Residual Entropy
The third law of thermodynamics says that the entropy of pure perfect crystalline substance is zero at absolute zero temperature. But in actual practice, it has been found that certain chemical reactions between crystalline substances, do not have ΔS = 0 at 0oK. It means that in the crystalline state, certain substances (i.e. CO, N2O, H2 or H2O etc.) have some definite value of entropy even at absolute zero temperature. This entropy is known as residual entropy and can be obtained by the following relation-
S = klnW
Where k is Boltzmann constant and the W is the thermodynamic probability which represents the number of equally probable orientations of the molecule under consideration.
For example, consider a sample of N number of carbon monoxide molecules. Since each molecule can have two orientations that are equally probable (CO CO OC CO OC OC), the thermodynamic probability will be W = 2N.
The residual entropy is-
S = klnW = kln2N
S = kN ln2
For one mole of sample kN = R, so the above equation becomes-
S = R ln2
or, S = 2.303R log2 = 5.85 JK−1mol−1
he value of residual entropy differs for different crystals according to the value of W, which is thermal probability. It depends on the maximum number of ways in which each molecule inside a crystal can be arranged in a different orientation. The third law has no practical application as the entropy cannot be zero. There is no possibility of a perfect crystal.
