Water entropy, table

Note that this change in entropy is greater than the decrease in entropy of the system, —22.0 J-K 1, which we calculated from the difference in entropy of the solid and liquid states of water in Table 7.2. Therefore, the total change in entropy is positive at — 10°C, and the freezing of water is spontaneous at that temperature. 

Solvent-solvent interactions reduce the entropy of the system and the break-down of the initial state solvation shell should therefore result in a positive contribution to AS which is greater than the negative contribution arising from the additional solvent-solute interactions in the transition state (Heppolette et al., 1959 Robertson, 1960). On this view, changes in the structure of the substrate which alter the extent of the breakdown of the initial state solvation shell will affect AG and AS in opposite directions. A constant AG jAS is therefore not expected for Sijl solvolysis, as observed in water (see Table 6). The predicted positive values of AS have been observed in some S l reactions in water, but not in others (see Table 6), and it seems likely that other factors are also of importance in determining the magnitude of AS. ... 

This is the Clausius-Clapeyron equation. From it, the slope (dpjdT) of the phase boundary and the observed volume difference between the two phases, the entropy of the transition and hence its latent heat can be found. These quantities, evaluated at the various triple points, are shown for ordinary water in table 3.1. 

A rule to bear in mind is that, at the same pressure, temperature and particle number, the entropy of a body will be greater, the heavier the atoms and the weaker the bonding forces. Diamond, which consists of atoms that are rather light and very firmly linked in four directions, has an unusually low entropy per mole. Lead, on the other hand with its heavy, loosely bound atoms, is rather rich in entropy. The characteristics of iron lie somewhere in between it has a medium value of molar entropy. Using the example of water, the table shows how entropy increases by transition from a solid to a liquid state and even more by transition from a liquid to a gaseous state. 

The properties of ions in solution depend, of course, on the solvent in which they are dissolved. Many properties of ions in water are described in Chapters 2 and 4, including thermodynamic, transport, and some other properties. The thermodynamic properties are mainly for 25°C and include the standard partial molar heat capacities and entropies (Table 2.8) and standard molar volumes, electrostriction volumes, expansibilities, and compressibilities (Table 2.9), the standard molar enthalpies and Gibbs energies of formation (Table 2.8) and of hydration (Table 4.1), the standard molar entropies of hydration (Table 4.1), and the molar surface tension inaements (Table 2.11). The transport properties of aqueous ions include the limiting molar conductivities and diffusion coefficients (Table 2.10) as well as the B-coefficients obtained from viscosities and NMR data (Table 2.10). Some other properties of... 

On the basis of the values of AS° derived in this way it appears that the chelate effect is usually due to more favourable entropy changes associated with ring formation. However, the objection can be made that and /3l-l as just defined have different dimensions and so are not directly comparable. It has been suggested that to surmount this objection concentrations should be expressed in the dimensionless unit mole fraction instead of the more usual mol dm. Since the concentration of pure water at 25°C is approximately 55.5 moldm , the value of concentration expressed in mole fractions = cone in moldm /55.5 Thus, while is thereby increased by the factor (55.5), /3l-l is increased by the factor (55.5) so that the derived values of AG° and AS° will be quite different. The effect of this change in units is shown in Table 19.1 for the Cd complexes of L = methylamine and L-L = ethylenediamine. It appears that the entropy advantage of the chelate, and with it the chelate effect itself, virtually disappears when mole fractions replace moldm . ... 

The heat of solution of silver bromide in water at 25°C is 20,150 cal/mole. Taking the value of the entropy and the solubility of the crystalline solid from Tables 44 and 33, find by the method of Secs. 48 and 49 the difference between the unitary part of the partial inolal entropy of the bromide ion Br and that of the iodide ion I-. 

We notice that, although there is only one solute species on the left-hand side, there are two on the right-hand side. The process is therefore accompanied by an increase in entropy, and the AF of the process will contain a term — T AScrat,c Let us first discuss the values of the unitary terms to do this we may carry out the process in a different manner. Choosing two distant water molecules, we transfer a proton from one to the other. According to Table 12, at 25°C the work required amounts... 

Furthermore, we noticed in Table 23 that solutes which have negative B-coefficients in water have large positive B-coefficients when dissolved in methanol. The correlation will therefore be complete, if we find that these same solutes introduce an increase of entropy in water and a decrease in entropy when dissolved in methanol. 

