Vapor-pressure

Vapor pressure is a physical property of a pure chemical component. It is the pressure that a pure component exerts at a given temperature when there are both liquid and vapor phases present. Laboratory vapor pressure data, usually generated by chemists, are available for most of the chemical components of importance in industry. 

Distillation Design and Control Using Aspen Simulation, Second Edition. William L. Luyben. 2013 John Wiley Sons, Inc. Published 2013 by John Wiley Sons, Inc. 

If we have a vessel containing a mixture of these two components with liquid and vapor phases present, the vapor phase will contain a higher concentration of benzene than will the liquid phase. The reverse is true for the heavier, higher-boiling toluene. Therefore, benzene and toluene can be separated in a distillation column into an overhead distillate stream that is fairly pure benzene and a bottoms stream that is fairly pure toluene. 

Equations can be fitted to the experimental vapor pressure data for each component using two, three, or more parameters. For example, the two-parameter version is 

The Cj and Dj are constants for each pure chemical component. Their numerical values depend on the units used for vapor pressure (mmHg, kPa, psia, atm, etc.) and on the units used for temperature (K or °R). 

The vapor pressure of an epoxy resin system will have an indirect effect on the final properties of the cured adhesive. However, vapor pressure of the epoxy adhesive and its components may have a direct effect on the health and safety of those who manufacture or apply these products. 

Vapor pressure is defined as the pressure of the gaseous phase of a substance in equilibrium with its liquid phase. Vapor pressure increases with temperature. When the vapor pressure equals the surrounding or atmospheric pressure, the component will boil. Thus, high-vapor-pressure materials will boil at relatively low temperatures, and their vapors are likely to be present in the surroundings at lower temperatures. 

High-vapor-pressure materials are more likely to be present in vaporous form in the surroundings. Thus, health and safety issues may be a concern if these materials are toxic or cause skin irritation. The occurrence of such events is always exacerbated by high temperatures because of the increase in vapor pressure. 

In hot mixing or elevated-temperature curing of an epoxy system, vapor pressure could also be of concern relative to the quality of the adhesive bond. If the components in an epoxy system become too hot, boiling can occur, resulting in gas bubbles. If gas bubbles become trapped in the cured adhesive film, they can lead to reduction of cohesive strength and stress risers. For many adhesive applications, particularly those in the electrical and electronic industries (due to possible ionization of air voids), complete removal of any gas bubbles from the epoxy is essential. 

Epoxy resins and curing agents must have a relatively low viscosity so that formulation compounding can be accomplished easily and without a great deal of energy or degradation of the components. Viscosity is defined as the resistance of a liquid material to flow. It is usually measured in fundamental units of poise (P) or centipoise (cP). Table 3.2 shows a relationship between various common fluids and their viscosity as measured in centipoise. 

The vapor pressure of water, denoted 7i , is the independent pressure exerted by the water vapor in the air, and it is expressed in Pa. The natural tendency for pressures to equalize will cause moisture to migrate from an area of high vapor pressure to an area of low vapor pressure. The saturation vapor pressure varies with temperature. 

The study of vapor pressure is an important part of investigation on molten salts. In connection with the mass spectroscopy method, which enables us to determine the composition of the gas phase, it is a useful tool to determine the activities of components and thus the composition of both the liquid and vapor phases. 

Formation of vapor includes all the processes in which gas is created from a system of condensed phases. Measurement of vapor pressure is closely connected to the determination of equilibrium between the gaseous and liquid or solid phases. 

Several critical temperatures and pressures cffe hsted in A Table 11.6. Notice that nonpolar, low-molecular-weight substances, which have weak intermolecular attractions, have lower critical temperatures and pressures them substcuices that are polar or of higher molecular weight. Notice also that water and ammonia have exceptionally high critical temperatures and pressures as a consequence of strong intermolecular hydrogen-bonding forces. 

Why are the critical temperature and pressure for H2O so much higher than those for H2S, a related substance (Table 11.6)  

Because they provide information about the conditions under which gases liquefy, critical temperatures and pressures are often of considerable importance to engineers and other people working with gases. Sometimes we want to hquefy a gas other times we want to avoid liquefying it. It is useless to try to liquefy a gas by applying pressure if the gas is above its critical temperature. For example, O2 has a critical temperature of 154.4 K. It must be cooled below this temperature before it can be Hquefied by pressure. In contrast, ammonia has a critical temperature of 405.6 K. Thus, it can be liquefied at room temperature (approximately 295 K) by applying sufficient pressure. 

