or liquid.

On the nanoscale level, the atoms in solids are constrained to one position; they can only vibrate around that position. The atoms in liquids are still close together but they are free to move around with respect to each other, so they are more disordered. The atoms in gases are far apart from each other, so they are much more disordered than either liquids or solids.

  • Entropies of large, complicated molecules are greater than those of smaller, simpler molecules (column 2).

Large, complicated molecules have more disorder because of the greater number of ways they can move around in three-dimensional space.

  • Entropies of ionic solids are larger when the bonds within them are weaker (columns 3 and 4).

If you think of ionic bonds as springs, a stronger bond will hold the ions in place more than a weaker bond. Therefore, the stronger bond will cause less disorder and less entropy.

Two more patterns emerge from considering the implications of the first three.

  • Entropy usually increases when a liquid or solid dissolves in a solvent.

Before mixing, the solute and solvent are completely separated from each other. After mixing, they are completely interspersed within each other. Thus, the entropy increases.

  • Entropy usually decreases when a gas dissolves in a liquid or solid.

There is more mixing involved, but the atoms of the gas go from being completely separated from each other to being closely packed with each other and the solvent. Thus, the entropy decreases.

Predict the sign of DS in the following reactions:

CaCO3 (s) CaO (s) + CO2 (g) Positive Negative
Ag+ (aq) + Cl- (aq) AgCl (s) Positive Negative
N2O4 (g) 2 NO2 (g) Positive Negative
soda can closed soda can opened Positive Negative
One mole of a gas and one mole of a solid are produced from one mole of a solid. Since gases have so much more entropy than solids, the entropy change of this reaction is positive.
One mole of a solid is produced from two moles of ions in aqueous solution. Since solids have less entropy than solutions, the entropy change of this reaction is negative.
Two moles of a gas are produced from one mole of a gas. Since the number of moles of gas has increased, the entropy change of this reaction is positive.
Carbon dioxide gas is dissolved under pressure in the soda before the can is opened. When the pressure is released (the can is opened), the gas comes out of solution. One mole of a gas is produced from one mole of a solution, so the entropy change is positive.

Patterns in the Entropies of Substances