Vapor pressure curve equilibrium

Nonvariant regions are points in the phase diagram (triple points r, i = 3) indicating equilibrium of three phases (g, 1, s or s, s, 1 or s, s, g, etc.). The vapor pressure curve (equilibrium 1 g) terminates in a critical point C. Above the critical temperature, liquid and gaseous states are indistinguishable (supercritical fluid state). 

The vapor pressure (P ) of a pure liquid at a given temperature (T) is the pressure exerted by its vapor in equilibrium with the liquid phase in a closed system. All liquids and solids exhibit unique vapor pressure-temperature curves. For instance, in Figure 2-79, lines BA and AC represent the equilibrium vapor pressure curves of the solid and liquid phases, respectively. 

Curve AC represents the vapor pressure curve of ice. At any point along this line, such as point A (0°C, 5 mm Hg) or point C, which might represent — 3°C and 3 mm Hg, ice and vapor are in equilibrium with each other. 

An exceptional case of a very different type is provided by helium [15], for which the third law is valid despite the fact that He remains a liquid at 0 K. A phase diagram for helium is shown in Figure 11.5. In this case, in contrast to other substances, the solid-liquid equilibrium line at high pressures does not continue downward at low pressures until it meets the hquid-vapor pressure curve to intersect at a triple point. Rather, the sohd-hquid equilibrium line takes an unusual turn toward the horizontal as the temperature drops to near 2 K. This change is caused by a surprising... 

If the lid is removed, and the external surroundings have partial pressure Ph2o less than 23.8 Torr ( relative humidity < 100% ), then water will evaporate from the beaker into the surroundings until the beaker is empty, because only vapor is stable under these conditions. However, if the external surroundings have partial pressure Ph2o >23.8 Torr, water will condense from the surroundings to fill the beaker, because only liquid is stable under these conditions. Thus, the saturation vapor pressure ( 100% relative humidity ) corresponds to the unique concentration (partial pressure) of water vapor that can coexist at equilibrium in the atmosphere above liquid water at 25°C. Other (T, P) points on the vapor-pressure curve can be interpreted analogously. 

It is normal to assume that the vapor leaving the top of a tower is at its dew point. That is, it is at equilibrium with the liquid on the top tray of the tower. Unfortunately, this assumption falls apart if the tower is flooding and liquid is being entrained overhead from the column, with the vapor. However, assuming a normal, nonflooded condition, we will guess that the tower-top temperature is 140°F. Using the vapor-pressure curves provided in Fig. 9.1, we would calculate as follows ... 

Pressure has a marked effect on the azeotropic composition and vapor-liquid equilibrium diagrams of alcohol-ketone systems (J). This is due to the fact that the slopes of the vapor pressure curves of alcohols are appreciably greater than for ketones it results in an unusually larger change in the relative boiling points of the components of an alcohol-ketone system with change in pressure. 

Figure 14.9 is a three-dimensional graph that shows the extension of (vapor + liquid) equilibrium isotherms or isobars to the critical region. Line ab at X2 = 0 is the vapor pressure line for pure component 1, with point b as the critical point. In a like manner, line cd at x2 = 1 is the vapor pressure line for pure component 2, with point d as the critical point. Note that at temperatures and pressures below points b and d, the isotherms and isobars (shown as the shaded areas) intersect the vapor pressure curves.k However,... 

Liquid and vapor are at equilibrium along the vapor pressure curves shown for pure water (solid line) and an aqueous solution (dashed line). The vapor pressure is lower for the solution, in accord with Raoult s law, and thus the boiling point is increased (liquids boil at 1 atm)... 

Figure 1. Pressure -Temperature Projection of Vapor Pressure Curve for Pentane and Solid-Liquid-Gas Equilibrium Curve for Pentane-TPP Mixtures.

Equation (26) represents the intersection of two surfaces in p(P, T) space. The intersection of two surfaces is a curve in the three-dimensional space. The projection of this curve on the PT plane is given by P(T). Because P is a function of T, at equilibrium between two phases, the system has been reduced to one degree of freedom by the requirement of Eq. (26). If one of the phases is a gas, P(T) is the vapor pressure curve of the condensed phase. If both phases are condensed, P is the externally applied pressure. Alternatively, we could consider T(P), which gives the temperature at which two phases are at equilibrium as a function of pressure. 

