Solution thermodynamic functions

The solubilities of 3-2 samarium sulphate hydrates in water and aqueous sulphuric acid have been investigated. The values in water decrease from 0.33 M at 25°C for the octahydrate to 8 x 10 M for lower hydrates at 350°C. The saturation effect of several sets of ionic species on the sulphuric acid solutions were tested by extended Debye-Huckel theory and the 3-2 samarium sulphate was suggested to behave predominantly as a 2-2 sulphate at high temperatures thereby producing Sm2(S04) and sol" ions in solution. Thermodynamic functions for the solubility of samarium sulphate hydrate at 150—250 °C based on its behaviour as a 2-2 salt were presented. 

The evaluation of thermodynamic data follows the same principles as described in the previous chapters but the existence of intermetallic phases or compounds must be taken into account. The extrapolation to well-defined limiting values is restricted. While for solid solutions thermodynamic functions are mostly defined for a composition A Bj ... 

Hydrogen chloride is completely ionized in aqueous solutions at all but the highest concentrations. Thermodynamic functions have been deterrnined electrochemicaHy for equations 7 and 8. Values are given in Table 7. 

The protonation equilibria for nine hydroxamic acids in solutions have been studied pH-potentiometrically via a modified Irving and Rossotti technique. The dissociation constants (p/fa values) of hydroxamic acids and the thermodynamic functions (AG°, AH°, AS°, and 5) for the successive and overall protonation processes of hydroxamic acids have been derived at different temperatures in water and in three different mixtures of water and dioxane (the mole fractions of dioxane were 0.083, 0.174, and 0.33). Titrations were also carried out in water ionic strengths of (0.15, 0.20, and 0.25) mol dm NaNOg, and the resulting dissociation constants are reported. A detailed thermodynamic analysis of the effects of organic solvent (dioxane), temperature, and ionic strength on the protonation processes of hydroxamic acids is presented and discussed to determine the factors which control these processes. 

By a statistical model of a solution we mean a model which does not attempt to describe explicitly the nature of the interaction between solvent and solute species, but simply assumes some general characteristic for the interaction, and presents expressions for the thermodynamic functions of the solution in terms of an assumed interaction parameter. The quasi-chemical theory is of this type, and we have noted that a serious deficiency is its failure to consider the vibrational effects in the solution. It is of interest, therefore, to consider briefly the average-potential model which does include the effect of vibrations. 

The relationship of thermodynamic functions of selective bonding of Hb to a series of carboxylic CP in the variation of the degree of ionization of carboxylic groups is expressed by the effect of enthalpy-entropy compensation (Fig. 18). The compensation effect of enthalpy and entropy components is the most wide-spread characteristic of many reactions in aqueous solutions for systems with a cooperative change in structure [78],... 

The excess molar thermodynamic function Z is defined as the difference in the property Zm for a real mixture and that for an ideal solution. That is,... 

Other thermodynamic functions may be derived from the partition function Q, or from the expression for the osmotic pressure. The chemical potential of the solvent in the solution (not to be confused with the excess chemical potential (mi —within a region of uniform segment expectancy, or density) is given, of course, by ... 

In systems with different components, the values of the thermodynamic functions depend on the nature and number of these components. One distinguishes components forming independent phases of constant composition (the pure components) from the components that are part of mixed phases of variable composition (e.g., solutions). 

The behaviour of most metallurgically important solutions could be described by certain simple laws. These laws and several other pertinent aspects of solution behaviour are described in this section. The laws of Raoult, Henry and Sievert are presented first. Next, certain parameters such as activity, activity coefficient, chemical potential, and relative partial and integral molar free energies, which are essential for thermodynamic detailing of solution behaviour, are defined. This is followed by a discussion on the Gibbs-Duhem equation and ideal and nonideal solutions. The special case of nonideal solutions, termed as a regular solution, is then presented wherein the concept of excess thermodynamic functions has been used. 

The thermodynamic chemical potential is then obtained by averaging the Boltzmann factor of this conditional result using the isolated solute distribution function Sa Sn). Notice that the fluctuation contribution necessarily lowers the calculated free energy. 

The thermodynamic functions (AH, AS, AG(298 K)) of hydrogen peroxide reactions with transition metal ions in aqueous solutions are presented in Table 10.1. We see that AG(298K) has negative values for reactions of hydroxyl radical generation with Cu1+, Cr2+, and Fe2+ ions and for reactions of hydroperoxyl radical generation with Ce4+, Co3+, and Mn3+. 

