Solute vapor pressure lowering

NaCl molecules in its aqueous solution. Vapor pressure lowering of dilute NaCl solutions obeys Raoult s law for the solvent water—that is, pw = PwXw— and the vapor pressure corresponds to fwo solute species. 

AP = X2P1 (12.4) pressure of a liquid to its vapor pressure in a solution. Vapor pressure lowering in terms of the... 

SOLUTE + SOLVENT = SOLUTION Vapor-pressure Lowering... 

In Section 14-6 we examined the lowering of the vapor pressure of a solvent produced by a dissolved solute. Vapor pressure lowering is not measured as frequently as certain properties directly related to it. In Figure 14-23 the blue curves represent the vapor pressure, fusion, and sublimation curves in the phase diagram for a pure solvent. The red curves represent the vapor pressure and fusion curves of the solvent in a solution. The sublimation curve for the solid solvent that freezes from the solution is shown in purple. Two assumptions are implicit in Figure 14-23. One is that the solute is nonvolatile, the other is that the solid that freezes from a solution is pure solvent. For many mixtures, these requirements are easily met. ... 

Vapor pressure lowering. Equation (8.20) shows that for any component in a binary liquid solution aj = Pj/Pi°. For an ideal solution, this becomes... 

Just as at low pH, concentration mechanisms substantially increase attack. The two principal mechanisms of concentration are evaporation and condensation. Evaporation increases solute concentrations of compounds with vapor pressures lower than water (such as caustic compounds). Condensation increases concentration of aggressive gases such as ammonia. 

Finally, we may note that every solution exerts a vapor pressure less than that of the pure solvent at the same temperature. Corresponding to this vapor-pressure lowering is an equivalent boiling-point raising. Dissolved substances lower the vapor pressure of the solvent. Such reduction increases with the concentration of solute. Since a solution boils when its vapor pressure reaehes that of its surroundings, it must be heated to a temperature above the boiling point of the pure... 

The properties of a solution differ considerably from those of the pure solvent Those solution properties that depend primarily on the concentration of solute particles rather than their nature are called colligative properties. Such properties include vapor pressure lowering, osmotic pressure, boiling point elevation, and freezing point depression. This section considers the relations between colligative properties and solute concentration, with nonelectrolytes that exist in solution as molecules. 

Vapor pressure lowering is a true colligative property that is, it is independent of the nature of the solute but directly proportional to its concentration. For example, the vapor pressure of water above a 0.10 M solution of either glucose or sucrose at 0°C is the same, about 0.008 mm Hg less than that of pure water. In 0.30 M solution, the vapor pressure lowering is almost exactly three times as great, 0.025 mm Hg. 

To obtain a direct expression for vapor pressure lowering, note that Xt = 1 — X2, where X2 is the mole fraction of solute. Substituting l — X2 for X in Raoulfs law,... 

The quantity (P° — Pi) is the vapor pressure lowering (AP). It is the difference between the solvent vapor pressure in the pure solvent and in solution. 

A solution contains 82.0 g of glucose, QH Oe, in 322 g of water. Calculate the vapor pressure lowering at 25°C (vapor pressure of pure water =... 

Boiling point elevation is a direct result of vapor pressure lowering. At any given temperature, a solution of a nonvolatile solute has a vapor pressure lower than that of the pure solvent. Hence a higher temperature must be reached before the solution boils, that is, before its vapor pressure becomes equal to the external pressure. Figure 10.8 (p. 270) illustrates this reasoning graphically. 

Boiling point elevation and freezing point lowering, like vapor pressure lowerings are colligative properties. They are directly proportional to solute concentration, generally expressed as molality, m. The relevant equations are... 

Effects of vapor pressure lowering. Because a nonvolatile solute lowers the vepor pressure of a solvent, the boiling point of a solution will be higher and the freezing point lower than the corresponding values for the pure solvent Water solutions freeze below 0°C at point A and boil above 100°C at point B. 

This reasoning is confirmed experimentally. Compare, for example, the vapor pressure lowerings for 1.0 M solutions of glucose, sodium chloride, and calcium chloride at 25°C. 

E7.14 Estimate the vapor pressure lowering and the osmotic pressure at 293.15 K for an aqueous solution containing 50.0 g of sucrose (Mi = 0.3423 kg-mol"1) in 1 kg of water. At this temperature, the density of pure water is 0.99729 g em"3 and the vapor pressure is 2.33474 kPa. Compare your results with those given in Table 7.3. 

Because the presence of a nonvolatile solute lowers the vapor pressure of the solvent, the boiling point of the solvent rises. This increase is called boiling-point elevation. The elevation of the boiling point has the same origin as vapor-pressure lowering and is also due to the effect of the solute on the entropy of the solvent. 

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... 

