Raoult effect

Because the detection of these particles is based on the condensation of a liquid, usually either water or butanol, surface effects come into play. The condensation process is the transfer of excess material in one of both phases gas or aerosol and is driven by evaporation/subUmation and condensation, which take place in parallel. Is the surface of an aerosol particle curved molecules can enter the gas phase more easily and the interaction between absorbed molecules is less in strength (Seinfeld and Pandis 2006). Therefore the saturation above a curved, i.e. smaller particle is larger and particles tend to evaporate. This effect is called Kelvin effect after Lord Kelvin, who figured out and explained the effect about 150 years ago. The second effect of relevance is the solution effect. Two different compounds with the potential to get dissolved in each other as for instance a salt in water, will stick to each other even at subsaturation because the evaporation/sublimation is drastically reduced (Raoult effect) (Friedlander 2000). 

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-... 

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. 

Other approaches to account for various effects have been developed. Negative deviations from Raoult s law (i.e., y < 1) are frequently... 

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. 

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... 

Increasing the temperature increases the vapor pressures and moves the liquid and vapor curves to higher pressure. This effect can best be seen by referring to Figure 8.14, which is a schematic three-dimensional representation for a binary system that obeys Raoult s law, of the relationship between pressure, plotted as the ordinate, mole fraction plotted as abscissa, and temperature plotted as the third dimension perpendicular to the page. The liquid and vapor lines shown in Figure 8.13 in two dimensions (with Tconstant)... 

A hypothetical solution that obeys Raoult s law exactly at all concentrations is called an ideal solution. In an ideal solution, the interactions between solute and solvent molecules are the same as the interactions between solvent molecules in the pure state and between solute molecules in the pure state. Consequently, the solute molecules mingle freely with the solvent molecules. That is, in an ideal solution, the enthalpy of solution is zero. Solutes that form nearly ideal solutions are often similar in composition and structure to the solvent molecules. For instance, methylbenzene (toluene), C6H5CH, forms nearly ideal solutions with benzene, C6H6. Real solutions do not obey Raoult s law at all concentrations but the lower the solute concentration, the more closely they resemble ideal solutions. Raoult s law is another example of a limiting law (Section 4.4), which in this case becomes increasingly valid as the concentration of the solute approaches zero. A solution that does not obey Raoult s law at a particular solute concentration is called a nonideal solution. Real solutions are approximately ideal at solute concentrations below about 0.1 M for nonelectrolyte solutions and 0.01 M for electrolyte solutions. The greater departure from ideality in electrolyte solutions arises from the interactions between ions, which occur over a long distance and hence have a pronounced effect. Unless stated otherwise, we shall assume that all the solutions that we meet are ideal. 

This molecular view of Figure 12-11 suggests that the extent of vapor pressure lowering will depend on the fraction of solvent molecules that has been replaced. In other words, the vapor pressure should be proportional to the mole fraction of the solvent. The molecular view also suggests that this effect does not depend on the nature of the solute, but only on its mole fraction. Experiments show that this is often the case, particularly for dilute solutions. A simple equation, Raoult s law, expresses this proportionality between vapor pressure and mole fraction V V /Jpuj-g solvent Raoulfs law states that the vapor pressure of a solution is the... 

The dissolution of a solute into a solvent perturbs the colligative properties of the solvent, affecting the freezing point, boiling point, vapor pressure, and osmotic pressure. The dissolution of solutes into a volatile solvent system will affect the vapor pressure of that solvent, and an ideal solution is one for which the degree of vapor pressure change is proportional to the concentration of solute. It was established by Raoult in 1888 that the effect on vapor pressure would be proportional to the mole fraction of solute, and independent of temperature. This behavior is illustrated in Fig. 10A, where individual vapor pressure curves are... 

The ammonia partial pressures given in Tables 1 and 2 are based on the concentration of ammonia found in the vapor stream times the total pressure. The actual pressures applied at each run condition are summarized in Table 3 where the pressures varied from 15 psia at 80°C to 90 psia at 120°C. Because nitrogen was used as a pressurizing fluid, the partial pressure of water and the total pressure excluding nitrogen have been computed in Tables 1 and 2 based on Raoult s law for water as noted at the bottom of Table 1. Raoult s law applies for the partial pressure of water because the activity coefficient of water is virtually unity at the low levels of ammonia used in the liquid phase. Minor effects due to vapor non- ideality have not been applied. 

At temperatures well below UCST, solubilities of hydrocarbons in water or water in hydrocarbons drop to very low values. The solutions are very nearly ideal in the Henry s law sense, and the isotope effects on solubility can be directly interpreted as the isotope effect on the standard state partial molar free energy of transfer from the Raoult s law standard state to the Henry s law standard state. Good examples include the aqueous solutions of benzene, cyclohexane, toluene,... 

In all the above discussions regarding liquid-vapor equilibria we have assumed that our representative systems were ideal, that is, there are no differences in attractions between molecules of different types. Few systems are ideal and most show some deviation from ideality and do not follow Raoult s law. Deviations from Raoult s law may be positive or negative. Positive deviations (for binary mixtures) occur when the attraction of like molecules, A-A or B-B, are stronger than unlike molecules, A-B (total pressure greater than that computed for ideality). Negative deviations result from the opposite effects (total pressure lower than that computed for ideality). A mixture of two liquids can exhibit nonideal behavior by forming an azeotropic mixture (a constant boiling mixture). 

Figure 17.3b compares G at two temperatures for the (cyclohexane+ hexane) system. The positive G indicates positive deviations from Raoult s law. The effect of temperature on G is related to the if results through the equation1... 

The Raoult law, the decrease of vapour pressure ps of a solution proportional to the solute concentration is a consequence of the model too. Solute molecules of which the own vapour pressure can be neglected have to be in the holes of the model (Fig. 1 right). Therefore, ps of the solvent decreases corresponding to Raoult s law. Now this effect is reduced by the increase of the sum of pair potentials because the coordina-... 

Clearly, when B22 = B, the term in square brackets equals 1, and the pressure deviation from the Raoult s-law value has the sign of fin this is normally negative. When the virial coefficients are not equal, a reasonable assumption is that species 2, taken here as the heavier species (the one with the smaller vapor pressure) has the more negative second virial coefficient. This has the effect of making the quantity in parentheses negative and the quantity in square brackets < 1. However, if this latter quantity remains positive (the most likely case), the sign of fin still determines the sign of the deviations. 

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