Question

The measured residual entropy of CH₃D is 10.1 JK^-1 mol ^-1. Explain how this can come about from the possible orientations of the molecules in the crystal and determine the fraction of CH₃D molecules that are randomly oriented.

Answer 1

For CDH_3, the residual entropy comes by asuming four different orientations of monodeuterated methane having same energy in the low temperature crystal.

Residual entropy is calculated using Boltzmann formula

S=k ln W =k ln 2^2N = Nk ln 4= nR ln 4=11.5 J K^-1 mole^-1 which is very close to experintal value of 10.1

k= Boltzmann constant

N= number of molecules

W is the number of permitted orientations and is also the fraction of molecules that are randomly oriented and is calculated as

W= 2^2N

For one mole, N= avpgadro's number