Nonvolatile solutes, phase equilibrium

The effect of a solute on the boiling point of a solution is opposite to its effect on the freezing point. A nonvolatile solute inereases the boiling point of a solution. This is because the solute blocks some of the solvent molecules from reaching the surface of the solution and thus decreases the rate of escape into the gas phase. To get back to dynamic equilibrium, the solution must be heated so that more molecules acquire sufficient energy to escape from the liquid phase. 

If a liquid is placed in a sealed container, molecules will evaporate from the surface of the liquid and eventually establish a gas phase over the liquid that is in equilibrium with the liquid phase. The pressure generated by this gas is the vapor pressure of the liquid. Vapor pressure is temperature-dependent the higher the temperature, the higher the vapor pressure. If the liquid is made a solvent by adding a nonvolatile solute, the vapor pressure of the resulting solution is always less than that of the pure liquid. The vapor pressure has been lowered by the addition of the solute the amount of lowering is proportional to the number of solute particles added and is thus a colligative property. 

To understand why a solute lowers the vapor pressure, we need to look at the thermodynamic properties of the solution. We saw in Section 8.2, specifically Eq. 1, that at equilibrium, and in the absence of any solute, the molar free energy of the vapor is equal to that of the pure solvent. We now need to consider the molar free energies of the solvent and the vapor when a solute is present. We shall consider only nonvolatile solutes, which do not appear in the vapor phase, and limit our considerations to ideal solutions. 

When a nonvolatile solute is dissolved in a volatile solvent, the solution is at equilibrium with the vapor phase. The thermodynamic condition for this equilibrium is ... 

When a nonvolatile solute is added to a solvent, the vapor pressure of the resulting solution will be lower than the vapor pressure of the pure solvent. Why does this occur To answer this, you have to remember back to our discussion of the equilibrium between vapor and liquid in a closed system. If you recall, equilibrium is reached when the rate that particles are escaping the liquid is equal to the rate that the particles are returning to the liquid. Also recall that these transitions take place on the surface of the liquid. Now, suppose you add a nonvolatile solute to the solvent. (The AP curriculum specifies that only the effects of nonvolatile solutes are required.) Because the solute is nonvolatile, it will not enter the gaseous phase above the liquid. What this means is that at the surface of the liquid, where particles of the solvent can escape, there are now some particles of the solute mixed in with the solvent. As a result, the number of solvent molecules that are able to escape will be less than the number that could have escaped in the pure solvent (they are blocked by the solute particles). The addition of a nonvolatile solute decreases the ability of solvent molecules to form vapors. This means that not as much vapor can form, which also means that there will be fewer gaseous molecules returning to the liquid state. Thus, the vapor pressure is reduced. 

A simple example of such a system would be a saturated solution of a nonvolatile solid in equilibrium with vapor of the solvent the three phases would then be (i) the solid component 1, e.g., a salt, (ii) a saturated solution of this substance in the liquid component 2, e.g., water, and (iii) the vapor of the latter. Suppose a smalfchange is made in the system, which is maintained in equilibrium,... 

It is also observed that the presence of the nonvolatile solute like phenanthrene has negligible effect on the vapor phase mole fractions of toluene and CO2, inasmuch as the latter for the ternary system are very much close to those for the binary (toluene and CO2) system at the same pressure and 298 K (60). The P-T trace for the constant liquid phase compositions at the S-L-V equilibrium is obtained from the isothermal plots of P vs (X3/I — X3) at three temperatures (Figure 28). It can be seen that the pressure required for attaining the S-L-V equilibrium increases with temperature at the same composition and increases with V3 at constant temperature. This trend is similar to that reported by Kikic et al. (41). Figure 29 depicts the effects of variations in pressure and temperature on isothermal and isobaric triangular... 