Carell and Olin (58) were the first to derive thermodynamic functions relating to beryllium hydrolysis. They determined the enthalpy and entropy of formation of the species Be2(OH)3+ and Be3(OH)3+. Subsequently, Mesmer and Baes determined the enthalpies for these two species from the temperature variation of the respective equilibrium constants. They also determined a value for the species Be5(OH) + (66). Ishiguro and Ohtaki measured the enthalpies of formation of Be2(OH)3+ and Be3(OH)3+ calorimetrically in solution in water and water/dioxan mixtures (99). The agreement between the values is satisfactory considering the fact that they were obtained with different chemical models and ionic media. 

In the case of reciprocal systems, the modelling of the solution can be simplified to some degree. The partial molar Gibbs energy of mixing of a neutral component, for example AC, is obtained by differentiation with respect to the number of AC neutral entities. In general, the partial derivative of any thermodynamic function Y for a component AaCc is given by... 

Aqueous hydrazine solutions, materials compatibility for, 13 587t Aqueous hydrazine specifications, 13 586t Aqueous hydrochloric acid reaction with metals, 13 826 thermodynamic functions of, 13 816t uses for, 13 834-835... 

As the laws of dilute solution are limiting laws, they may not provide an adequate approximation at finite concentrations. For a more satisfactory treatment of solutions of finite concentrations, for which deviations from the limiting laws become appreciable, the use of new functions, the activity function and excess thermodynamic functions, is described in the following chapters. 

An alternative approach that is particularly applicable to binary solutions of nonelectrolytes is that of excess thermodynamic functions for the solution instead of activities for the components. That approach is most useful in treatments of phase equihbria and separation processes [1], and it will be discussed in Section 16.7. 

We can summarize our conclusions about the thermodynamic properties of the solute in the hypothetical 1-molal standard state as follows. Such a solute is characterized by values of the thermodynamic functions that are represented by p2. 77m2. and 5m2- Frequently a real solution at some molality m2(j) also exists (Fig. 16.4) for which p.2 = that is, for which the activity has a value of 1. The real solution for which // i2 is equal to H 2 is the one at infinite dilution. Furthermore, 5 n,2 has a value equal to 5 2 for some real solution only at a molahty m2(k) that is neither zero nor m2( j). Thus, three different real concentrations of the solute exist for which the thermodynamic qualities p,2, //mi. and S a respectively, have the same values as in the hypothetical standard state. 

Excess thermodynamic functions can be evaluated most readily when the vapor pressures of both solute and solvent in a solution can be measured. 

Whether obtained from an actual experimentally feasible process or from a thought process, As i Gg, which is obtained from Eq. (2.9) by re-arrangement, pertains to the solvation of the solute and expresses the totality of the solute-solvent interactions. It is a thermodynamic function of state, and so are its derivatives with respect to the temperature (the standard molar entropy of solvation) or pressure. This means that it is immaterial how the process is carried out, and only the initial state (the ideal gaseous solute B and the pure liquid solvent) and the final state (the dilute solution of B in the liquid) must be specified. 

One of the main conceptual differences between the models discussed so far and aqueous solutions is that the units which are used to define thermodynamic functions are often different. This is because they apply to the properties which are actually measured for aqueous systems, and molarity (cj) and molality (m,) are far more common units than mole fraction. Molarity is defined as... 

Entropy, which has the symbol 5, is a thermodynamic function that is a measure of the disorder of a system. Entropy, like enthalpy, is a state function. State functions are those quantities whose changed values are determined by their initial and final values. The quantity of entropy of a system depends on the temperature and pressure of the system. The units of entropy are commonly J K" mole". If 5 has a ° (5°), then it is referred to as standard molar entropy and represents the entropy at 298K and 1 atm of pressure for solutions, it would be at a concentration of 1 molar. The larger the value of the entropy, the greater the disorder of the system. 

In fact, AHinter determines the shape of the total AH for very concentrated defect solutions. Simple statistical descriptions putting AHi ter = 0 (independent defects) fail completely to describe the experimentally determined behaviour of the thermodynamic functions ... 

The magnitude and sign of the distribution constants and of the thermodynamic functions of the transfered solute to the mixed micelle, when compared with those predicted from the binary systems, indicate that the formation of a mixed micelle between BE and NaDec is a highly favorable event. 

When all lengths associated with polymers are measured in units of the Kuhn statistical segment length 2q, the thermodynamic functions AF, II, and g, given by Eqs. (19)-(21), contain two molecular parameters N = L/2q and d s d/2q and two state variables c = (2q)3 c and a. Thus, numerical solution to Eqs. (23) and (31) provides ci, cA, and a as functions of N and d. The results for the phase boundary concentrations have been found to be represented to a good approximation by the following empirical expressions ... 

CHNC equation and compare the solutions and thermodynamic functions from the two equations. 

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