Solubility and Thermodynamics

It follows directly from the first law of thermodynamics that if a quantity of heat Q is absorbed by a body then part of that heat will do work W and part will be aecounted for by a rise in the internal energy AE of that body, i.e. 

This expression states that there will be energy free to do work when Q exceeds AE. Expressed in another way work ean be done, that is an action can proceed, if AE - 0 is negative. If the difference between AE and Q is given the symbol AA, then it can be said that a reaction will proceed if the value of AA is negative. Since the heat term is the product of temperature T and change of entropy AS, for reactions at constant temperature then 

AA is sometimes referred to as the change in work function. This equation simply states that energy will be available to do work only when the heat absorbed exceeds the increase in internal energy. For proeesses at constant temperature and pressure there will be a rise in the heat content (enthalpy) due both to a rise in the internal energy and to work done on expansion. This can be expressed as 

This is the so-called free energy equation where AF (equal to AA H- FAT) is known as the free energy. 

It has already been shown that a measure of the total work available is given by the magnitude of -A A. Since some of the work may be absorbed in expansion (FAT) the magnitude of -AF gives an estimate of the net work or free energy available. 

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ALC/BEL] Alcock, C. B., Belford, T. N., Thermodynamics and solubility of oxygen in liquid metals from E.M.F. measurements involving solid electrolytes. Part 1 lead, Trans. Faraday Soc., 60, (1964), 822-835. Cited on pages 107,310. 

Wad] Wada, H., Thermodynamics and Solubility of Carbides in the Ferretic Fe-Mo-C Alloys at... 

Prediction of Organic Crystal Structure, Thermodynamics, and Solubility... 

M. J. Schnieders, J. Baltrusaitis, Y. Shi, G. Chattree, L. Zheng, W. Yang, and P. Ren, /. Chem. Theory Comput., 8(5), 1721-1736 (2012). The Structure, Thermodynamics and Solubility of Organic Crystals from Simulation with a Polarizable Force Field. 

Whatever the specific system or situation, the key issue in diffusion interphase adhesion is physical compatibility. This is once again, a thermodynamic issue and may be quantified in terms of mutual solubility. Most of the strategies for predicting diffusion interphase adhesion are based on thermodynamic compatibility criteria. Thus it is appropriate to review briefly the relevant issues of solution thermodynamics and to seek quantitative measures of compatibility between the phases to be bonded. 

The thermodynamic behaviour of silver and solubilities of silver and its compounds have been computed in an electrochemical study of silver in potassium hydroxide solutions at high temperature ". ... 

Many subtleties associated with ED, for instance, accompanying thermodynamic cooling issues, failure processes, and effects of localized stresses, are discussed in detail in the extensive review on this topic by Briscoe et al. Other workers have observed similar fracture effects arising from rapid temperature increases while maintaining pressure the connection with ED is via Henry s law linking dissolved gas concentration and solubility coefficient, and the fact that solubility coefficient decreases (in an Arrhenius fashion, as it happens) for readily condensable (i.e., less volatile) gases when temperature increases. 

Su YO, Kuwana T, Chen SM. 1990. Electrocatalysis of oxygen reduction by water-soluble iron porphyrins. Thermodynamic and kinetic advantage studies. J Electroanal Chem 288 177. 

The physical properties of the mobile phase, mainly viscosity, diffusivity and solubility, affect the flow characteristics, column efficiency (kinetics), and retention (thermodynamics) in the chromatographic process. These physical properties are affected by temperature. Chromatographic techniques, although basically simple in... 

A chemical system is a mixture of individual components. Chemical systems can be described by interactions that occur within the system and by the effect these processes have on the chemical composition and phases of the system. Interactions that change the chemical structure of system components are called chemical reactions. (Other interactions, such as processes that alter the solubility of system components, change the system without altering chemical structures.) Whether one reaction or a set of reactions occurs and how quickly the reaction proceeds are determined by the thermodynamics and kinetics of the system. 

Dixon, J. and Johnston, K. (1991) Molecular thermodynamics of solubilities in gas antisolvent crystallization. AIChE Journal, 37 (10), 1441-1449. 

