Thermodynamics colligative properties

Osmotic pressure is a thermodynamic colligative property that measures the free energy difference between a polymer solution and a pure solvent [see Eq. (4.62) for the proper definition of osmotic pressure]. In practice, the two are separated by a membrane that allows solvent to pass through easily, but restricts polymer to stay on one side, as shown schematically in Fig.1.21. 

Completely ah initio predictions can be more accurate than any experimental result currently available. This is only true of properties that depend on the behavior of isolated molecules. Colligative properties, which are due to the interaction between molecules, can be computed more reliably with methods based on thermodynamics, statistical mechanics, structure-activity relationships, or completely empirical group additivity methods. 

Osmotic pressure is one of four closely related properties of solutions that are collectively known as colligative properties. In all four, a difference in the behavior of the solution and the pure solvent is related to the thermodynamic activity of the solvent in the solution. In ideal solutions the activity equals the mole fraction, and the mole fractions of the solvent (subscript 1) and the solute (subscript 2) add up to unity in two-component systems. Therefore the colligative properties can easily be related to the mole fraction of the solute in an ideal solution. The following review of the other three colligative properties indicates the similarity which underlies the analysis of all the colligative properties ... 

As noted above, all of the colligative properties are very similar in their thermodynamics if not their experimental behavior. This similarity also extends to an application like molecular weight determination and the kind of average obtained for nonhomogeneous samples. All of these statements are also true of osmotic pressure. In the remainder of this section we describe osmotic pressure experiments in general and examine the thermodynamic origin of this behavior. 

The alternative value, which describes the polymer-solvent interaction is the second virial coefficient, A2 from the power series expressing the colligative properties of polymer solutions such as vapor pressure, conventional light scattering, osmotic pressure, etc. The second virial coefficient in [mL moH] assumes the small positive values for coiled macromolecules dissolved in the thermodynamically good solvents. Similar to %, also the tabulated A2 values for the same polymer-solvent systems are often rather different [37]. There exists a direct dependence between A2 and % values [37]. 

In Chapters 6, 7, and 8, the thermodynamic framework is successively apphed to phase transformations of single-component systems, chemical reactions, and ideal solutions. Included are discussions of the thermodynamics of open systems, the phase rule, and colligative properties. Chapter 9 gives the framework for discussing nonideal multicomponent systems and describes a... 

The Standard-State chemical potentials of substances in the gas, liquid, and .olul phases, as well as of solutes in aqueous solution, can be determined by a v.uiely of experimental methods, among them spectroscopic, colorimetric, mi 11 ib i lily, colligative-property, and electrochemical techniques.817 The accepted values of these fundamental thermodynamic properties are and should be undergoing constant revision under the critical eyes of specialists. It is not the puipose of this book lo discuss the practice of determining values of /i° for all < (impounds of interest in soils. This is best left lo. specialized works on... 

These phenomena that were previously considered anomalies of the mentioned colligative properties of the solutions, have been dealt with by Arrhenius in his effort to explain such anomalies by his well known theory of electrolytic dissociation. According to this explanation the molecules of a dissolved electrolyte partly split to form smaller particles, i. e. ions, which from the thermodynamic point of view are as effective as the undissociated molecules themselves. As the number of particles of matter is thus greater, the manifestations of colligative properties are increased, compared to what they would be with an undissociated electrolyte. 

Since the density p appears in a dimensionless combination here, the concentration dependence of the chemical potential comes with a choice of concentration units. The first term on the right side of Eq. (3.1) expresses the colligative property of dilute solutions that the thermodynamic activity of the solute, is proportional to its concentration, p. The excess chemical potential accounts for intermolecular interactions between the solution molecules, and is given by the potential distribution theorem (Widom, 1963 1982) ... 

The four colligative properties that are of importance are 1) the vapor pressure lowering 2) the elevation of boiling point 3) the freezing-point depression and 4) the osmotic pressure. An attempt is made below to describe qualitatively and quantitatively each colligative property of solutions, with an emphasis on their interrelationship and their application later in measurement and adjustment of the tonicity of solutions, with particular reference to parenteral formulations. Although theoretical derivations based on thermodynamics can be used to show how each of the colligative properties of solution arises and relate to each other, textbooks on physical chemistry for theoretical derivations are recommended. 

Colligative property. A thermodynamic property that depends on the number of particles in solution, and not on the nature of these particles. 

Thermodynamic equations relating ni and ai to various colligative properties are found in any textbook on thermodynamics. The following relationships are obtained on using the expression for ... 

A substance in solution has a chemical potential, which is the partial molar free energy of the substance, which determines its reactivity. At constant pressure and temperature, reactivity is given by the thermodynamic activity of the substance for a so-called ideal system, this equals the mole fraction. Most food systems are nonideal, and then activity equals mole fraction times an activity coefficient, which may markedly deviate from unity. In many dilute solutions, the solute behaves as if the system were ideal. For such ideally dilute systems, simple relations exist for the solubility of substances, partitioning over phases, and the so-called colligative properties (lowering of vapor pressure, boiling point elevation, freezing point depression, osmotic pressure). 

It is assumed that the reader has already been introduced to colligative properties here we will simply state the basic relationships, which will be derived in Chapter 5 from thermodynamics. 

We have seen in Chapter 3 that measurements of the colligative properties are of great value in obtaining molecular weights. The colligative properties of solutions depend largely on the relative amounts of solvent and solute present, and only to a small extent on the nature of the solute species. We can derive the relationship between the colligative properties from thermodynamics. 

A review of dielectric, spectroscopic, thermodynamic, colligative and conductivity properties of complexes of carboxylic acids with pyridines and pyridine A -oxides in non-aqueous solution was reported <94H(37)627). 

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