When the temperature exceeds the critical temperature and the pressure exceeds the critical pressure, the liquid and gas phases are indistinguishable from each other, and the substance is in a state called a supercritical fluid. A supercritical fluid expands to fill its container (like a gas), but the molecules are still quite closely spaced (Hke a Hquid). 

Like liquids, supercritical fluids can behave as solvents dissolving a wide range of substances. Using supercritical fluid extraction, the components of mixtures can be separated from one another. Supercritical fluid extraction has been successfully used to separate complex mixtures in the chemical, food, pharmaceutical, and energy industries. Supercritical CO2 is a popular choice because it is relatively inexpensive and there are no problems associated with disposing of solvent, nor are there toxic residues resulting from the process. 

This equilibrium is dynamic both processes—vaporization and condensation—are taking place, even though we cannot see or measure a change. The number of molecules leaving the liquid in a given time interval is equal to the number of molecules returning to the liquid. 

Evaporation Condensation begins Rate of evq)oration = rate of condensation 

Substances that have tngh vapor pressures at room temperature are said to be volatile. Note that this does not mean that a substance is explosive—only that it has a high vapor pressure 

CHAPTER 12 intermolecular Forces and the Physical Properties of Liquids and Solids 

The processes of vaporization and condensation are examples of phase changes. These and other phase changes are discussed in detail in Section 12.6. 

We often use the simpler term vapor pressure to mean equilibrium vapor pressure. 

The units of R are those that enable us to cancel the units of J/mol (or kJAnol) associated with4hL,p[M Section 11.3, Table 11.4]. 

By increasing the temperature, the vapor pressure of the reaction mass may increase. The resulting pressure can be estimated by the Clausius-Clapeyron law, which links the pressure to the temperature and the latent enthalpy of evaporation A Hv  

The universal gas constant to be used in this equation is 8.314-Jmor1 KT1 and the molar enthalpy of vaporization is expressed in J moT1. Since the vapor pressure increases exponentially with temperature, the effects of a temperature increase, for example due to an uncontrolled reaction, may be considerable. As a rule of thumb, the vapor pressure doubles for a temperature increase of about 20 K. 

By measuring the vapor pressure of a hquid at several different temperatures and plotting In P versus 1/7) we can determine the slope of the line, which is equal to - A/7vap/7 - (AT/yap is assumed to be independent of temperature.) 

Rudolf Julius Emanuel Clausius (1822-1888). German physicist. Clausius s work was mainly in electricity, kinetic theory of gases, and thermodynamics. 

Benoit Paul Emile Clapeyron (1799-1864). French engineer. Clapeyron made contributions to the thermodynamics of steam engines. 

A useful application of Dalton s law is the case of a gas that is confined to a container in which there is also some liquid water. The water tends to evaporate 

Water—indeed, all liquids—tend to evaporate regardless of temperature. The boiling point of water does not need to be achieved for liquid water to escape the liquid phase and become a gas. We are all aware that a drop of water left on a tabletop would eventually evaporate to dryness even though we are not boiling it. Wet laundry hung on a clothes line dries because water tends to evaporate, even though it is not being boiled. 

The molecules of water in the air space exert a partial pressure like all gases in a mixture of gases. If the component of the mixture is present due to the evaporation of a liquid also present in the container, like the water vapor in this example, this partial pressure is called the vapor pressure. The formal definition of vapor pressure is the pressure exerted by the molecules of a gas in equilibrium with its liquid present in the same sealed container. 

Two important points about vapor pressure are (1) all liquids have a vapor pressure and (2) vapor pressure varies with temperature. All liquids 

The vapor pressure of water is another example of a property of water that is influenced by hydrogen bonding (Chapter 6). The hydrogen bonds that bind water molecules to each other are relatively strong, so water molecules require more energy than most other liquids to break free of each other and enter the gas phase. Thus the vapor pressure of water is typically much lower than other liquids at equivalent temperatures, reflecting the fact that there are fewer water molecules in the gas phase to be exerting pressure. 