Aqueous solubility, potency and permeability are three factors under medicinal chemistry control that must be optimized to achieve a compound with acceptable oral absorption. Typically, a lead (chemistry starting point) is deficient in all three parameters. The inter-relationships of these three parameters has been described in a series of publications from Pfizer researchers [7, 8]. Figure 9.1 depicts graphically the minimum acceptable solubility as a function of projected clinical potency and intestinal permeability. A minimum thermodynamic aqueous solubility of 52... 

McFarland et al. recently [1] published the results of studies carried out on 22 crystalline compounds. Their water solubilities were determined using pSOL [21], an automated instrument employing the pH-metric method described by Avdeef and coworkers [22]. This technique assures that it is the thermodynamic equilibrium solubility that is measured. While only ionizable compounds can be determined by this method, their solubilities are expressed as the molarity of the unionized molecular species, the intrinsic solubility, SQ. This avoids confusion about a compound s overall solubility dependence on pH. Thus, S0, is analogous to P, the octanol/water partition coefficient in both situations, the ionized species are implicitly factored out. In order to use pSOL, one must have knowledge of the various pKas involved therefore, in principle, one can compute the total solubility of a compound over an entire pH range. However, the intrinsic solubility will be our focus here. There was one zwitterionic compound in this dataset. To obtain best results, this compound was formulated as the zwitterion rather than the neutral form in the HYBOT [23] calculations. 

However, from our point of view, there remains a lack of sufficiently precise and reliable methods to compute thermodynamic water solubility. The majority of methods work only for congeneric series of compounds, and many have not been developed to function in areas of pharmaceutical research using drug-like molecules. Most of the methods do not use the three-dimensional structure of the compounds, while some depend on previous knowledge of certain experimental properties of the compounds of interest. Moreover, all of the methods are dependent upon the quality of solubility values in the training set used to develop the model indeed, this latter point is a critical limitation that has a major influence on solubility estimations. 

When in solid solution in the solid state, an impurity will alter the crystallinity by introducing impurity defects into the crystal lattice, thereby changing the thermodynamic and other physical properties of the solid, including the solubility and dissolution rate [2,37]. Prolonged equilibration of the solid state with the saturated solution, however, usually leads to recrystallization of the solute and to a consequent return of the crystallinity and the measured solubility of the solid state to that of the pure, highly crystalline solid. 

The thermodynamic activity of nickel in the nickel oxide layer varies from unity in contact with the metal phase, to 10 8 in contact with the gaseous atmosphere at 950 K. The sulphur partial pressure as S2(g) is of the order of 10 30 in the gas phase, and about 10 10 in nickel sulphide in contact with nickel. It therefore appears that the process involves the uphill pumping of sulphur across this potential gradient. This cannot occur by the counter-migration of oxygen and sulphur since the mobile species in the oxide is the nickel ion, and the diffusion coefficient and solubility of sulphur in the oxide are both very low. 

This expression has been written in terms of concentration if activity coefficients sue known or estimated, then a thermodynamically ideal solubility product may be obtained from the Emalogous product of ionic activities. As the concentration of ions in solutions of lanthanide fluorides is low, the concentration and activity solubility products will not differ markedly, although activity coefficients for these salts of 3 + cations are significantly less than unity even in such dilute solutions (4a). 

One of the most basic requirements in analytical chemistry is the ability to make up solutions to the required strength, and to be able to interpret the various ways of defining concentration in solution and solids. For solution-based methods, it is vital to be able to accurately prepare known-strength solutions in order to calibrate analytical instruments. By way of background to this, we introduce some elementary chemical thermodynamics - the equilibrium constant of a reversible reaction, and the solubility and solubility product of compounds. More information, and considerably more detail, on this topic can be found in Garrels and Christ (1965), as well as many more recent geochemistry texts. We then give some worked examples to show how... 

The design of crystallization processes for the manufacture of Active Pharmaceutical Ingredients is a significant technical challenge to Process Research and Development groups throughout the Pharmaceutical and related industries. It requires an understanding of both the thermodynamic and kinetic aspects of crystallization, to ensure that the physical properties of the product will consistently meet specification. Failure to address these issues may lead to production problems associated with crystal size, shape and solubility, and to dissolution and bioavailability effects in the formulated product. 

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