Volume ideal solutions

These terms are simply additive in ideal solutions. Volume is the most intuitive of these terms, and we illustrate the additivity of volumes in ideal solutions in 10.2.1. This leads to Equation (10.4), the generalized form of which is... 

At the outset it will be profitable to deal with an ideal solution possessing the following properties (i) there is no heat effect when the components are mixed (ii) there is no change in volume when the solution is formed from its components (iii) the vapour pressure of each component is equal to the vapour pressure of the pure substances multiplied by its mol fraction in the solution. The last-named property is merely an expression of Raoult s law, the vapour pressure of a substance is pro-... 

P rtl IMol r Properties. The properties of individual components in a mixture or solution play an important role in solution thermodynamics. These properties, which represent molar derivatives of such extensive quantities as Gibbs free energy and entropy, are called partial molar properties. For example, in a Hquid mixture of ethanol and water, the partial molar volume of ethanol and the partial molar volume of water have values that are, in general, quite different from the volumes of pure ethanol and pure water at the same temperature and pressure (21). If the mixture is an ideal solution, the partial molar volume of a component in solution is the same as the molar volume of the pure material at the same temperature and pressure. 

Gibbs free energy, 311 molar volume, 151 ideal gas law, 147 ideal solution, 331 ilmenite, 662 iminodisuccinate ion. 675 implant, 344 incandescence, 8, 647 inch, A4... 

Fig. 108.—The activity of benzene in solution with rubber plotted against the volume fraction of rubber. The solid curve represents smoothed experimental data of Gee and Treloar. The upper dashed curve represents the calculated ideal curve for an ideal solution of a solute with M = 280,000 dissolved in benzene. The diagonal dashed curve corresponds to ai — Vi. (From the data of Gee and Treloar. )...

For an ideal solution, the partial molal volumes equal the molar volumes of the pure liquid components. Denoting component the main components as 1 and the impurities as > 1, the volume becomes ... 

For mixtures, it is usually sufficient to take the specific volume of the components as additive even for non-ideal solutions, as is illustrated by Example 8.1. 

Here Jv is the volumetric flow rate of fluid per unit surface area (the volume flux), and Js is the mass flux for a dissolved solute of interest. The driving forces for mass transfer are expressed in terms of the pressure gradient (AP) and the osmotic pressure gradient (All). The osmotic pressure (n) is related to the concentration of dissolved solutes (c) for dilute ideal solutions, this relationship is given by... 

Vapour pressure osmometry is the second experimental technique based on colligative properties with importance for molar mass determination. The vapour pressure of the solvent above a (polymer) solution is determined by the requirement that the chemical potential of the solvent in the vapour and in the liquid phase must be identical. For ideal solutions the change of the vapour pressure p of the solvent due to the presence of the solute with molar volume V/1 is given by... 

As seen from Eq. (130) an activity coefficient may deviate significantly from unity at higher salt concentrations. The activity coefficient can therefore also be used as a measure of the deviation of the salt solution from a thermodynamically ideal solution. If the chemical potential of a solute in a (pressure-dependent) standard state of infinite dilution is /x°, we find the standard partial molar volume from... 

Now we turn to an example of experimental significance. If we mix certain quantities of benzene and toluene, which form an ideal solution, the total volume V will be given by the expression... 

The volume function then is homogeneous of the first degree, because the parameter X, which factors out, occurs to the first power. Although an ideal solution has been used in this illustration. Equation (2.31) is true of all solutions. However, for nonideal solutions, the partial molar volume must be used instead of molar volumes of the pure components (see Chapter 9). 

No change in volume occurs when pure components that form an ideal solution are mixed. This statement can be validated for an ideal solution as follows. At any fixed... 

Altered thermodynamic activity of proteins in solution arises when unreactive (or inert) macromolecules are added to a solution and occupy more than a few percent of total solution volume. Terms such as unreactive , "background, or inert are used to emphasize that the added protein need not exhibit and direct binding interaction with the protein of interest. Instead, the consequences have more to do with molecular crowding, and approximate theoretical models show that this effect depends on the shapes and sizes of the macromolecules. Thus, biological fluids are anything but ideal or dilute solutions. 

One of the approaches to calculating the solubility of compounds was developed by Hildebrand. In his approach, a regular solution involves no entropy change when a small amount of one of its components is transferred to it from an ideal solution of the same composition when the total volume remains the same. In other words, a regular solution can have a non-ideal enthalpy of formation but must have an ideal entropy of formation. In this theory, a quantity called the Hildebrand parameter is defined as ... 

Consider the equilibrium in a vertical cylinder of suspension of density pi in a suspension medium of density of unit cross-section and height. o o. If at a height x there are n particles per unit volume and at a height xJr x,n->cM particles per unit volume the difference in osmotic pressures due to the particles on the assumption that the suspension conforms to the laws of an ideal solution will be... 

In general, if rarh = 1 and if the chain termination constants for oxidations of A alone and B alone are the same ( ideal reactivities), then the total rates of oxidation of mixtures at constant rate of initiation are a linear function (for ideal solutions) of the volume % of B in the A—B feed. Russell (30,31, 32) and Alagy and co-workers (1, 2,3,4, 8, 33) have shown for several systems that when B has a higher termination constant than A and when B is sufficiently reactive, B can reduce (sometimes fourfold) the rate of oxidation to less than the ideal rate. A secondary objective was to see if there were any other important abnormalities (particularly rates much greater than ideal) in co-oxidations of hydrocarbons. 

The concept of ideal solutions (41) was used by the industry early in the period covered by this discussion. Hydrocarbons follow this type of behavior with reasonable accuracy at pressures somewhat above their vapor pressures. However, important divergences occur at higher pressures. Serious deviations from ideal solutions are experienced for components at reduced temperatures markedly greater than unity. Lewis (48) proposed a modified type of ideal solution by neglecting the volume of the liquid phase. This modification simplified the application of the concept. The Lewis generalization has been widely employed by the industry. 

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