The essential point in the operation of an effusion source is to know the vapor pressure of the evaporant material. Fortunately, in a major effort in the 1960 s a group of researchers at the RCA laboratories headed by R.E. Hoing [5-8] measured and published vapor pressure data for virtually all of the elements in the periodic table. These data are reproduced in the data tables in the Appendix. 

The general behavior of the vapor pressure curves can be approximated well by an exponential relationship between temperature and pressure  

There are several points to note about the vapor pressure curves. First notice that most of the curves are roughly parallel on the scale of these plots. Based on the fits to the data it is apparent that the evaporation prefactor changes relatively little from element to element, while the primary changes are in the evaporation energy. This is a direct result of changes in the cohesive energy of the solid as reflected in the heat of vaporization. Note that the heat of vaporization is temperature dependent, which, in part, accounts for the curvature of the vapor pressure plots. 

An additional point of note is that the vapor pressure does not correlate with the melting point of the solid. Thus, As boils (its vapor pressure exceeds one atom-sphere) before it melts. Ga, by contrast, melts at 27°C but has a negligible vapor 

Morozov and Morozov [32] have also investigated the temperature dependence of the pressure and composition of the vapors and confirmed that the vapors contain aluminum chloride as well as sodium tetra-chloroaluminate. This could be shown experimentally by condensing the vapors which occurred in two zones. In a temperature range from 600 to 800 °C the pressures of A1C13 and NaAlCl4 over sodium tetrachloroaluminate are quite similar they rise from about 10 mm Hg at 

600 °C to about 130 mmHg at 800 °C. Over mixtures which are NaCl-rich (i.e., AlCl, 25mol%, NaCl 75 mol%) the partial pressure of A1C13 becomes significantly less than for the pure tetrachloroaluminate. The vapor pressure of A1C13 amounts at 790 °C to 14.9 mm Hg and that of NaAlCI4 to 56.6 mm Hg. 

In the discharged state of ZEBRA batteries NaCl is formed in the positive electrode, which is beside the NaAlCl4. In abuse experiments, e.g., overheating, less volatile material will be released in the discharged state compared with the charged state where no NaCl is present. This is due to the lower vapor pressure of mixtures with increased NaCl content. 

For the calculation of free volume inside the cell, which is essential for the design of a ZEBRA cell to keep internal pressure low for safety reasons, the density of molten NaAlCl4 over the full temperature range between 160 and 600 °C should be known. Berg et al. [33] have compared these values with the literature. The densities are compiled in Table 9. 

The viscosity of the NaCl-AlCL, melt system was investigated near the NaAlCl4 region by Cleaver and Koronaios 

With increasing content of AlCl, the viscosity increases. 

At the lower temperature, a smaller fraction of the molecules have the energy required to escape from the liquid, so evaporation is slower and the equilibrium vapor pressure (Section 13-7) is lower. 

The two opposing rates are not zero, but are equal to one another—hence we call this dynamic, rather than static, equilibrium. Even though evaporation and condensation are both continuously occurring, no net change occurs because the rates are equal. 

If the vessel were left open to the air, however, this equilibrium could not be reached. Molecules would diffuse away, and slight air currents would also sweep some gas molecules away from the liquid surface. This would allow more evaporation to occur to replace the lost vapor molecules. Consequendy, a hquid can eventually evaporate entirely if it is left uncovered. This situation illustrates LeChatelier s Principle  

A system at equilibrium, or changing toward equilibrium, responds in the way that tends to relieve or undo any stress placed on it. 

In this example the stress is the removal of molecules in the vapor phase. The response is the continued evaporation of the liquid to replace molecules in the vapor. 

Molecules can escape from the surface of a liquid into the gas phase by evaporation. Suppose we place a quantity of ethanol (CH3CH2OH) in an evacuated, closed container, as in FIGURE 11.23. The ethanol quickly begins to evaporate. As a result, the pressure exerted by the vapor in the space above the liquid increases. After a short time the pressure of the vapor attains a constant value, which we call the vapor pressure. 

