The Third Law of Thermodynamics states that a pure crystalline substance at absolute zero has an entropy of . Mathematically, this formula is expressed as:

where is the Boltzmann constant and W is the number of microstates of a gaseous atom in the system. Because microstates are used to describe this gaseous atom, there has to be at least one or more.

If only one microstate exists for the system, then the entropy is zero , and can only increase from this point. It is therefore mathematically impossible for any element to have a negative standard entropy.

Remark: keep in mind that entropy changes can be negative, but the entropy of pure compounds cannot be negative.