Entropy, the measure of distribution of energy in a system, is quoted in units of J mol
-1 K
-1, that is,
joules per
mole per
kelvin. The entropy of a
system is given by the equation:
S = k ln w
where S is entropy, k is the Boltzmann constant and w is the number of ways of arranging the energy in the system.
As far as chemistry is concerned, the entropy of elements and compounds (known as the standard molar entropy) is given the symbol Sθ and refers to the entropy of that substance under standard conditions.
The physical state of a substance has a strong effect on its standard entropy - gases have the most freedom to distribute themselves randomly, so they tend to have the highest entropies, while at the opposite end at the scale, solids tend to have the lowest entropies. Among the elements, for example, gaseous oxygen has a standard molar entropy of 102.5 J mol-1 K-1, liquid mercury one of 76.0, and solid iron 27.3.
When there is a chemical change, there will also be an entropy change. The total entropy change, ΔSθtotal, will be the sum of the entropy change of the system and the entropy change of the surroundings. Since the universe tends towards increasing entropy, only those reactions with a positive total entropy change will occur spontaneously, and those with strongly negative values will be hard to achieve even artificially.
The entropy change of the system, ΔSθsystem, is simply the entropy of the products minus the entropy of the reactants. The entropy change of the surroundings, ΔSθsurroundings, is given by the enthalpy change of the reaction, ΔH, quoted in joules (NOT kilojoules), divided by the absolute temperature of the surroundings, which under standard conditions is 298K.
Given that values for standard entropies and enthalpy changes have been systematically measured and recorded, it is possible to calculate the feasibility of a reaction from published data. If the total entropy change is more than +200 J mol-1 K-1, the reaction will probably go to completion. Between +200 and -200, it will be reversible. If the total entropy change is less than -200, the reaction probably won't go at all.
The entropy change of the system tends to be positive when the products have a more entropic physical state than the reactants, e.g. solid to liquid or liquid to gas. Increasing the number of moles also has a positive increase on entropy. Conversely, the opposite processes have the opposite effect.
The entropy change of the surroundings is positive for exothermic reactions, because heat is being given out, so the surroundings have more energy and thus more ways of arranging their energy. Endothermic reactions, on the other hand, lead to a negative entropy change of surroundings, and the majority of spontaneous reactions are exothermic.
Reference: Revised Nuffield Advanced Science Book of Data, 1984