Solutes in Methanol Solution. In Table 23 we have seen that for four solutes in methanol the viscosity //-coefficients are positive. This is the case even for KC1 and KBr, for which the coefficients are negative in aqueous solution. In Sec. 88 it was pointed out that it would be of interest to see whether this inversion is likewise accompanied by a change in sign for the ionic entropy. Although no accurate values for the entropy of solution of salts in methanol arc available, reliable estimates have been made for KC1, KBr, and NaCl.1 Since the /1-coefficients of KC1 and KBr have been determined both in methanol and in water, all the required data are available for these two solutes. The values of A/S" given in Table 29 have been taken from Table 34 in Chapter 12, where the method of derivation is explained. The cratie term included in each of these values is 14 cal/deg, as already mentioned in Sec. 90. 

Table 29. Entropies of Solution and Viscosities in Methanol and in Water...

Let us now consider the same charged sphere immersed in various liquids with widely different values of n. By diluting water with dioxane at constant temperature, we can reduce n from 3.3 X 1022 toward zero. Clearly when n, the number of dipoles per unit volume, approaches zero, the total entropy lost per unit volume must approach zero. From this point of view the expression (170) is seen to have a somewhat paradoxical appearance, since e, which, according to Table 32, is roughly proportional to n, occurs in the denominator. This means that, as the number of dipoles per cubic centimeter decreases, the total amount of entropy lost progressively increases. The reason for this is that, when... 

Turning next to the unitary part of AS0, this is given in Table 36 under the heading — N(dL/dT). It was pointed out in Secs. 90 and 106 that, to obtain the unitary part of AS0 in aqueous solution, one must subtract 16.0 e.u. for a uni-univalent solute, and 24.0 e.u. for a uni-divalent solute. In methanol solution the corresponding quantities are 14.0 and 21.0 e.u. In Table 36 it will be seen that, except for the first two solutes KBr and KC1, the values are all negative, in both solvents. It will be recalled that for KBr and KC1 the B-coefficients in viscosity are negative, and we associate the positive values for the unitary part of the entropy, shown in Table 29, with the creation of disorder in the ionic co-spheres. In every solvent the dielectric constant decreases with rise of temperature and this leads us to expect that L will increase. For KBr and KC1 in methanol solution, we see from Table 36 that dL/dT has indeed a large positive value. On the other hand, when these crystals dissolve in water, these electrostatic considerations appear to be completely overbalanced by other factors. 

As seen from Tables 23 and 21 the ion pair (K+ + Cl") increases the viscosity of methanol but diminishes that of water. We recall that the values for the entropy of solution in Table 29 show a parallel trend in the galvanic cells of Sec. 112 placed back to back, this difference in ionic entropy between aqueous and methanol solutions would alone be sufficient to give rise to an e.m.f. We must ask whether this e.m.f. would be in the same direction, or in the direction opposite to the e.m.f. that would result from a use of (199). 

Table 45. Conventional Partial Molal Entropies of Ions in Water at 25°C...

Tables of standard free energies of formation at 25°C of compounds and ions in solution are given in Appendix 1 (along with standard heats of formation and standard entropies). Notice that, for most compounds, AG is a negative quantity, which means that the compound can be formed spontaneously from the elements. This is true for water ...

Steam tables indicate an arbitrary zero internal energy and entropy for water in its liquid state, at the triple point of water. 

Finally, a 1 1 mixture of acetic and propionic acids containing 2 % of water has been used in order to study the rates of chlorination of polyalkylbenzenes at low temperatures. Second-order rate coefficients were obtained and the values are recorded in Table 58 together with the energies and entropies of activation (which are given with the errors for 95 % confidence limits) from which it was concluded... 

Second-order rate coefficients have been obtained for chlorination of alkyl-benzenes in acetic acid solutions (containing up to 27.6 M of water) at temperatures between 0 and 35 °C, and enthalpies and entropies of activation (determined over 25 °C range) are given in Table 63 for the substitution at the position indicated266. 

Self-Test 7.6B Calculate the standard entropy of vaporization of water at its boiling point (see Table 6.3). 

TABLE 7.2 Standard Molar Entropy of Water at Various Temperatures... 

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... 

The use of direct electrochemical methods (cyclic voltammetry Pig. 17) has enabled us to measure the thermodynamic parameters of isolated water-soluble fragments of the Rieske proteins of various bci complexes (Table XII)). (55, 92). The values determined for the standard reaction entropy, AS°, for both the mitochondrial and the bacterial Rieske fragments are similar to values obtained for water-soluble cytochromes they are more negative than values measured for other electron transfer proteins (93). Large negative values of AS° have been correlated with a less exposed metal site (93). However, this is opposite to what is observed in Rieske proteins, since the cluster appears to be less exposed in Rieske-type ferredoxins that show less negative values of AS° (see Section V,B). 

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