Entropy of freezing

Self-Test 7.6B Calculate the standard molar entropy of freezing of benzene at its freezing point (see Table 6.2). 

Icebergs are less ordered than ice. Compare the entropy per molecule of inserting a nonpolar solute into water with the entropy of freezing w ater. 

A smaller increase in entropy occurs when solids melt than when liquids vaporize, because a liquid is only slightly more disordered than a solid (Fig. 7.5). By applying the same argument used for vaporization to the standard entropy of fusion of a substance at its melting (or freezing) point, we obtain... 

An example of the role of the surroundings in determining the spontaneous direction of a process is the freezing of water. We can see from Table 7.2 that, at 0°C, the molar entropy of liquid water is 22.0 J-K 1-mo -1 higher than that of ice... 

SOLUTION We can expect the entropy of the surroundings to increase when water freezes because the heat released stirs up the thermal motion of the atoms in the surroundings (Fig. 7.17). To calculate the change in entropy of the surroundings when water freezes we write AHfrceze = —AHflls = —6.0 kj-mol 1 and T = ( — 10. + 273) K = 263 K. Then... 

Note that the increase in entropy of the surroundings is indeed greater than the decrease in entropy of the system, —22.0 J-K, the value at 0°C (the value at —10.°C is similar), so the overall change is positive and the freezing of water is spontaneous at -10.°C. 

Furthermore, antibodies should be capable of efficiently catalyze reactions with unfavorable entropies of activation by acting as entropy traps the binding energy of the antibody being used to freeze out the rotational and translational degrees of freedom necessary to form the activated complex. This principle has been applied to the design of antibodies that catalyze both unimolecular and bimolecular reactions (see below). 

We can see from Table 7.2 that at 0°C the molar entropy of liquid water is 22.0 J-K -mol 1 higher than that of ice at the same temperature. This difference makes sense, because the molecules in liquid water are more disordered than in ice. It follows that when water freezes at 0°C, its entropy decreases by 22.0 J-K -mol-1. Entropy changes do not vary much with temperature so just below 0°C, we can expect almost the same decrease. Yet we know from everyday experience that water freezes spontaneously below 0°C. Clearly, the surroundings must be playing a deciding role if we can show that their entropy increases by more than 22.0 J-K -mol 1 when water freezes, then the total entropy change will be positive and freezing will be spontaneous. 

Figure 8.34a shows how the standard molar free energies of the liquid and solid phases of a pure solvent vary with temperature. The solid is the more stable phase below the freezing point, where the free energy of the solid is lower than that of the liquid. As before, the presence of a solute in the liquid phase of the solvent raises the entropy of the solvent and hence lowers its free energy (Fig. 8.34b) without affecting the free energy of the solid phase of the solvent (because the solute is insoluble in... 

From our earlier discussion, you might expect that the dissociation of a proton from a carboxylic acid, which increases the number of independent particles, would lead to an increase in entropy. However, this effect is more than counterbalanced by solvation effects. The charged anion and proton both freeze out many of the surrounding molecules of water (fig. 2.4). Thus the ionization of a weak acid decreases the number of mobile molecules and so leads to a decrease in entropy. The entropy of ionization of a typical carboxylic acid in water is about —22 eu/mole. The entropy of dissociation of a proton from a quaternary ammonium... 

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