Entropy values solutions

Let us apply this to the values for silver chloride at 25° given above. Dividing 15,740 by the temperature, we obtain for the entropy of solution of crystalline AgCl in its saturated solution the value... 

Since the saturated solutions of AgT and AgCl are both very dilute, it is of interest to examine their partial molal entropies, to see whether we can make a comparison between the values of the unitary terms. As mentioned above, the heat of precipitation of silver iodide was found by calorimetric measurement to be 1.16 electron-volts per ion pair, or 26,710 cal/mole. Dividing this by the temperature, we find for the entropy of solution of the crystal in the saturated solution the value... 

Solutes in Aqueous Solution. As mentioned in See. 88, when we say that we expect to find a correlation between the /1-coefficients of viscosity of various species of ions, and their entropy of solution, this refers only to the unitary part of the entropy, the part associated with the ionic co-sphere. We are inclined to adopt the view that a negative //-coefficient for a pair of ions should be accompanied by a positive increment in entropy, while a positive //-coefficient should be accompanied by a decrease in entropy. The values of AS0, the conventional entropy of solution, to be found in the literature, do not, give a direct answer to this question, since they contain the cratic term, which in water at room temperature amounts to 16 e.u. This must be subtracted. 

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. 

The Number of Dipoles per Unit Volume. The Entropy Change Accompanying Proton Transfers. The Equilibrium between a Solid and Its Saturated Solution. Examples of Values of L and AF°. The Change of Solubility with Temperature. Uni-divalent and Other Solutes. Lithium Carbonate in Aqueous Solution. H2COj in Aqueous Solution. Comparison between HjCOj and Li2C03 in Aqueous Solution. Heats of Solution and the Conventional Free Energies and Entropies of Solution. 

Turning next to AgBr, we see from Table 33 that the value of L increases from 0.931 electron-volt at 15° to 0.935 at 35°, a difference of 0.004. Dividing by 20, we find that the average value of dL/dT in the neighborhood of 25° is 2 X 10 1 electron-volt/deg. Multiplying by 23,060, we find this is equivalent to 4.6 cal/mole. It follows that the value of the conventional entropy of solution AS0 in the neighborhood of 25°C is approximately... 

Heats of Solution and the Conventional Free Energies and Entropies of Solution. Table 34 gives for various common salts the observed values of the heat of solution, and the conventional free energy... 

The heat of solution tends at extreme dilution to the value +4207 cal/mole. Calculate the conventional free energy of solution at 25°C and the conventional entropy of solution. 

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). 

In addition to chemical reactions, the isokinetic relationship can be applied to various physical processes accompanied by enthalpy change. Correlations of this kind were found between enthalpies and entropies of solution (20, 83-92), vaporization (86, 91), sublimation (93, 94), desorption (95), and diffusion (96, 97) and between the two parameters characterizing the temperature dependence of thermochromic transitions (98). A kind of isokinetic relationship was claimed even for enthalpy and entropy of pure substances when relative values referred to those at 298° K are used (99). Enthalpies and entropies of intermolecular interaction were correlated for solutions, pure liquids, and crystals (6). Quite generally, for any temperature-dependent physical quantity, the activation parameters can be computed in a formal way, and correlations between them have been observed for dielectric absorption (100) and resistance of semiconductors (101-105) or fluidity (40, 106). On the other hand, the isokinetic relationship seems to hold in reactions of widely different kinds, starting from elementary processes in the gas phase (107) and including recombination reactions in the solid phase (108), polymerization reactions (109), and inorganic complex formation (110-112), up to such biochemical reactions as denaturation of proteins (113) and even such biological processes as hemolysis of erythrocytes (114). 

This is an expression of Nernst s postulate which may be stated as the entropy change in a reaction at absolute zero is zero. The above relationships were established on the basis of measurements on reactions involving completely ordered crystalline substances only. Extending Nernst s result, Planck stated that the entropy, S0, of any perfectly ordered crystalline substance at absolute zero should be zero. This is the statement of the third law of thermodynamics. The third law, therefore, provides a means of calculating the absolute value of the entropy of a substance at any temperature. The statement of the third law is confined to pure crystalline solids simply because it has been observed that entropies of solutions and supercooled liquids do not approach a value of zero on being cooled. 