Referring to Figure 8, temperature Tc is the chamber temperature and Ts is the surface temperature at the salt solution/vapor interface. The temperature of the chamber is well defined and is an experimental variable, whereas Ts must be higher than Tc due to condensation of vapor on the saturated solution surface. We can determine Ts by applying the Clausius-Clapeyron equation to the problem. Assume that the vapor pressures of the surface and chamber are equal (no pressure gradients), indicating that the temperature must be raised at the surface (to adjust the vapor pressure lowering of the saturated solution) to Pc (at Tc) = Ps (at Tc). However, there is a difference in relative humidity between the surface and the chamber, where RHC is the relative humidity in the chamber and RH0 is the relative humidity of the saturated salt solution, and we obtain... 

Not all solutions obey Raoult s law. Any solution that follows Raoult s law is an ideal solution. However, many solutions are not ideal solutions. A solution may have a vapor pressure higher than predicted by Raoult s law. A solution may have a vapor pressure lower than predicted by Raoult s law. Solutions with a... 

Colligative properties are those properties of solutions that depend on the number of solute particles present and not their identity. Colligative properties include vapor pressure lowering, freezing point depression, boiling point elevation, and osmotic pressure. Colloids are homogeneous mixtures, in which the solute particles are intermediate in size between suspensions and true solutions. We can distinguish colloids from true solutions by the Tyndall effect. 

Vapor pressure lowering—The vapor pressure of the solvent is lower in a solution than in the pure solvent. 

Lindsay, W. T., Jr. Liu, C. T. "Vapor Pressure Lowering of Aqueous Solutions at Elevated Temperatures" Office of Saline Water, U.S. Government Printing Office,... 

As we saw in Section 17.5, the activity coefficient of a nonelectrolyte solute can be calculated from the activity coefficient of the solvent, which, in turn, can be obtained from the measurement of colligative properties such as vapor pressure lowering, freezing point depression, or osmotic pressure. We used the Gibbs-Duhem equation in the form [Equation (17.33)]... 

Vapor pressure lowering. Raoult s law says that the vapor pressure of a solution component, A, whose pure vapor pressure is P is proportional to... 

As we have seen in Chapter 9, there are a variety of dissolved solutes in atmospheric particles, which will lower the vapor pressure of droplets compared to that of pure water. As a result, there is great interest in the nature and fraction of water-soluble material in atmospheric particles and their size distribution (e.g., Eichel el al., 1996 Novakov and Corrigan, 1996 Hoffmann et al., 1997). This vapor pressure lowering effect, then, works in the opposite direction to the Kelvin effect, which increases the vapor pressure over the droplet. The two effects are combined in what are known as the Kohler curves, which describe whether an aerosol particle in the atmosphere will grow into a cloud droplet or not under various conditions. 

This vapor pressure lowering by the solute acts simultaneously with, and counteracts, the vapor pressure increase due to the Kelvin effect [Eq. (BB)]. Multiplying the two, the net result for the vapor pressure above a solution containing a dissolved solute is given by... 

This relationship constitutes the basic definition of the activity. If the solution behaves ideally, a, =x, and Equation (18) define Raoult s law. Those four solution properties that we know as the colligative properties are all based on Equation (12) in each, solvent in solution is in equilibrium with pure solvent in another phase and has the same chemical potential in both phases. This can be solvent vapor in equilibrium with solvent in solution (as in vapor pressure lowering and boiling point elevation) or solvent in solution in equilibrium with pure, solid solvent (as in freezing point depression). Equation (12) also applies to osmotic equilibrium as shown in Figure 3.2. 

According to (7.65), the vapor-pressure lowering AP = PA — P is directly proportional to xB. As shown in the diagram, the dashed vapor-pressure curve for solution therefore falls below the solid pure-solvent curve, corresponding to the well-known effect of a nonvolatile solute in reducing the vapor pressure of solution. 

Consistent with the vapor-pressure lowering, the boiling point (7 p) of pure solvent is perforce shifted to a higher value Tb°p(xB) for any finite solute concentration xB. As shown by the diagram, the vapor-pressure lowering AP (proportional to xB) and boiling-point... 

ACTIVITY COEFFICIENT. A fractional number which when multiplied by the molar concentration of a substance in solution yields the chemical activity. This term provides an approximation of how much interaction exists between molecules at higher concentrations. Activity coefficients and activities are most commonly obtained from measurements of vapor-pressure lowering, freezing-point depression, boiling-point elevation, solubility, and electromotive force. In certain cases, activity coefficients can be estimated theoretically. As commonly used, activity is a relative quantity having unit value in some chosen standard state. Thus, the standard state of unit activity for water, dty, in aqueous solutions of potassium chloride is pure liquid water at one atmosphere pressure and the given temperature. The standard slate for the activity of a solute like potassium chloride is often so defined as to make the ratio of the activity to the concentration of solute approach unity as Ihe concentration decreases to zero. 

Alternatively, the amount of vapor-pressure lowering can be calculated by multiplying the mole fraction of the solute times the vapor pressure of the pure solvent. That is,... 

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