At any instant, some of the ethanol molecules at the liquid surface possess sufficient kinetic energy to overcome the attractive forces of their neighbors and, therefore, escape into the gas phase. At any particular temperature, the movement of molecules from liquid phase to gas phase goes on continuously. As the number of gas-phase molecules 

Molecules leave and enter liquid at equal rates, pressure reaches steady-state value 

The condition in which two opposing processes occur simultaneously at equal rates is called dynamic equilibrium (or simply equiltbrium). A liquid and its vapor are in dynamic equilibrium when evaporation and condensation occur at equal rates. It may appear that nothing is occurring at equilibrium because there is no net change in the system. In fact, though, a great deal is happening as molecules continuously pass from liquid state to gas state and from gas state to liquid state. The vapor pressure of a liquid is the pressure exerted hy its vapor when the liquid and vapor are in dynamic equilibrium. 

The experimental methods used for the study of thermodynamic parameters such as Xi and 0 of a polymer in dilute solutions are numerous. Among them are intrinsic viscosity, light scattering, diffusion, sedimentation, vapor pressure, and phase equilibrium. Here we discuss vapor pressure and phase equilibrium, leaving the other methods for later chapters. 

The classical way to describe thermodynamic properties of a solution, such as vapor pressure and osmotic pressure, is to describe the behavior of solvent activity a over the whole concentration range. By definition. 

Poly(vinyl chloride) Cyclohexane Benzyl alcohol 155.4 

Poly(methyl methacrylate) Benzene, ra-Butyl chloride 35.4 

The parameter Inaj can be determined by measuring the vapor pressure of the solvent in the polymer solution, p, and in its pure phase, p  

If a quantity of a pure liquid is placed in an evacuated container that has a volume greater than that of the liquid, a portion of the liquid will evaporate so as to fill the remaining volume of the container with vapor. Provided that some liquid remains after the equilibrium is established, the pressure of the vapor in the container is a function only of the temperature of the system. The pressure developed is the vapor pressure of the liquid, which is a characteristic property of a liquid it increases rapidly with temperature. The temperature at which the vapor pressure is equal to 1 atm is the normal boiling point of the liquid, T. Some solids are sufficiently volatile to produce a measurable vapor pressure even at ordinary temperatures if it should happen that the vapor pressure of the solid reaches 1 atm at a temperature below the melting point of the solid, the solid sublimes. This temperature is called the normal sublimation point, T. The boiling point and sublimation point depend upon the pressure imposed upon the substance. 

The existence of a vapor pressure and its increase with temperature are consequences of the Maxwell-Boltzmann energy distribution. Even at low temperatures a fraction of the molecules in the liquid have, because of the energy distribution, energies in excess of the cohesive energy of the liquid. As shown in Section 4.10, this fraction increases rapidly with increase in temperature. The result is a rapid increase in the vapor pressure with increase in temperature. The same is true of volatile solids. 

From the general Boltzmann distribution, the relation between the vapor pressure and heat of vaporization can be made plausible. A system containing liquid and vapor in 

The auxiliary Eq. (5.8) suffices to evaluate the constant p Taking logarithms, Eq. (5.7) becomes 

A convenient method f or determining the heat of vaporization of a liquid is to measure its vapor pressure at several temperatures. After the experimental data are plotted in the manner of Fig. 5.1, the slope of the line is measured and from this the value of is calculated. If only simple apparatus is used, this method is capable of yielding results of higher accuracy than would a calorimetric determination of Qvap rising simple apparatus. 

Imagine a pure liquid in a vacuum-sealed container. If we were to examine the space inside the container, above the liquid, we would find that it is not really a vacuum. Instead it would contain vapor molecules from the liquid. The liquid molecules are held in the liquid by intermolecular bonds. However, they contain a certain amount of kinetic energy, which depends upon the temperature. Some of the liquid molecules at the surface contain enough kinetic energy to break the intermolecular bonds that hold them in the liquid. These molecules launch themselves into the open space above the liquid. As the space fills with molecules, some of the molecules crash back into the liquid. When the rate of molecules leaving the liquid equals the rate of molecules entering the liquid, equilibrium has been established. At this point, the pressure created by the molecules in the open space is called the vapor pressure of the liquid. 

Lecture 4 Solutions 71 When solutions form, entropy increases. 

Equilibrium between the liquid and gas phases of a compound occurs when tine molecules move from liquid to gas as quickijy as they move from gas to liquid. The vapor pressure necessary to bring the liquid and gas phases of a compound to equilibrium is called the vapor pressure of the compound. 

