Raoult solution

Figure 5 shows the isothermal data of Edwards (1962) for n-hexane and nitroethane. This system also exhibits positive deviations from Raoult s law however, these deviations are much larger than those shown in Figure 4. At 45°C the mixture shown in Figure 5 is only 15° above its critical solution temperature. Again, representation with the UNIQUAC equation is excellent.

Raoult s law When a solute is dissolved in a solvent, the vapour pressure of the latter is lowered proportionally to the mole fraction of solute present. Since the lowering of vapour pressure causes an elevation of the boiling point and a depression of the freezing point, Raoult s law also applies and leads to the conclusion that the elevation of boiling point or depression of freezing point is proportional to the weight of the solute and inversely proportional to its molecular weight. Raoult s law is strictly only applicable to ideal solutions since it assumes that there is no chemical interaction between the solute and solvent molecules. 

Using the Gibbs-Diihem equation ((A2.1.27) with dT = 0, dp = 0), one can show that the solvent must obey Raoult s law over the same concentration range where Hemy s law is valid for the solute (or solutes) ... 

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-... 

Let us consider a mixture forming an ideal solution, that is, an ideal liquid pair. Applying Raoult s law to the two volatile components A and B, we have ... 

An ideal gas obeys Dalton s law that is, the total pressure is the sum of the partial pressures of the components. An ideal solution obeys Raoult s law that is, the partial pressure of the ith component in a solution is equal to the mole fraction of that component in the solution times the vapor pressure of pure component i. Use these relationships to relate the mole fraction of component 1 in the equilibrium vapor to its mole fraction in a two-component solution and relate the result to the ideal case of the copolymer composition equation. 

Finally, we note that Raoult s law (see Example 7.1) is a limiting law that is observed to apply in all solutions in the limit Xj 1 ... 

A solution which obeys Raoult s law over the full range of compositions is called an ideal solution (see Example 7.1). Equation (8.22) describes the relationship between activity and mole fraction for ideal solutions. In the case of nonideal solutions, the nonideality may be taken into account by introducing an activity coefficient as a factor of proportionality into Eq. (8.22). 

This is an expression of Raoult s law which we have used previously. Freezing point depression. A solute which does not form solid solutions with the solvent and is therefore excluded from the solid phase lowers the freezing point of the solvent. It is the chemical potential of the solvent which is lowered by the solute, so the pure solvent reaches the same (lower) value at a lower temperature. At equilibrium... 

At equilibrium, a component of a gas in contact with a liquid has identical fugacities in both the gas and liquid phase. For ideal solutions Raoult s law applies ... 

For systems other than air—water vapor or for total system pressures different from 101.3 kPa (1 atm), humidity diagrams can be constmcted if basic phase-equihbria data are available. The simplest of these relations is Raoult s law, apphcable at small solute concentrations ... 

When both phases form ideal thermodynamic solutions, ie, no heat of mixing, no volume change on mixing, etc, Raoult s law apphes ... 

Idea.1 Liquid Solutions. Two limiting laws of solution thermodynamics that are widely employed are Henry s law and Raoult s law, which represent vapor—Hquid partitioning behavior in the concentration extremes. These laws are used frequently in equiUbrium problems and apply to a variety of real systems (10). 

In equation 21 the vapor phase is considered to be ideal, and all nonideaHty effects are attributed to the Hquid-phase activity coefficient, y. For an ideal solution (7 = 1), equation 21 becomes Raoult s law for the partial pressure,exerted by the Hquid mixture ... 

The solvent and the key component that show most similar liquid-phase behavior tend to exhibit little molecular interactions. These components form an ideal or nearly ideal liquid solution. The ac tivity coefficient of this key approaches unity, or may even show negative deviations from Raoult s law if solvating or complexing interactions occur. On the other hand, the dissimilar key and the solvent demonstrate unfavorable molecular interactions, and the activity coefficient of this key increases. The positive deviations from Raoult s law are further enhanced by the diluting effect of the high-solvent concentration, and the value of the activity coefficient of this key may approach the infinite dilution value, often aveiy large number. 

Pure-component vapor pressures can be used for predicting solu-bihties for systems in which RaoiilFs law is valid. For such systems Pa = Pa a, where p° is the pure-component vapor pressure of the solute andp is its partial pressure. Extreme care should be exercised when attempting to use pure-component vapor pressures to predict gas-absorption behavior. Both liquid-phase and vapor-phase nonidealities can cause significant deviations from the behavior predicted from pure-component vapor pressures in combination with Raoult s law. Vapor-pressure data are available in Sec. 3 for a variety of materials. 

It follows that die separation of cadmium must be carried out in a distillation column, where zinc can be condensed at the lower temperamre of each stage, and cadmium is preferentially evaporated. Because of the fact that cadmium-zinc alloys show a positive departure from Raoult s law, the activity coefficient of cadmium increases in dilute solution as the temperature decreases in the upper levels of the still. The separation is thus more complete as the temperature decreases. 

