Solutions, ideal vapour pressure

All the above deals with gases and gas phase processes. We now turn to non-gaseous components of the system. There are many ways of expressing this. Probably the simplest is to consider an ideal solution of a solute in a solvent. If the solution is ideal, the vapour pressure of the solute is proportional to its concentration, and we may write p = kc, where c is the concentration and k is the proportionality constant. Similarly, = Arc , which expresses the fact that the standard pressure is related to a standard concentration. Thus we may write from equation 20.198 for a particular component... 

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. 

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-... 

It has been assumed in the deduction of (1) that the solute is an ideal gas, or at least a volatile substance. The extension of the result to solutions of substances like sugar, or metallic salts, must therefore be regarded as depending on the supposition that the distinction between volatile and non-volatile substances is one of degree rather than of kind, because a finite (possibly exceedingly small) vapour pressure may be attributed to every substance at any temperature above absolute zero. This assumption is justified by the known continuity of pleasure in measurable regions, and by the kinetic theory of gases. 

For a solution of a non-volatile substance (e.g. a solid) in a liquid the vapour pressure of the solute can be neglected. The reference state for such a substance is usually its very dilute solution—in the limiting case an infinitely dilute solution—which has identical properties with an ideal solution and is thus useful, especially for introducing activity coefficients (see Sections 1.1.4 and 1.3). The standard chemical potential of such a solute is defined as... 

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... 

According to Henry s law, the vapour pressure of a gas above its solution is directly proportional to the concentration c, or the mole fraction Xg of this gas in solution. It applies if the solutions are sufficiently ideal. 

However, if the B atom is bound into the solution because of negative interactions (i.e., n — ve) the vapour pressure of B above the alloy is less than if the mixing was ideal. In this circumstance there is a negative deviation from ideality and the plot of activity vs composition is as shown in Fig. 3.9(a). In the case where there are positive interactions (H + ve) there is a positive deviation from ideality as shown in Fig. 3.9(b), and the vapour pressure of B is greater than if mixing is ideal. 

The vaporization of solvent molecules from the pure liquid solvent described above should not differ from its vaporization from an infinitely dilute solution of some solute(s) in it, since the vast majority of solvent molecules have other solvent molecules in their surroundings in both cases. As the solute concentration increases in the dilute solution range, it is expected that Raoulf s law will be obeyed, that is, the vapour pressure of the solvent will be proportional to its mole fraction in the solution. If this is indeed the case, the solution is an ideal solution. At appreciable concentrations of the solute this will no longer be the case, due to solute-solute interactions and modified solute-solvent ones. The vapour pressure as well as other thermodynamic functions of the solvent and, of course, of the solute will no longer obey ideal solution laws. The consideration of these effects is beyond the scope of this book. 

Liquids A and B are completely miscible and forms an ideal solution. The vapour pressures of two liquids are 2xl0 3atm and 5xl0 3atm at temperature T, respectively. Calculate the mole fraction of A in liquid phase when the vapour pressure is 4xl0 3 atm. 

The positive deviation is characterised by vapour pressures higher than those calculated for ideal solution. If the attraction between the unlike molecules (i-j) is weaker than the mutual attraction of like molecules (i-i or j-j), then the escaping tendencies of the molecules are higher than the escaping tendencies in the individual pure states. 

Problem 13 What are ideal solutions Explain the vapour pressure of ideal solutions. 

Before defining ideal solutions, we must understand Raoult s law. Raoult measured the vapour pressures of a number of binary solutions of volatile liquids and made the important generalisation, known as Raoult s law. It can be stated as follows ... 

The vapour pressure of an ideal binary solution of two components A and B is shown in Fig. 6. It is clear from the graph that the curve of the partial pressure of each component against its mole fraction in the solution is a straight line and the total vapour pressure of the solution for a given concen-... 

Consider a binary solution of two components A and B, forming an ideal solution. Let aA and aB be the activities, and xA and xB be the mole fractions of the constituents A and 5, respectively. According to Raoult s law, the partial vapour pressure (pA) pf constituent A is given by... 

TypeL Non-ideal solutions of this type show small deviations from ideal behaviour and total pressure remains always within the vapour pressures of the pure components, as shown in figure (8), in which the dotted lines represent ideal behaviour. It is observed that the total pressure of each component shows a positive deviation from Raoult s law. However, the total pressure remains within the vapour pressures of the pure constituents A and B. 

The condition (compare Frame 32, section 32.2) that the liquids form an ideal liquid mixture is that their vapour pressure P (Figure 33.1(b)) must be such that Raoult s Law (Frame 32, equation (32.8) for solvent and involatile solute) is obeyed. In its extended form, for the present case of two volatile liquids A and B, this latter Law takes the extended form ... 

Few liquid mixtures are actually ideal over their entire composition range. Figure 33.2 illustrates two cases where the vapour pressure of liquid mixtures (solutions) deviate from Raoult s Law (Frame 32 and this frame, equations (33.3) and (33.4)) (positively A/B or negatively C/D) over the composition range but shows (see caption to figure) the end composition members (both representing cases of dilute solutions) do follow Raoult s Law for a limited, small, composition range. 

Figure 33.3 Henry s Law behaviour for solutes in ideal dilute solutions. Reproduction of Figure 33.2 but with tangents (C K, DL, HJ and Gl) appropriately drawn to the partial vapour pressure curves at the ends where they are acting as solute. ...

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