The entropy of materials at T = 0 K should be zero; however, for some substances, this is not true. The difference between the measured value and expected value of zero is known as residual entropy. This residual entropy arises because the molecules can have a number of different orientations in the crystal and can be estimated by applying Boltzmann’s formula (equation 13.1) with an appropriate value for W.

Eq.13.1

(a) Given that a CO molecule can have one of two possible orientations in a crystal (CO or OC), calculate the residual entropy for a crystal consisting of one mole of CO at T = 0 K.

(b) Ice consists of water molecules arranged in a tetrahedral pattern. In this configuration the question is whether a given hydrogen atom is halfway between two oxygen atoms or closer to one oxygen atom than the other. Starting with a series of basic assumptions, Linus Pauling used the agreement of his calculated residual entropy and the experimental value to determine that a given hydrogen atom is closer to one oxygen atom. An approach used by Pauling to calculate the residual entropy can be summarized as follows.

i) Place four oxygen atoms in a tetrahedral arrangement around a central water molecule.

ii) Determine the number of orientations of the central water molecule, assuming that it forms two hydrogen bonds with the surrounding oxygen atoms.

iii) Using this approach, plus the additional observation made by Pauling that only one-quarter of the orientations identified in (ii) are accessible, calculate the residual entropy of one mole of H₂O.

Transcribed Image Text:

(13.1)