- The third law of thermodynamics states that a perfect crystal at 0 K has an entropy of 0 J/K.
- The entropy of a reaction can be calculated using a modification of Hess' law:
.
The third law of thermodynamics sets a reference value for entropy. The third law states that the entropy of a perfect, pure crystal at T = 0 K is zero. Conceptually, this can be best understood from a statistical mechanics perspective. From statistical mechanics, a system with a fixed number of particles, volume, and total energy, the entropy can be calculated using the Boltzmann equation introduced in section 3.1:
where S is the entropy, kB is the Boltzmann constant (), and W is the total number of microstates (degeneracy).
A pure, perfect crystal has exactly one microstate (there is only one way to achieve a perfect crystal, so the total number of microstates is one).
With the third law of thermodynamics acting as a reference point, we can determine absolute values for entropy, So, at higher temperatures. Absolute values of molar entropies are available in data tables (usually at standard pressure and a temperature specified in the table). There is a small, but important, difference between tabulated data for enthalpies of formation and entropies. Enthalpies of formation () are changes in enthalpies (going from elements in their standard states to form one mole of the chemical species), while the tabulated entropies (
) are absolute values in J/Kmol.
Entropy, like enthalpy, is a state function, which means that changes in entropy for chemical reactions () can be calculated taking the same approach used with enthalpy and Hess’s Law:
where is the sum of the molar entropies of the products multiplied by their stoichiometric coefficients, m, in the balanced reaction and
is the sum of the molar entropies of the reactants multiplied by their stoichiometric coefficients, n, in the balanced reaction.