To explore how a nonvolatile solute affects a solvent, we will consider the experiment represented in Fig. 11.9, in which a sealed container encloses a beaker containing an aqueous sulfuric acid solution and a beaker containing pure water. Gradually, the volume of the sulfuric acid solution increases and the volume of the pure water decreases. Why We can explain this observation if the vapor pressure of the pure solvent is greater than that of the solution. Under these conditions, the pressure of vapor necessary to achieve equilibrium with the pure solvent is greater than that required to reach equilibrium with the aqueous acid solution. Thus, as the pure solvent emits vapor to attempt to reach equilibrium, the aqueous sulfuric acid solution absorbs vapor to try to lower the vapor pressure toward its equilibrium value. This process results in a net transfer of water from the pure water through the vapor phase to the sulfuric acid solution. The system can reach an equilibrium vapor pressure only when all the water is transferred to the solution. This experiment isjust one of many observations indicating that the presence of a nonvolatile solute lowers the vapor pressure of a solvent... 

First, we describe the real system. An ebullioscopic apparatus resembles closely to an apparatus suitable for chemical operations done under reflux, but it has a very sensitive thermometer. In fact, the boiling point of a solvent in presence of a nonvolatile solute is measured, more precisely the dependence of the boiling point on the concentration of the nonvolatile solute. The boiling point is the temperature at which equilibrium of liquid and gaseous phase at standard pressure is established. 

In vapor pressure osmometry, the system ( ) is a droplet of a volatile liquid (1) in which a nonvolatile solute (2) is dissolved. The system ( ) can exchange energy of compression with the gas phase (") that consists entirely of the solvent. Further, solvent (1) may move freely from the liquid phase into the gas phase. The gas phase is in contact with a thermostat and a manostat. We address this as a combined system (" ) Thus, the conditions of equilibrium are... 

After a nonvolatile solute is added to a liquid solvent, only a fraction of the molecules at a liquid-gas interface are now volatile and capable of escaping into the gas phase. The vapor consists of essentially pure solvent that is able to condense freely. This imbalance drives equilibrium away from the vapor phase and into the liquid phase and lowers the vapor pressure by an amount proportional to the solute particles present. 

To understand why a nonvolatile solute changes the boiling point and freezing point, you must consider equilibrium vapor pressure. Vapor pressure is the pressure caused by molecules in the gas phase that are in equilibrium with the liquid phase. Experiments show that the vapor pressure of a solvent containing a nonvolatile solute is lower than the vapor pressure of the pure solvent at the same temperature, as shown in Figure 2.2. As the number of solute particles increases in a given volume of solution, the proportion of solvent (water) molecules decreases. Fewer water molecules will be available to escape from the liquid. As a result, the tendency of water molecules to leave the solution and enter the vapor phase decreases. Thus, the vapor pressure of the solution is less than the vapor pressure of pure water. 

From a molecular level, it is easy to rationalize why nonvolatile solutes lower the vapor pressure of the solvent. Figure 7.27 shows a molecular representation of a pure solvent and a solution with a nonvolatile solute. The particles of solute literally block the solvent molecules from escaping into the vapor phase, thus lowering the equilibrium vapor pressure of the solution with respect to the pure liquid. 

Consider a volatile solvent (component 1) and a nonvolatile solute (component 2) in a solution that is at equilibrium with the gaseous solvent at a constant pressure. We assume that the gas phase is an ideal gas and that the solvent acts as though it were ideal. Our development closely parallels the derivation of the freezing point depression formula earlier in this section. The fundamental fact of phase equilibrium gives... 

Because polyelectrolytes are nonvolatile, the most important thermodynamic property for vapor + liquid phase equilibrium considerations is the vapor pressure of water above the aqueous solution. Instead of the vapor pressure, some directly related other properties are used, e.g., the activity of water a, the osmotic pressure 71, and the osmotic coefficient < . These properties are defined and discussed in Sect. 4. Membrane osmometry, vapor pressure osmometry, and isopiestic experiments are common methods for measuring the osmotic pressure and/or the osmotic coefficient. A few authors also reported experimental results for the activity coefficient y i of the counterions (usually determined using ion-selective electrodes) and for the freezing-point depression of water AT p. The activity coefficient is the ratio of activity to COTicentration ... 