At the end of the 1930s, the only generally available method for determining mean MWs of polymers was by chemical analysis of the concentration of chain end-groups this was not very accurate and not applicable to all polymers. The difficulty of applying well tried physical chemical methods to this problem has been well put in a reminiscence of early days in polymer science by Stockmayer and Zimm (1984). The determination of MWs of a solute in dilute solution depends on the ideal, Raoult s Law term (which diminishes as the reciprocal of the MW), but to eliminate the non-ideal terms which can be substantial for polymers and which are independent of MW, one has to go to ever lower concentrations, and eventually one runs out of measurement accuracy . The methods which were introduced in the 1940s and 1950s are analysed in Chapter 11 of Morawetz s book. 

Raoult s law States that at equilibrium, the partial pressure of a solute vapor over a liquid mixture is equal to the vapor pressure of the pure solute at the given temperature times the mole fraction of the solute liquid component in the mixture. 

Some organic compounds can be in solution with water and the mixture may still be a flammable mixture. The vapors above these mixtures such as ethanol, methanol, or acetone can form flammable mixtures with air. Bodurtha [39] and Albaugh and Pratt [47] discuss the use of Raoult s law (activity coefficients) in evaluating the effects. Figures 7-52A and B illustrate the vapor-liquid data for ethyl alcohol and the flash point of various concentrations, the shaded area of flammability limits, and the UEL. Note that some of the plots are calculated and bear experimental data verification. 

Henry s Law applies to the vapor pressure of the solute in dilute solutions, and is a modification of Raoult s Law Henry s Law—... 

Raoult s Law. The molar composition of a liquid phase (ideal solution) in equilibrium with its vapor at any temperature T is given by... 

Molecular Weight Determination by Application of Raoult s Law. If a small amount (m in grams) of a nonvolatile, nonionized substance (solute, 2) is dissolved in m, grams of a volatile liquid (solvent, 1), it experiences a lowering of vapor pressure from the pure solvent value (P ) to the solution value (P) at the system temperature. This is a consequence of Raoult s law because the total vapor pressure of the dilute solution (x 1) is given by P = x P + x P = 1 -... 

Henry s Law. This is an empirical formulation that describes equilibrium solubilities of noncondensable gases in a liquid when Raoult s law fails. It states that the mole fraction of a gas (solute i) dissolved in a liquid (solvent) is proportional to the partial pressure of the gas above the liquid surface at given temperature. That is,... 

Raoult s law over the whole range of composition, this is because the total change in the free energy, on mixing the particles, is given by nAkT In xA + n0kT In xB, where xA is the mole fraction of A in the solution and xB is the mole fraction of B. For a solution that contains in addition nc particles of species C, and so on, terms must be added, thus... 

At the same time it is recognized that the pairs of substances which, on mixing, are most likely to obey Raoult s law are those whose particles are most nearly alike and therefore interchangeable. Obviously no species of particles is likely to fulfill this condition better than the isotopes of an element. Among the isotopes of any element the only difference between the various particles is, of course, a nuclear difference among the isotopes of a heavy element the mass difference is trivial and the various species of particles are interchangeable. Whether the element is in its liquid or solid form, the isotopes of a heavy element form an ideal solution. Before discussing this problem we shall first consider the solution of a solid solute in a liquid solvent. 

In this equation, Pt is the vapor pressure of solvent over the solution, P° is the vapor pressure of the pure solvent at the same temperature, and Xj is the mole fraction of solvent. Note that because Xj in a solution must be less than 1, P must be less than P°. This relationship is called Raoult s law Francois Raoult (1830-1901) carried out a large number of careful experiments on vapor pressures and freezing point lowering. 

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... 

But Langmuir s isotherm for the solute entails the generalized form of Raoult s law (Eq. 13) as a necessary thermodynamic consequence. This can best be seen from the Gibbs-Duhem equation,... 

These results were all experimentally verified by Raoult, who found the value 0 0104 for the mean molecular lowering with 12 solvents and a variety of organic solutes, in a solution with... 

Equation (7) is true for volatile as well as involatile solutes, provided n denotes the number of mols of solute in the liquid phase, andp is the -partial pressure of the vapour of the solvent, the latter being independent of the presence of other gases in the vapour space. The sole remaining problem is therefore the determination of the partial pressure of the solute, or, what will lead to this, the total pressure in the vapour space. The partial pressure of the solvent is, from Raoult s law ... 

Raoult expressed his results in terms of the molecular depression , for a mol. of solute in 100 grams of solvent. The volume of the solvent is 100/p, and this may be taken as the volume of the dilute solution. The corresponding osmotic pressure P, on the assumption that the law of proportionality holds good at this concentration (which is only a fictitious extrapolation) is given by ... 

Raoult observed that many substances dissolved in benzene, nitrobenzene, and ethylene dibromide, gave depressions only half the normal, and this he explained as due to a polymerisation of the solute to double molecules ... 

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