Components of a solution

The same relations are then applied to each component of a solution... 

Solvation increases solubility above predicted values. When the components of a solution possess an abnormally large attraction for each other, solvates are formed. Thus certain oxygen-containing compounds have a great tendency to form hydrates, thus contributing to increased water solubility hydrogen bondir also plays an important role. 

Nonporous Dense Membranes. Nonporous, dense membranes consist of a dense film through which permeants are transported by diffusion under the driving force of a pressure, concentration, or electrical potential gradient. The separation of various components of a solution is related directiy to their relative transport rate within the membrane, which is determined by their diffusivity and solubiUty ia the membrane material. An important property of nonporous, dense membranes is that even permeants of similar size may be separated when their concentration ia the membrane material (ie, their solubiUty) differs significantly. Most gas separation, pervaporation, and reverse osmosis membranes use dense membranes to perform the separation. However, these membranes usually have an asymmetric stmcture to improve the flux. 

Radioactivity The ability possessed by some natural and synthetic isotopes to undergo nuclear transformation to other isotopes, 513 applications, 516-518 biological effects, 528-529 bombardment reactions, 514-516 diagnostic uses, 516t discovery of, 517 modes of decay, 513-514 nuclear stability and, 29-30 rate of decay, 518-520,531q Radium, 521-522 Radon, 528 Ramsay, William, 190 Random polymer 613-614 Randomness factor, 452-453 Raoult s law A relation between the vapor pressure (P) of a component of a solution and that of the pure component (P°) at the same temperature P — XP°, where X is the mole fraction, 268... 

The components of a solution are the pure substances that are mixed to form the solution. If there are two components, one is sometimes called the solvent and the other the solute. These are merely terms of convenience. Since both must intermingle to form the final solution, we cannot make any important distinction between them. When chemists make a liquid solution from a pure liquid and a solid, they usually call the liquid component the solvent. 

In the present state of thermodynamics the calculation of the chemical potential of a component of a solution can be effected explicitly in two cases only ... 

The determination of the chemical potentials of the components of a solution, in terms ofp, T and the masses (or concentrations) is, from what precedes, equivalent to finding the conditions of equilibrium.. 

A solution is a mixture of two or more substances. The substances involved are mixed so intimately (on the atomic scale) that it is not possible to distinguish their individual properties. A solution constitutes a single phase, as distinct from heterogeneous systems which contain several phases. A solution, however, differs from a chemical compound in that its composition is not fixed but can vary over a range. It is customary to designate the major component of a solution as the solvent, and the minor ones as the solutes. A solvent as well as a solute can be a gas, a solid or a liquid. Depending upon the state of the solute and/or the solvent, several types of solutions may exist. 

Expressing the concentrations of the components of a solution in terms of mole fractions or atom fractions is adequate only in some limiting cases of solution behaviour. A more... 

Thermodynamic methods also measure the activity coefficient of the solvent (it should be recalled that the activity coefficient of the solvent is directly related to the osmotic coefficient—Eq. 1.1.19). As the activities of the components of a solution are related by the Gibbs-Duhem equation, the measured activity coefficient of the solvent can readily be used to calculate the activity coefficient of a dissolved electrolyte. 

In the solid or liquid state the activity, a, is introduced to express the chemical potential of the components of a solution. It is defined by... 

The sum of all the mole fractions of the components of a solution should equal 1.00. 

A plot of absorbance versus wavelength may be used to identify a component of a solution or to determine the wavelength of maximum absorbance (maximum molar absorptivity = a). A more common plot is one of absorbance versus concentration. For this type of plot the instrument is set at the wavelength of maximum molar absorptivity and the absorbances of solutions of various known concentrations (c) are measured. This plot should be a straight line. This linear relationship is called Beer s law and has the form of A = abc. The concentration of an unknown solution may be determined by measuring its absorbance and using the plot to find its concentration. 

Two other conventions exist for the choice of standard states for components of a solution. One convention chooses the pure component at 1 bar of pressure, for conformance with the usual standard state for pure components. This choice has the disadvantage that it requires aterm for the effect of pressure in the relation between the chemical potentials of the pure component and of the component in solution. The other convention chooses the pure component at the vapor pressure of the solution. This choice has the disadvantage of having different standard states for each composition of solution. 

Solvent in Solution. We shall use the pure substance at the same temperature as the solution and at its equilibrium vapor pressure as the reference state for the component of a solution designated as the solvent. This choice of standard state is consistent with the limiting law for the activity of solvent given in Equation (16.2), where the limiting process leads to the solvent at its equilibrium vapor pressure. To relate the standard chemical potential of solvent in solution to the state that we defined for the pure liquid solvent, we need to use the relationship... 

Let us compare for a real solution with 5, 2 of the hypothetical l-moM solution. For any component of a solution, from Equation (9.20), we can write... 

The standard state for the heat capacity is the same as that for the enthalpy. For a proof of this statement for the solute in a solution, see Exercise 2 in this chapter. This choice of standard state for components of a solution is different fixjm that used by many thermodynamicists. It seems preferable to the choice of a 1-bar standard state, however, because it is more consistent with the extrapolation procedure by which the standard state is determined experimentally, and it leads to a value of the activity coefficient equal to 1 when the solution is ideal or very dilute whatever the pressure. It is also preferable to a choice of the pressure of the solution, because that choice produces a different standard state for each solution. For an alternative point of view, see Ref. 2. 

Various functions have been used to express the deviation of observed behavior of solutions from that expected for ideal systems. Some functions, such as the activity coefficient, are most convenient for measuring deviations from ideality for a particular component of a solution. However, the most convenient measure for the solution as a whole, especially for mixtures of nonelectrolytes, is the series of excess functions (1) (3), which are defined in the foUowing way. 

The fundamental relationship between the chemical potentials of the two components of a solution at a fixed temperature and pressure is the Gibbs-Duhem Equation (9.34) ... 

Like all the mass transfer operations, liquid extraction is a means of separating the components of a solution, and it is accomplished by bringing the solution into contact with another insoluble phase. The unequal distribution of the components of the solution between the two phases which then results provides the separation. In the case of liquid extraction, of course, the two phases in question are both liquids, but, just as in the other mass transfer operations, intimacy of contact and large interfacial area between the phases are required for rapid diffusional transfer of substance from one phase to the other. 

Electrophoresis is the migration of ions in solution under the influence of an electric field. In the capillary electrophoresis experiment shown in Figure 26-17, components of a solution are separated by applying a voltage of —30 kV from end to end of a fused-silica (Si02) capillary tube that is 50 cm long and has an inner diameter of 25-75 p,m. Different solutes... 

In this section we consider the value of the free energy function in understanding how energetically unfavorable reactions are coupled with energetically favorable ones to do synthetic work. In table 2.4, we made use of the principle that the free energies of all the components of a solution are... 

Occasionally the problem arises of converting values of various thermodynamic functions of the components of a solution that have been determined on the basis of one reference state to values based on another reference state. To do so we equate the two relations of the thermodynamic function of interest obtained for the two reference states, because the value of the function at a given temperature, pressure, and composition must be the same irrespective of the reference state. We also equate the relation for the thermodynamic function for the component in the new reference state expressed in terms of the new reference state to that for the same state expressed in terms of the old reference state. The desired relation is obtained when the chemical potentials of the component in the different standard states are eliminated from the two equations. For examples, we use only the chemical potentials and discuss three cases. 

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