Water molecule translational entropy

Molecular Nature of Steam. The molecular stmcture of steam is not as weU known as that of ice or water. During the water—steam phase change, rotation of molecules and vibration of atoms within the water molecules do not change considerably, but translation movement increases, accounting for the volume increase when water is evaporated at subcritical pressures. There are indications that even in the steam phase some H2O molecules are associated in small clusters of two or more molecules (4). Values for the dimerization enthalpy and entropy of water have been deterrnined from measurements of the pressure dependence of the thermal conductivity of water vapor at 358—386 K (85—112°C) and 13.3—133.3 kPa (100—1000 torr). These measurements yield the estimated upper limits of equiUbrium constants, for cluster formation in steam, where n is the number of molecules in a cluster. 

Translational entropy of mobile ions and water molecules (i A, C, OH—,... 

Entropy effects. The replacement of the coordination shell of the cation by a multidentate ligand has also the very important effect of decreasing the free energy of the system by the increase in translational entropy of the displaced water molecules. If there were no variation in solvation and internal entropies of the free ligand and of the complexes, the increase in translational entropy would amount to about 8 e.u., where x is the number of displaced solvent molecules minus one (38). This estimate is, however, very inaccurate large deviations are expected, especially in the case of complicated multidentate ligands for which complex formation may produce appreciable internal and solvation entropy changes. 

The entropy decrease resulting from solvation. When a salt is dissolved in water, the entropy of the dissociated cations and anions increases because of the increased possibilities for translation and rotation. But at the same time the movement of water molecules becomes restricted in the vicinity of the ions. The net effect is frequently a decrease in the entropy of the solution. Such a decrease in entropy can occur if the solution releases heat to the surroundings, because this increases the entropy of the surroundings. 

The average entropy decrease on adsorption of approximately 0.75 erg per sq. cm. when converted to a molar basis from the volume adsorbed at saturation vapor pressure is 1.8 0.4 e.u. less than liquid water at 25° C. or about that of liquid water at 0° C. The large uncertainty is due to difficulty in extrapolating to P/P° = 1. Since the entropy of adsorbed water molecules in the outermost layer must approximate that of liquid water at 25° C., then the inner layers, to maintain the average of 1.8 e.u., must be icelike with loss of translational modes. 

One has to know the free volume available to the unbonded molecule, and its temperature dependence, so that the translational entropy may be calculated. The term V g may be found from sound velocity measurements [Eq. (2.96)]. If one takes a number of unassociated liquids and plots their free volumes Vy- obtained from the velocity of soimd against their molar weights, an extrapolation through a molar weight of 18 will give for a freely rotating monomer of water. A value of 0.2 cm mol for is obtained. The temperature dependence of V g is obtained from the integration of the heat capacity... 

Another criterion which may be useful for a distinction between the Al and A2 mechanisms is the evaluation of the entropy change on activation, AS. In the A2 mechanism, the loss of translational and rotational freedom of the attacking water molecule in the transition state leads to a substantial negative contribution to AS. Therefore, AS values for A2 reactions are expected to be much more negative than for Al reactions. 

By analyzing experimental data Akmal and Munoz [18] conclude that the top of the free energy barrier is reached when the protein in its search for the native state reaches a critical native density , i.e. is close enough to the native state to expel the interstitial water molecules and form a folding nucleus. At that point the stabilization energy starts to overcome the decrease of conformational entropy. In addition, the expelled interstitial solvent gains translational entropy as well [19]. 

The thermodynamic stability constant k which represents the free energy of complex formation (AF° = — RT In k ) can be subdivided into heat and entropy terms (AF° = AH° — TAS°). The entropy of complex formation has been discussed elsewhere (Cobble, 1953 Schwarzenbach, 1954 Williams, 1954). The factors involved include (1) the size and geometry of metal ions and ligand molecules 2) the change in the number of molecules in the system on complex formation as they affect translational freedom (3) restrictions on the freedom of rings imposed by chelation and other restrictions of internal rotation and (4) the entropy of hydration for the water molecules displaced by ligands. 

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