Boiling pressure curve

Boiling Pressure Curve (Vapor Pressure Curve)... 

When all the dew points measured in this way are coimected, a steep curve to the right is the result, the so-called boiling pressure curve or vapor pressure curve (Fig. 11.7). It gives the values of pressure and temperature at which gas and... 

Fig. 11.7 Temperature dependency of a liquid s vapor pressure (boiling pressure curve or vapor pressure curve).

No dew point exists above the critical temperature 7).. This is the highest temperature at which a liquid can exist. For this reason, the boiling pressure curve ends at the critical temperature— in the critical point mentioned above. 

How can we now quantitatively approximate the boiling pressure curve To do this we will need to refer back to the chemical potential. As we have seen, every phase of a substance has its own chenucal potential, which is dependent upon temperature and pressure. We can easily calculate these potentials for different temperatures and pressures. At an arbitrary condition, the most stable phase is the one with the lowest chemical potential. The stability range of the liquid phase is characterized by the chemical potential p p, T) being lowest there. Where the gaseous phase is stable, Pg(p, T) is minimal. 

If instead of choosing an arbitrary initial state when calculating the boiling pressure curve (characterized by temperature To and pressure po), we use the special case of an equilibrium state, meaning a known boiling point, e.g., the standard boiling point Tj , the relation (11.9) can be simplified In equilibrium, the drive of the vaporization process equals zero, and we find... 

The other phase boundaries can also be calculated using the chemical potential. For example, the sublimation pressure curve can be described analogously to the boiling pressure curve. We only need the drive Ag,o = /sublimation entropy A gSo (both at temperature To and pressure po)-... 

In practice, however, it is recommended to adjust the coefficient m, in order to obtain either the experimental vapor pressure curve or the normal boiling point. The function f T ) proposed by Soave can be improved if accurate experimental values for vapor pressure are available or if it is desired that the Soave equation produce values estimated by another correlation. 

The vapour pressure of a liquid increases with rising temperature. A few typical vapour pressure curves are collected in Fig. 7,1, 1. When the vapour pressure becomes equal to the total pressure exerted on the surface of a liquid, the liquid boils, i.e., the liquid is vaporised by bubbles formed within the liquid. When the vapour pressure of the liquid is the same as the external pressure to which the liquid is subjected, the temperature does not, as a rale, rise further. If the supply of heat is increased, the rate at which bubbles are formed is increased and the heat of vaporisation is absorbed. The boiling point of a liquid may be defined as the temperature at which the vapour pressure of the liquid is equal to the external pressure dxerted at any point upon the liquid surface. This external pressure may be exerted by atmospheric air, by other gases, by vapour and air, etc. The boiling point at a pressure of 760 mm. of mercury, or one standard atmosphere, may be termed the normal boiling point. 

The effect of superheated steam may be illustrated by reference to baizaldehyde, which boils at 178° at 760 mm. It distils with steam at 97-9° (Pj = 703-5 mm. and pg = 56-5 mm.) and the distillate contains 32-1 per cent, of benzaldehyde by weight. If one employs steam superheated to 133°, the vapour pressure of benzaldehyde (extrapolated from the boUing point - pressure curve) is 220 mm. hence pj = 540 (water), Pg = 220 (benzaldehyde), and... 

Fig. 8. Boiling and freezing temperatures of KOH solutions (33). The boiling point curve assumes a pressure of 101.3 kPa (760 mm Hg).

Because trichlor is 99.9% overhead, use it only to select boiling point from vapor pressure curves at 10 psig overhead pressure = 223°F (1,280 mm Hg abs). 

That this value of T is greater for the solution than for the solvent, follows from the fact that the curve of the latter is intersected first, for the vapour-pressure curve of the solution (s s ) must lie beneath that of the pure solvent (ss) in the vicinity of the boiling-point. The corollary (1) to equation (7) below extends this conclusion over the whole length of t. u... 

Use the vapor-pressure curve in Fig. 8.3 to estimate the boiling point of water when the atmospheric pressure is... 

Figure 2.40 Heat transfer coefficient for film boiling of potassium on a horizontal type 316 stainless steel surface as a function of pressure. Curve A shows the experimental results of Padilla (1966). Curve B is curve A minus the radiant heat contribution. Curve C represents Eq. (2-150) with the proportionality constant arbitrarily increased to 0.68. (From Dwyer, 1976. Copyright 1976 by American Nuclear Society, LaGrange Park, IL. Reprinted with permission.)...

Increases in boiling points of many common solvents are significant with modest rises in pressure. The temperature versus pressure curves have points of inflection beyond which considerable increases in pressure afford relatively modest elevations in the boiling point [20]. These properties indicate that reaction pressures of 2-3 MPa would facilitate temperatures in the order of 200 °C for common solvents such as EtOAc, MeOH, EtOH, MeCN and Me2CO, all of which boil below 85 °C at atmospheric pressure. 

The dissolution of a solute into a solvent perturbs the colligative properties of the solvent, affecting the freezing point, boiling point, vapor pressure, and osmotic pressure. The dissolution of solutes into a volatile solvent system will affect the vapor pressure of that solvent, and an ideal solution is one for which the degree of vapor pressure change is proportional to the concentration of solute. It was established by Raoult in 1888 that the effect on vapor pressure would be proportional to the mole fraction of solute, and independent of temperature. This behavior is illustrated in Fig. 10A, where individual vapor pressure curves are... 

On the Theory of Steam Distillation.—The ideal case occurs when the substance to be distilled is insoluble, or, more accurately, sparingly soluble in water (examples toluene, bromobenzene, nitrobenzene) so that the vapour pressures of water and the substance do not affect each other, or hardly so. The case of substances which are miscible with water (alcohol, acetic acid) is quite different and involves the more complicated theory of fractional distillation. Let us consider the first case only and take as our example bromobenzene, which boils at 155°. If we warm this liquid with water, its vapour pressure will rise in the manner shown by its own vapour pressure curve and independently of that of water. Ebullition will begin when the sum of the vapour pressures of the two substances has become equal to the prevailing atmospheric pressure. This is the case, as we can find from the vapour pressure curves, at 95-25° under a pressure of 760 mm. 

Supercritical fluids represent a different type of alternative solvent to the others discussed in this book since they are not in the liquid state. A SCF is defined as a substance above its critical temperature (Tc) and pressure (Pc)1, but below the pressure required for condensation to a solid, see Figure 6.1 [1], The last requirement is often omitted since the pressure needed for condensation to occur is usually unpractically high. The critical point represents the highest temperature and pressure at which the substance can exist as a vapour and liquid in equilibrium. Hence, in a closed system, as the boiling point curve is ascended, increasing both temperature and pressure, the liquid becomes less dense due to thermal expansion and the gas becomes denser as the pressure rises. The densities of both phases thus converge until they become identical at the critical point. At this point, the two phases become indistinguishable and a SCF is obtained. 

In a very similar way as discussed above for estimating pi from boiling point data, one can treat the vapor pressure curve below the melting point. Again we use the Clausius-Clapeyron equation ... 

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