Since vapor pressure is related to the kinetic energy of the molecules, vapor pressure is a function of temperature. A derivation of tine Clausius-Clapeyron equation relates vapor pressure and temperature to the heat of vaporization  

When vapor pressure equals local atmospheric pressure, a compound boils. Solids also have a vapor presssure. The melting point is the temperature at which the vapor pressures of the solid is equal to the vapor pressure of the liquid. Above the melting point the liquid vapor pressure is greater than that of the solid below the melting point the liquid vapor pressure is less than that of the solid. 

If these various physical and chemical properties are known, then we can predict in which phase (and to what extent) an organic compound would end up. Let us look at these properties one by one. 

Vapor pressure is essentially the solubility of a compound in air. Permanent gases, such as methane, have high vapor pressures in fact, they have a vapor pressure of 1 atmosphere (atm) or 760 Torr. Some pesticides have medium vapor pressures for example, hexa-chlorobenzene has a vapor pressure of about 10 7 atm. Some compounds, such as decachlorobiphenyl, have vapor pressures that are so low that they are essentially nonvolatile (10 1(1 atm). For our purposes, the interesting range is 10 4 to 10 x atm. 

Vapor pressures are a strong function of temperature. The relationship is given by the Clausius-Clapeyron equation  

If we know a compound s boiling point (which is the temperature at which its vapor pressure is 1 atm), we can predict its vapor pressure at a given temperature (T) from 

This refers to the saturated solubility of the organic compound in water. We will give it the symbol of C which is in mol/L. For typical organic pollutants, this value is usually very low. For example, a relatively 

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American Petroleum Institute, Bibliographies on Hydrocarbons, Vols. 1-4, "Vapor-Liquid Equilibrium Data for Hydrocarbon Systems" (1963), "Vapor Pressure Data for Hydrocarbons" (1964), "Volumetric and Thermodynamic Data for Pure Hydrocarbons and Their Mixtures" (1964), "Vapor-Liquid Equilibrium Data for Hydrocarbon-Nonhydrocarbon Gas Systems" (1964), API, Division of Refining, Washington. 

Boublik, T., V. Fried, and E. Hala "The Vapor Pressure of Pure Substances," Elsevier, Amsterdam, 1973. 

Compilation of physical properties for 321 heavy hydrocarbons. Vapor pressures at low pressures. ... 

Correlation and compilation of vapor-pressure data for pure fluids. Normal and low pressure region. 

Source for liquid-liquid and vapor-liquid equilibrium data and vapor-pressure data. 

Jordan, T. E. "Vapor Pressure of Organic Compounds," Interscience, New York, 1954. 

Compilation of vapor-pressure data for organic compounds data are correlated with the Antoine equation and graphs are presented. 

Vapor-liquid equilibrium data and vapor pressure data, Vol. 2 (2a) and Vol. 4 (4b) and liquid-liquid equilibrium data, Vol. 2 (2b, 2c). 

Nesmeyanov, A. N. "Vapor Pressure of the Chemical Elements," Elsevier, New York, 1963. 

Vapor-pressure data correlated with the Antoine equation. Results displayed graphically. 

Vapor-pressure data and other thermodynamic properties. 

Wichterle, I., and J. Linek "Antoine Vapor Pressure Constants of Pure Compounds," Academia, Prague, 1971. 

Presents vapor-pressure data for a large number of substances. 

Presents Antoine vapor-pressure constants for pure compounds for two pressure ranges. 

Zwolinski, B. J., and R. C. Wilhoit "Vapor Pressures and Heats of Vaporization of Hydrocarbons and Related Compounds," Thermodynamic Research Center, Dept, of Chemistry, Texas A M University, College Station, Texas, 1971. 

Compilation of vapor pressures of organic and related compounds to one atmosphere. 

Normally, Henry s constant for solute 2 in solvent 1 is determined experimentally at the solvent vapor pressure Pj. The effect of pressure on Henry s constant is given by... 

P the other terms provide corrections which at low or moderate pressure are close to unity. To use Equation (2), we require vapor-pressure data and liquid-density data as a function of temperature. We also require fugacity coefficients, as discussed in Chapter 3. 

