The vapor pressure of a pure liquid

Substituting for dP from Equation (6.38) into Equation (6.36) yields 

The molar volume of the vapor will be much greater than that of the liquid and, if it is assumed that the vapor is an ideal gas, the difference 

Substitution of Equation (6.40) into Equation (6.39) yields an expression that may be integrated as follows  

Upon integration this yields the well-known Kelvin equation which relates the vapor pressure of a liquid droplet of radius r to that for the same liquid in hulk  

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Why is the vapor pressure of a solution less than the vapor pressure of a pure liquid How does this impact boiling point What is the quantitative relationship between solute concentration and vapor pressure ... 

Increasing temperature will decrease the solubility of a gas in a liquid because kinetic energy opposes intermolecular attractions and permits more molecules to escape from the liquid phase. The vapor pressure of a pure liquid increases with temperature for the same reason. Greater kinetic energy will favor material in the gas phase. 

Other Thermometric Devices. The vapor pressure of a pure liquid or solid is a physical property sensitive to temperature and thus suitable for use as a thermometer. The use of a liquid-nitrogen vapor-pressure thermometer is suggested for the range 64 to 78 K in Exp. 47. At very low temperatures (1 to 4.2 K), the vapor pressure of liquid helium can be used. 

The vapor pressure of a pure liquid is determined solely by the temperature. (Section 12.6 showed that the vapor pressure of water is determined by its temperature alone.) If the surface area for evaporation is larger, so also is the surface area for condensation. If there is more volume for the gas to occupy, more molecules will be able to evaporate before the rate of condensation equals the rate of evaporation, but it will take that many more molecules to build up to the same vapor pressure. The volume and shape occupied by the liquid also have no effect on the vapor pressure of a pure liquid. 

We still have a formula that relates mole fraction to pressure. Note, however, that with the exception of the atmospheric pressure (P t n) the other pressures are those of pure liquids ( and Pg). Now, how does the vapor pressure of a pure liquid vary with temperature Smite your forehead and say that you could have had a V-8. The Clausius-Clapeyron equation ... 

An indication of whether or not the above condition for ideality is met is obtained from the vapor pressure of the solution. At a given temperature, the vapor pressure of a pure liquid is a measure of the ability of molecules to escape from the liquid to the gas phase. By studying the vapor pressure of a solution as a function of its composition at constant temperature one may assess the solution s ideality or its degree of departure from ideality. For an ideal solution, the tendency of molecule A to escape is proportional to its mole fraction, that is, to its concentration expressed in terms of the fraction of molecules which are of type A. The proportionality constant must be the vapor pressure of pure component A because this vapor pressure is reached when the mole fraction is unity. This result is Raoult s law, which is expressed mathematically as... 

To understand the principles of distillation, a review of the effect of impurities on the vapor pressure of a pure liquid is necessary. The discussion starts with consideration of the consequences of having nonvolatile impurities present and then turns to the more common case of contamination of the liquid with other volatile substances. 

Equation 8.4.15 shows that the curve of a plot of n(p/p°) versus /T (where p is the vapor pressure of a pure liquid or solid) has a slope at each temperature equal, usually to a high degree of accuracy, to — Ayap/f/i or — at that temperature. This kind of... 

We have already addressed vapor pressure depression, in the form of Raoult s law. The vapor pressure of a pure liquid is lowered when a solute is added, and the vapor pressure is proportional to the mole fraction of the solvent ... 

In Section 8.4.2 we recognized the vapor pressure of a pure liquid - at a specified temperature - as the pressure read by a manometer when this liquid is in equilibriiun with the vapor above it. Thus, if in the vapor-liquid equilibrium experiment of Section 13.5.1 we introduced a pure liquid, the pressure read by the manometer represents the vapor pressure of this liquid at the bath temperature. 

Clausius-Clapeyron Equation. This equation was originally derived to describe the vaporization process of a pure liquid, but it can be also applied to other two-phase transitions of a pure substance. The Clausius-Clapeyron equation relates the variation of vapor pressure (P ) with absolute temperature (T) to the molar latent heat of vaporization, i.e., the thermal energy required to vajxirize one mole of the pure liquid ... 

The Peng-Robinson equation of state, Equation 4-35, will be used with Equation 15-7 to develop a procedure for calculating of the vapor pressure of a pure substance.3 The vapor pressure is simply the pressure, points e on Figure 15-2, for which the fiigacity of the liquid equals the fugacity of the gas. 

The procedure to calculate the vapor pressure of a pure substance involves Equations 15-9 through 15-17. Once temperature is selected, the results of Equations 15-9 through 15-12 are fixed. The problem then is to find a pressure for use in Equations 15-14 through 15-16 which will give values of z-factors for gas and liquid which will result in equal values of fugacities of gas and liquid from Equation 15-17. 

Recall from Section 10.5 that a liquid in a closed container is in equilibrium with its vapor and that the amount of pressure exerted by the vapor is called the vapor pressure. When you compare the vapor pressure of a pure solvent with that of a solution at the same temperature, however, you find that the two values are different. If the solute is nonvolatile and has no appreciable vapor pressure of its own, as occurs when a solid is dissolved, then the vapor pressure of the solution is always lower than that of the pure solvent. If the solute is volatile and has a significant vapor pressure of its own, as often occurs in a mixture of two liquids, then the vapor pressure of the mixture is intermediate between the vapor pressures of the two pure liquids. 