You may be wondering Why does the solvent vapor pressure always decrease when solute is added To explain, let us consider the addition of a nonvolatile solute to a pure liquid solvent. We begin with the fact that when the gas phase and liquid phase are in equilibrium with each other, the chemical potential of the solvent molecules, /ua, is the same in the two phases. (Recall that the subscript A refers to the solvent.)... 

Once a stable particle is formed, it can grow or shrink owing to mass transfer processes between the gas and the particle phase. These processes are governed mainly by the actual particle size, by the ratio of mean free path and particle diameter (Knudsen number), by the molecular diffusion coefficient, and most importantly, by the difference between the gas phase and the particle surface equilibrium vapor pressures of the transferred chemical species. Vapor pressures in the gas phase that are higher than the equilibrium vapor pressure at the particle surface result in a net mass flux toward the particle surface (i.e., the particle gains mass and growth takes place). Gas-phase vapor pressures that are lower than the equilibrium vapor pressure at the particle surface cause a net mass flux directed away from the particle (i.e., the particle loses mass and shrinks). The most important mechanisms that influence the equilibrium vapor pressure at the particle surface are the Kelvin effect, the effect of nonvolatile solute, aqueous-phase chemical reactions, and latent heat release. 

Phase equilibrium is the basic principle used to obtain expressions for the magnitude of the different colligative properties. It is known from thermodynamics that when two phases are in equilibrium, the frigacity, /, of a given component is the same in each phase. Thus, if, as shown in Figure 8.1, pure vapor A is in equilibrium at temperature Tand pressure P with a liquid mixture of A and B, where B is a nonvolatile solute. 

It is desirable that the equilibrium constant for a solute be not zero or very large lest there be no net retention or near infinite retention. The catch comes in the fact that liquids, which are relatively good solvents for a given type of molecule are also solvents for each other. This means the risk involved is by washing off the stationary phase with the mobile phase. Yet liquid-liquid methods offer much promise for relatively nonvolatile but soluble molecules and their separation of one from the other. The discovery of liquid-liquid chromatography earned Martin and Synge the Nobel Prize when they applied it to amino acids with water mobile phases and organic liquid stationary phases. 

The distillation technique is not used to separate complex mixtures, but finds its acceptance more for the preparation of large quantities of pure substances or the separation of complex mixtures into fractions. The technique depends on the distribution of constituents between the liquid mixture and component vapors in equilibrium with the mixture two phases exist because of the partial evaporation of the liquids. How effective the distillation becomes depends upon the type equipment employed, the method of distillation, and the properties of the mixture components. The distinguishing aspects of distillation and evaporation are that in the former all components are volatile, whereas in the latter technique volatile components are separated from nonvolatile components. An example of distillation would be the separation of ethyl alcohol and benzene. An evaporative separation would be the separation of water from an aqueous solution of some inorganic salt, for example, sodium sulfate. 

In gas absorption operations the equilibrium of interest is that between a relatively nonvolatile absorbing liquid (solvent) and a solute gas (usually the pollutant). As described earlier, the solute is ordinarily removed from a relatively large amount of a carrier gas that does not dissolve in the absorbing liquid. Temperature, pressure, and the concentration of solute in one phase are independently variable. The equilibrium relationship of importance is a plot (or data) of x, the mole fraction of solute in the liquid, against y, the mole fraction in the vapor in equilibrium with x. For cases that follow Henry s law, Henry s law constant m, can be defined by the equation... 

For binary solvent-polymer systems, and since the vapor phase can be considered to contain pure solvent (the polymer is nonvolatile). Equation 16.20 can be simplified to give the following expression for the equilibrium pressure of the solution ... 

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