Enthalpies are referred to the ideal vapor. The enthalpy of the real vapor is found from zero-pressure heat capacities and from the virial equation of state for non-associated species or, for vapors containing highly dimerized vapors (e.g. organic acids), from the chemical theory of vapor imperfections, as discussed in Chapter 3. For pure components, liquid-phase enthalpies (relative to the ideal vapor) are found from differentiation of the zero-pressure standard-state fugacities these, in turn, are determined from vapor-pressure data, from vapor-phase corrections and liquid-phase densities. If good experimental data are used to determine the standard-state fugacity, the derivative gives enthalpies of liquids to nearly the same precision as that obtained with calorimetric data, and provides reliable heats of vaporization. 

This chapter presents quantitative methods for calculation of enthalpies of vapor-phase and liquid-phase mixtures. These methods rely primarily on pure-component data, in particular ideal-vapor heat capacities and vapor-pressure data, both as functions of temperature. Vapor-phase corrections for nonideality are usually relatively small. Liquid-phase excess enthalpies are also usually not important. As indicated in Chapter 4, for mixtures containing noncondensable components, we restrict attention to liquid solutions which are dilute with respect to all noncondensable components. 

An apparent systematic error may be due to an erroneous value of one or both of the pure-component vapor pressures as discussed by several authors (Van Ness et al., 1973 Fabries and Renon, 1975 Abbott and Van Ness, 1977). In some cases, highly inaccurate estimates of binary parameters may occur. Fabries and Renon recommend that when no pure-component vapor-pressure data are given, or if the given values appear to be of doubtful validity, then the unknown vapor pressure should be included as one of the adjustable parameters. If, after making these corrections, the residuals again display a nonrandom pattern, then it is likely that there is systematic error present in the measurements. ... 

Correlations for standard-state fugacities at 2ero pressure, for the temperature range 200° to 600°K, were generated for pure fluids using the best available vapor-pressure data. 

The correlations were generated by first choosing from the literature the best sets of vapor-pressure data for each fluid. 

These were converted from vapor pressure P to fugacity using the vapor-phase corrections (for pure components), discussed in Chapter 3 then the Poynting correction was applied to adjust to zero pressure ... 

The user may also choose to use the vapor-pressure equation instead of the fugacity at zero pressure. 

If the data are correlated assuming an ideal vapor, the reference fugacity is just the vapor pressure, P , the Poynting correction is neglected, and fugacity coefficient is assumed to be unity. Equation (2) then becomes... 

Third and Fourth cards FORMAT(3E20.14), constants for zero-pressure reference fugacity equation, vapor pressure equation, or hypothetical-liquid reference fugacity equation of the form... 

VAPOR PRESSURE EQUATION AND IDEAL VAPOR PHASE... 

ASSOCIATION AND SOLVATION PARAMETERS CONSTANTS FOR ZERO PRESSURE PEFEPENCE FUGACITY EQUATION IF IVAP.EQ.I OR CONSTANTS FOR VAPOR PRESSURE EQUATION IF IVAP.GT.I... 

CALCULATE PURE COMPONENT LIQUID FUGACITY AT SPECIFIED TEMP AND ZERO PRESSURE IF IVAP.LE.2 C PURE CCMPDNENT VAPOR PRESSURE IF IVAP.EQ.3... 

Liquid chromatography, having a resolving power generally less than that of gas phase chromatography, is often employed when the latter cannot be used, as in the case of samples containing heat-sensitive or low vapor-pressure compounds. 

The analyst now has available the complete details of the chemical composition of a gasoline all components are identified and quantified. From these analyses, the sample s physical properties can be calculated by using linear or non-linear models density, vapor pressure, calorific value, octane numbers, carbon and hydrogen content. 

For non-polar components like hydrocarbons, the results are very satisfactory for calculations of vapor pressure, density, enthalpy, and specific, heat and reasonably close for viscosity and conductivity provided that is greater than 0.10. 

If the vapor pressure is of interest, the acentric factor is calculated by the Lee and Kesler formula or by the Soave method, which are given in article 4.5.2. 

For our needs, the saturation pressure of a mixture will be defined as the vapor pressure of a pure component that has the same critical constants as the mixture ( JT... 

Each fluid is described by a BWR equation of state whose coefficients are adjusted to obtain simultaneously the vapor pressure, enthalpies of liquid and gas as well as the compressibilities. The compressibility z of any fluid is calculated using the equation below ... 

At the saturation pressure, the viscosity variation with temperature follows a law analogous to that of Clapeyron for the vapor pressure f ) ... 

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