The vapor pressure over a pure liquid droplet at equilibrium ps depends on its radius of curvature. The Kelvin equation gives this relationship as ... 

Let and 2 be values of the saturation vapor pressure of a pure liquid at absolute... 

We note that at the vapor pressure of a pure system, the chemical potentials of the liquid and vapor... 

The dependence of vapor pressure of a pure liquid on the liquid s temperature is ... 

For the Lewis-Randall ideal solution, all terms in these equations must be at the same temperature, pressure, and phase, even if some of those states are not physically realizable. For example, if P is below the vapor pressure of a pure substance, then that substance cannot exist as a liquid nevertheless, the properties of a hypothetical liquid at that P might still be useful. Note that these results for ideal solutions are functionally the same as those given in 4.1.4 for ideal-gas mixtures. This reinforces our comment that an ideal-gas mixture is merely one kind of ideal solution. 

Figure 2.11 The influence of curvature on the vapor pressure of a pure substance and the dewpoint pressure of a hydrocarbon mixture (a) system in the single-phase gaseous state. (6) fbr a pure substance, as pressure increases, gas may condense and the condensation will occur first in Tube 1. (c) For a hydrocarbon gas mixture with retrograde condensation behavior, as pressure decreases, liquid may form also in Tube 1 (liquid wets the substrate ...

We have seen that a liquid exerts a characteristic vapor pressure [W Section 12.2]. When a nonvolatile solute (one that does not exert a vapor pressure) is dissolved in a liquid, the vapor pressure exerted by the liquid decreases. The difference between the vapor pressure of a pure solvent and that of the corresponding solution depends on the concentration of the solute in the solution. This relationship is expressed by Raoult s law, which states that the partial pressure of a solvent over a solution, Pu is given by the vapor pressure of the pure solvent. Pf, times the mole fraction of the solvent in the solution, X -... 

Critical Regions. At very high pressures special phenomena associated with the critical region are encountered in vapor-liquid equilibria. If the vapor pressure of a pure component is plotted vs. the temperature, a line concave upward is obtained. This line terminates at the critical point. Conditions below the line in region A, Fig. 4-1,... 

We are all familiar with vapor-liquid equilibrium, in the case of water and steam. For pure water and steam to be in equilibrium (without air mixed in) the pressure of the gas must equal the vapor pressure of the liquid. If the pressure of the gas is less than the vapor pressure of the liquid, then the liquid will boil, expelling gas. If the pressure of the gas is greater than the vapor pressure of the liquid, then the gas will condense into the liquid. If these processes occur in a closed container (Figure 3.4), then they will continue until the two pressures (and temperatures) become the same, at which time we will have phase equilibrium. From our previous studies, we know that the vapor pressure of any pure liquid is a simple function of the temperature, called the vapor-pressure curve. Its values for many liquids are presented in textbooks and handbooks and are discussed in detail in Chapter 5. 

The calculation of vapor pressure of a pure substance consists of finding the pressure for which the fugacities of the liquid and vapor are equal. 

The normal boiling point of a binary liquid mixture is the temperature at which the total vapor pressure is equal to 1 atm. If we were to heat a sample of pure benzene at a constant pressure of 1 atm, it would boil at 80.1°C. Similarly, pure toluene boils at 110.6°C. Because, at a given temperature, the vapor pressure of a mixture of benzene and toluene is intermediate between that of toluene and benzene, the boiling point of the mixture will be intermediate between that of the two pure liquids. In Fig. 8.37, which is called a temperature-composition diagram, the lower curve shows how the normal boiling point of the mixture varies with the composition. 

Raoult s law The vapor pressure of a liquid solution of a nonvolatile solute is directly proportional to the mole fraction of the solvent in the solution P = soiventPm,re, where Ppurc is the vapor pressure of the pure solvent. 

Saturated vapor pressure of a pure solid substance (Ps) or of its subcooled liquid (Pl) is an indicator of the substance volatility. These and other physical-chemical properties and distribution coefficients can be found in the handbook (Mackay et al., 1992b). 

A further aspect of volatility that receives considerable attention is the vapor pressure of petroleum and its constituent fractions. The vapor pressure is the force exerted on the walls of a closed container by the vaporized portion of a liquid. Conversely, it is the force that must be exerted on the liquid to prevent it from vaporizing further (ASTM D323). The vapor pressure increases with temperature for any given gasoline, liquefied pefioleum gas, or other product. The temperature at which the vapor pressure of a liquid, either a pure compound or a mixture of many compounds, equals 1 atm pressure (14.7 psi, absolute) is designated as the boiling point of the liquid. 

The vapor pressure of a compound is not only a measure of the maximum possible concentration of a compound in the gas phase at a given temperature, but it also provides important quantitative information on the attractive forces among the compound s molecules in the condensed phase. As we will see below, vapor pressure data may also be very useful for predicting equilibrium constants for the partitioning of organic compounds between the gas phase and other liquid or solid phases. Finally, we should note that knowledge of the vapor pressure is required not only to describe equilibrium partitioning between the gas phase and a condensed phase, but also for quantification of the rate of evaporation of a compound from its pure phase or when present in a mixture. 

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