Vapor pressure lowering mole fractional concentration

Vapor-pressure lowering depends on concentration expressed as mole fraction, x-Boiling-point elevation depends on concentration expressed as molality, m. Freezing-point depression depends on concentration expressed as molality, m. Osmotic pressure depends on concentration expressed as molarity, M. 

The vapor pressure of a pure substance is dependent only on the nature of the substance and the temperature (Chapter 14). If we add a solute to the substance, its vapor pressure is lowered because the molecules of the substance cannot evaporate from the surface as rapidly as they could in the absence of the solute. The vapor-pressure lowering depends on the concentration of the solute particles, not on their nature. Raoult s law states that the vapor pressure of a component of an ideal solution is equal to the mole fraction of the component times its vapor pressure when it is a pure substance. That is, for component Z ... 

The left term is the relative vapor pressure lowering, which is solely dependent on the mole fraction concentration of a single solute or the sum of mole fraction of each solute dissolved in the solution. Thus, the relative vapor pressure lowering is a direct measure of the total number of dissolved solute particles, irrespective of their physicochemical nature. The mole fractions can be converted into molality (m moles of solute per 1000 g of solvent) to result in the following equation for water as the solvent ... 

Raoult s law n. The quantitative relationship between vapor-pressure lowering and concentration in an ideal solution is stated in Raoult s law the partial vapor pressure of a component in solution is equal to the mole fraction of that component times its vapor pressure when pure at a temperature ... 

Raoult s law predicts that when we increase the mole fraction of nonvolatile solute particles in a solution, the vapor pressure over the solution will be reduced. In fact, the reduction in vapor pressure depends on the total concentration of solute particles, regardless of whether they are molecules or ions. Remember that vapor-pressure lowering is a colligative property, so it depends on the concentration of solute particles and not on their kind. In our applications of Raoult s law, however, we will limit ourselves to solutes that are not only nonvolatile but nonelectrolytes as well. We consider the effects of volatile substances on vapor pressure in the "Closer Look" box in this section, and we will consider the effects of electrolytes in our discussions of freezing points and boiling points. 

From this equation, you can see that the vapor-pressure lowering is a colligative property—one that depends on the concentration, but not on the nature, of the solute. Thus, if the mole fraction of ethylene glycol, X, in an aqueous solution is doubled from 0.010 to 0.020, the vapor-pressure lowering is doubled from 0.18 nunHg to 0.36 mmHg. Also,... 

Just as the freezing point depression of a solution containing an electrolyte solute is greater than that of a solution containing the same concentration of a nonelectrolyte solute, so the vapor pressure lowering is greater (for the same reasons). The vapor pressure for a sodium chloride solution, for example, is lowered about twice as much as it is for a nonelectrolyte solution of the same concentration. To calculate the vapor pressure of a solution containing an ionic solute, we need to account for the dissociation of the solute when we calculate the mole fraction of the solvent, as shown in Example 12.12. 

Air-water partition coefficients and Flenry s law constants are strongly temperature dependent because of the temperature dependencies of vapor pressure and of solubility. FI is also slightly dependent on the temperature dependence of water density and, hence, molar volume. The constants may be concentration dependent because of variations in yw, although the effect is believed to be negligible at low concentrations of non-associating solutes. Noted that these simple relationships break down at high concentrations, i.e., at mole fractions in excess of approximately 0.01. For most environmental situations, the concentrations are (fortunately) usually much lower. For thermodynamic purposes, H is usually preferred, whereas for environmental purposes, H is more convenient. 

According to Raoult s law, the lowering of the vapor pressure of a solution is proportional to the mole fraction of the solute aw can then be related to the molar concentrations of solute ( [) and solvent (n2) ... 

Example 2.3. Activity and Activity Coefficient of Aqueous NaCl Water vapor pressures have been measured over NaCl solutions of varying molal concentrations. Results of such measurements allow calculations of relative vairor pressure lowering, 4>, and 7., for a range of NaCl concentrations in water. Robinson and Stokes (1959) provide such data for concentrations ranging fn)m 0.1 to 6.0 molal. Table 2.1 shows results for three different concentrations. The mole fraction of H2O, Xfy, is also included. From such data the activity of aqueous NaCl can be computed, (see also Figure 2.4.)... 

Direct experimental proof that the true driving force for diffusive transport is the gradient of chemical potential rather than the concentration gradient is provided by the experiments of Haase and Siry who studied diffusion in binary liquid mixtures near the consolute point. At the consolute point the chemical potential (and the vapor pressure) are independent of composition so, according to Eq. (5.6), the diffusivity should be zero. The consolute point for the system n-hexane-nitrobenzene occurs at 20 C at a mole fraction 0.422 of nitrobenzene. The system shows complete miscibility above this temperature and forms two separate phases at lower temperatures. Opposite behavior is shown by the system water-triethylamine, for which the consolute tempera-... 

When we compare the vapor pressures of various solvents with those of dieir solutions, we find that adding a nonvolatile solute to a solvent always lowers the vapor pressure. This effect is illustrated in Figure 13.20 . The extent to which a nonvolatile solute lowers die vapor pressure is proportional to its concentration. This relationship is expressed by Raoult s law, which states tiiat the partial pressure exerted by solvent vapor above a solution, P, equals die product of die mole fraction of die solvent in die solution, X, times fte vapor pressure of the pure solvent ... 

Saturation concentration. From A G we can calculate the mole fraction of solute in water ifthe vapor pressure of the solute was 1 atm. Itisx = exp(—AG /RT). Since in equilibrium the vapor pressure is lower than 1 atm (otherwise the substance would not be in the liquid phase), we still have to multiply with Pq /I atm. To obtain the respective concentration we multiply the mole fraction with 55.35 mol 1, the concentration of pure water at 25 °C. Thus, for hexane we get... 

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