Solutions Raoult s law

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 ... 

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. 

These equations are the same as Equation (14.6) and Equation (14.7), statements of Raoult s law thus, the solvent obeys Raoult s law when the solute obeys Henry s law. As Henry s law is a limiting law for the solute in dilute solution, Raoult s law... 

For an ideal solution, where there is no heat of solution, Raoult s law applies to the partial pressures of both components ... 

Figure 5.16 Partial pressure of solution, Raoult s law solution, and regular solutions with a range of values for A /RT...

The vapor pressure of a solvent is lowered on dissolving the solute in it. This lowering for dilute solutions is proportional to die mole fraction of the solute (Raoult s Law). The lowering of the vapor pressure of the solution can be related to the lowering of the freezing point and the elevation of the boiling point. These phenomena serve as a basis for molecular weight determinations. If both components of the solution are volatile, each lowers the vapor pressure of the other and the ratios of the two substances in the liquid and vapor phase are not necessarily the same. Use is made of this fact to separate the two substances by distillation. 

Just as the ideal gas law discussed in Section 9.3 applies only to "ideal" gases, Raoult s law applies only to ideal solutions. Raoult s law approximates the behavior of most real solutions, but significant deviations from ideality occur as the solute concentration increases. The law works best when solute concentrations are low and when solute and solvent particles have similar intermolecular forces. 

As with nonvolatile solutes, Raoult s law for a mixture of volatile liquids applies only to ideal solutions. Most real solutions show behavior that deviates slightly from the ideal in either a positive or negative way, depending on the kinds and strengths of intermolecular forces present in the solution. 

Further, Raoult s law can be applied when two volatile components are mixed. In systems of liquids that mix in all proportions to form ideal solutions, Raoult s law in the form of the second equation applies to the partial pressure of each volatile component separately. 

In true chemical solutions mixing on the molecular level leads to substantial increases in the entropy of the system and, consequently, negative deviations from the linear relationship between composition and the free energy of the solution (Raoult s law). If this is the only deviation from the Henry s law behavior of equation 3.1, then the solution is referred to as being ideal. 

Figure 3 Acetone-chloroform solution Raoult s law activity coefficients solid curve ...

We have seen earlier (in Frames 32 and 33) that in order to be classified as an ideal solution then Raoult s Law (Frame 32, 33) must be obeyed over the entire concentration range. In the case of ideal dilute solutions Raoult s Law (Frame 32, equation (32.8) and Frame 33, equation (33.6)) must apply to the solvent and Henry s Law (Frame 33, equation (33.7)) must apply to the solute, albeit over a very small (dilute) and limited concentration range (see Figure 36.1). 

Figure 10.8 Pxy diagrams at constant T. (a) Tetrahydrofuran(1)/carbon tetrachlo-ride(2) at 303.15K (30°C) (b) chloroform(1)/tetrahydrofuran(2) at 303.15K (30°C) fcj furan(1)/carbon tetrachloride(2) at 303.15 K (30°C) (of) ethanol(1)/toluene(2) at 338.15 K (65°C). Dashed lines Px relation for ideal liquid solutions (Raoult s law)...

Eq. (4) is known as Henry s law, and solute is the Henry s law constant, which is less than Psoiute- Therefore, Henry s law applies to the solute in dilute solutions, and Raoult s law applies to solvent in dilute non-ideal solutions. Note the similarities between Eqs. (1) and (2) and between Eqs. (3) and (4) for the non-ideal dilute solution case. When the solution is ideal, Henry s law becomes identical to Raoult s law, and fsoiute becomes identical to f oiute- When the partial pressures of the solute and the solvent are directly proportional to their molefractions over the entire range, the solution is ideal. In a non-ideal solution, Raoult s law will apply to the solvent over the entire concentration range, whereas Henry s law will apply to the solute in a limited concentration range in which it is in a sufficiently diluted form. 

In dilute solutions of nonvolatile solutes, Raoult s law (see section 2.3.1) can usually be assumed to be obeyed and the chemical potential of the solute is given by equation (3.50) ... 

Of all the methods that are available for determining the molecular weight of an organometallic compound, the most straightforward is undoubtedly that developed by Signer (24.). This method is based on the simple idea that the vapor pressure of an ideal solution is proportional to the concentration of the solute (Raoult s Law). The major advantages of this technique is that it does not require any sophisticated equipment, only about 0.05 g of the unknown compound are needed and it can be suited to... 

Relation (3.11) was obtained empirically by Raoult and is called Raoult s law. Hence in ideal solutions Raoult s law holds over the entire range of compositions, this being represented by a straight line in the v or pressure composition curve (Fig. 3.1). In reality, most solutions do not obey Eqs. (3.9) and (3.11). Such solutions are called nonideal, or real. Polymer solutions characteristically display sharp negative deviations from ideality, as can be seen in Fig. 3.1. 

Few liquid mixtures are ideal, so vapor-liquid equilibrium calculations can be more complicated than is the case for the hexane-triethylamine system, and the system phase diagrams can be more structured than Fig. 10.1-6. These complications arise from the (nonlinear) composition dependence of the species activity coefficients. For example, as a result of the composition dependence of y, the equilibrium pressure in a fixed-temperature experiment will no longer be a linear function of mole fraction. Thus nonideal solutions exhibit deviations from Raoult s law. We will discuss this in detail in the following sections of this chapter. However, first, to illustrate the concepts and some of the types of calculations that arise in vapor-liquid equilibrium in the simplest way, we will assume ideal vapor and liquid solutions (Raoult s law) here, and then in Sec. 10.2 consider the calculations for the more difficult case of nonideal solutions.. ... 

Expressing the relationship between the vapor pressure of solvent above a solution and its mole fraction in the solution (Raoult s law) (407) ... 

A liquid-liquid solution that obeys Raoult s law is called an ideal solution. Raoult s law is to solutions what the ideal gas law is to gases. As with gases, ideal behavior for solutions is never perfectly achieved but is sometimes closely approached. Nearly ideal behavior is often observed when the solute-solute, solvent-solvent, and solute-solvent interactions are very similar. That is, in solutions where the solute and solvent are very much alike, the solute simply acts to dilute the solvent. However, if the solvent has a special affinity for the solute, such as if hydrogen bonding occurs, the tendency of the solvent molecules to escape will be lowered more than expected. The observed vapor pressure will be lower than the value predicted by Raoult s law there will be a negative deviation from Raoult s law. 

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