Entropy zero-point

Conventional Partial Molal Entropy of (H30)+ and (OH)-. Let us now consider the partial molal entropy for the (1I30)+ ion and the (OH)- ion. If we wish to add an (HsO)+ ion to water, this may be done in two steps we first add an H2O molecule to the liquid, and then add a proton to this molecule. The entropy of liquid water at 25°C is 16.75 cal/deg/mole. This value may be obtained (1) from the low temperature calorimetric data of Giauque and Stout,1 combined with the zero point entropy predicted by Pauling, or (2) from the spectroscopic entropy of steam loss the entropy of vaporization. 2 Values obtained by the two methods agree within 0.01 cal/deg. 

Chapter 9, on entropy and molecular rotation in crystals and liquids, is concerned mostly with statistical mechanics rather than quantum mechanics, but the two appear together in SP 74. Chapter 9 contains one of Pauling s most celebrated papers, SP 73, in which he explains the experimentally measured zero-point entropy of ice as due to water-molecule orientation disorder in the tetrahedrally H-bonded ice structure with asymmetric hydrogen bonds (in which the bonding proton is not at the center of the bond). This concept has proven fully valid, and the disorder phenomenon is now known to affect greatly the physical properties of ice via the... 

This essential absence of longer-range proton order in tetrahedral H-bond networks is the origin of the famous zero-point entropy of ice L. Pauling, J. Am. Chem. Soc. 57 (1935), 2680 and L. Pauling, note 16, pp. 466-468. 

In a perfect crystal at 0 K all atoms are ordered in a regular uniform way and the translational symmetry is therefore perfect. The entropy is thus zero. In order to become perfectly crystalline at absolute zero, the system in question must be able to explore its entire phase space the system must be in internal thermodynamic equilibrium. Thus the third law of thermodynamics does not apply to substances that are not in internal thermodynamic equilibrium, such as glasses and glassy crystals. Such non-ergodic states do have a finite entropy at the absolute zero, called zero-point entropy or residual entropy at 0 K. 

SIDEBAR 5.20 STATISTICAL MECHANICAL MODEL OF ZERO-POINT ENTROPY... 

Kelley et al. (1 ), suggested that there may be a zero-point entropy due to randomness of the cations. The authors estimated S (0 K) from the following alternative assumptions (a) all the Mg and Ti ions are randomly distributed among the latice sites... 

The error limits of the entropy were increased in order to incorporate a possible zero-point entropy of 1.17 J-K -moP. These selections agree with the selections in [92GRE/FUG] but there considered to apply to a-USe2. 

Zero-Point Entropy All entropy capable of movement will escape an absolutely cold enviroimient, meaning that any atomic motion comes to a standstill. This is the subject of the third law of thermodynamics. Entropy caught in a lattice defect is just about immovable at low temperatures. It can therefore neither escape nor contribute... 

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