The fact that the water molecules forming the hydration sheath have limited mobility, i.e. that the solution is to certain degree ordered, results in lower values of the ionic entropies. In special cases, the ionic entropy can be measured (e.g. from the dependence of the standard potential on the temperature for electrodes of the second kind). Otherwise, the heat of solution is the measurable quantity. Knowledge of the lattice energy then permits calculation of the heat of hydration. For a saturated solution, the heat of solution is equal to the product of the temperature and the entropy of solution, from which the entropy of the salt in the solution can be found. However, the absolute value of the entropy of the crystal must be obtained from the dependence of its thermal capacity on the temperature down to very low temperatures. The value of the entropy of the salt can then yield the overall hydration number. It is, however, difficult to separate the contributions of the cation and of the anion. 

The entropies of solution are almost all positive, the positive values of the entropies of lattice vaporization predominating over the negative entropies of hydration of the pairs of ions. 

Variations of solubility with temperature are illustrated in Fig. 4 for 10 gases in cyclohexane. The slopes of the lines times the gas constant R give values for the entropy of solution. In decending from C2H > to He the... 

Equation 23 is simple to use if entropy values are readily available, but this is seldom the case, especially when solutions are involved. One can often calculate the values he needs from available fundamental data coupled with reasonable assumptions, but this is time-consuming. For present purposes a less rigorous and more practical method of showing the effect of irreversibilities can be used. 

What values might we expect for AHsoln and ASsoin Let s take the entropy change first. Entropies of solution are usually positive because molecular randomness usually increases during dissolution +43.4 J/(K mol) for NaCl in water, for example. When a solid dissolves in a liquid, randomness increases on going from a well-ordered crystal to a less-ordered state in which solvated ions or molecules are able to move freely in solution. When one liquid dissolves in another, randomness increases as the different molecules intermingle (Figure 11.2). Table 11.2 lists values of ASsoin for some common ionic substances. 

The entropy of solution of a nonpolar substance (liquids or gases) in water is always negative at 25°C, and its absolute value decreases as the temperature increases (see Tables IV and V). 

The negative value of the entropy of solution of nonpolar substances in water is an immediate consequence of the small (liquids) or rather negative (gases) enthalpies of solution along with the large and positive Gibbs... 

These examples and some others that are given in Table III show that for selected ions, which form strong complexes, it is possible to make unambiguous structure determinations from solution diffraction data and to obtain direct information on coordination changes that take place during the stepwise formation of complexes. Thermodynamic data provide only indirect information on these structural changes, indicated, for example, by abnormal changes in enthalpy and entropy values or in stability constants for the formation of the complexes. 

This ordering of the water structure makes a negative contribution to the entropy of solution and in certain cases leads to a negative value of AS° in. In fact, this unfavorable entropy contribution resulting from cage formation could be an important reason why nonpolar solutes are insoluble in water. 

Appearance potential data (5) may be used to calculate a value of 5.0 2.0 kcal. per mole for the heat of formation of gaseous HO2. [The indicated uncertainty of 2 kcal. is that estimated by the authors (5).] By estimating the entropy of gaseous HO2 and the enthalpy and entropy of solution, we obtain the following approximate E values. 

The kinetics of the isomerization in tetrachloroethene at 413-433 K show an E/ of 25 1 kcal mol an enthalpy of activation of 24 + 1 kcal moP and an entropy of activation of — 22.4 eu. Changing the solvent to benzonitrile does not increase the rate and is consistent with a nonpolar transition state such as a vinylcarbene, but the entropy value indicates a more concerted mechanism. Indenes were also produced when a solution of the cyclopropene in cyclohexane was heated with copper stearate at 60 C for 30 minutes or when a solution in dichloromethane was heated with trifluoracetic acid, or when 1,3,3-triphenylcyclopropene was treated with [(C2H4)PtCl2]2- Reactions catalyzed by rhodium(I) heptafluorobutanoate have also been reported. ... 

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