Entropy residual, of ice

The equation for synchronized resonance with L = 4 and v - 2 gives R In 3/2 for the residual entropy of ice (14). This value differs by only 1.1% from that given by calculations that do not involve the approximations made in our simple treatment. It is likely that the accuracy of Eq. 4 is also reasonably high. 

The existence of this residual entropy of ice at very low temperatures was discovered by Giauque and Ashley (ref. 7), who preliminarily ascribed it to the persistence of rotation of ortho-water molecules (comprising 3/< of the total) about their electric-moment axes, giving an entropy of 3/ R In 2 = 1.03 E. U. 

Use your results from parts (a) and (b) to calculate the residual entropy of ice. The measured value is 3.4J/molK. 

Nagle JF (1966) Lattice statistics of hydrogen bonded crystals. I. The residual entropy of ice. J Math Phys 7 1484-1491... 

It is interesting to note that, for L = 4 and v = 2, eqn. (5) gives R n(3/2) for the residual entropy of ice this value differs by only 1% from that given by calculations not involving the approximations made here [48]. 

Pauling, L. The structure and entropy of ice and of other crystals with some randomness of atomic arrangement. J. Amer. Chem. Soc. 57,2680-2684(1935). Nagle, J. F. Lattice statistics of hydrogen bonded crystals. I. The residual entropy of ice. J. Math. Phys. 7, 1484-1491 (1966). 

This result would not have been so remarkable had it not been related to the residual entropy of ice (see Appendix B). 

The agreement between the experimental and the theoretical values of the residual entropy of ice clearly indicates that the distribution of hydrogen atoms within the ice lattice is not unique. There are many possible configurations that are consistent with the two ice conditions. 

Photo 38 Linus Pauling lecturing on hydrogen bonding and ionic hydration, ca. 1975. In the upper right comer of the blackboard is the statistical factor (3/2), which is the basis of Pauling s famous calculation of the residual entropy of ice (SP 73). To the left of (3/2) is depicted a tetrahedrally coordinated water molecule. 

This number has been used to estimate the residual entropy of ice, SQ k nS2 = 0.805 e.u. 

---