Thus, temperature and pressure can both be varied while remaining in a region of a single phase, whereas only temperature or pressure can be varied (e.g., on a vapor-pressure curve) while retaining equilibrium between two phases. The triple point is completely invariant. More interesting applications of the phase rule are obtained with multicomponent systems, as indicated in the following examples. 

The third plane identified in Fig. 12.1 is the vertical one perpendicular to the composition axis and indicated by MNQRSLM. When projected on a parallel plane, the lines from several such planes present a diagram such as that shown by Fig. 12.4. This is the PT diagram lines t/C, and KC2 are vapor-pressure curves for the pure species, identified by the same letters as in Fig. 12.1. Each interior loop represents the PT behavior of saturated liquid and of saturated vapor for a mixture of fixed composition the different loops are for different compositions. Clearly, the PT relation for saturated liquid is different from that for saturated vapor of the same composition. This is in contrast with the behavior of a pure species, for which the bubble line and the dew line coincide. At points A and B in Fig. 12.4 saturated-liquid and saturated-vapor lines intersect. At such points a saturated liquid of one composition and a saturated vapor of another composition have the same T and P, and the two phases are therefore in equilibrium. The tie lines connecting the coinciding points at A and at B are perpendicular to the PT plane, as illustrated by the tie line VX in Fig. 12.1. 

The equilibrium relations between the two crystalline forms of sulfur and the liquid may be clarified "by Figure 17-2, which shows the vapor-pressure curves for... 

If tlie tube is only partially filled with liquid (the remainder being vapor in equilibrium with the liquid), heating at first causes changes described by the vapor-pressure curve (solid line) of Fig. 3.3. For the process indicated by line J Q on Fig. 3.2(b), the meniscus is initially near tire top of the hibe (point J), and the liquid expands upon heating until it completely fills tire hibe (point Q). On Fig. 3.3 the process traces a path from (J, K) to Q, and with further heating departs from the vapor-pressure curve along the line of constant molar volume Vl-... 

You know that a substance s state depends on temperature and that pressure affects state changes. To get a complete picture of how temperature, pressure, and states are related for a particular substance, you can look at a phase diagram. A phase diagram has three lines. One line is a vapor pressure curve for the liquid-gas equilibrium. A second line is for the liquid-solid equilibrium, and a third line is for the solid-gas equilibrium. All three lines meet at the triple point. The triple point is the only temperature and pressure at which three states of a substance can be in equilibrium. 

The horizontal line at 101.3 kPa intersects the vapor pressure curve for the solid at -78.5°C. Therefore, solid carbon dioxide sublimes at this temperature. This sublimation point is equivalent to the normal boiling point of a liquid such as water. Because dry ice is at equilibrium with carbon dioxide gas at -78.5°C, it is frequently used to provide this low temperature in the laboratory. 

Pure solid solvent coexists at equilibrium with its characteristic vapor pressure, determined by the temperature (Section 10.4). Solvent in solution likewise coexists with a certain vapor pressure of solvent. If solid solvent and the solvent in solution are to coexist, they must have the same vapor pressure. This means that the freezing temperature of a solution can be identified as the temperature at which the vapor-pressure curve of the pure solid solvent intersects that of the solution (Fig. 11.12). As solute is added to the solution, the vapor pressure of the solvent falls and the freezing point, the temperature at which the first crystals of pure solvent begin to appear, drops. The difference ATf = T/ — Tf is therefore negative, and a freezing-point depression is observed. 

A term commonly applied to the vapor-liquid portion of the vapor-pressure curve is the word saturated, meaning the same thing as vapor and liquid in equilibrium with each other. If a gas is just ready to start to condense its first drop of liquid, the gas is called a saturated gas if a liquid is just about to vaporize, it is called a saturated liquid. These two conditions are also known as the dew point and bubble point, respectively. 

The region to the right of the vapor-pressure curve in Fig. 3.9 is called the superheated region and the one to the left of the vapor-pressure curve is called the sub-cooled region. The temperatures in the superheated region, if measured as the difference (0-N) between the actual temperature of the superheated vapor and the saturation temperature for the same pressure, are called degrees of superheat. For example, steam at 500 F and 100 psia (the saturation temperature for 100 psia is 327.8°F) has (500 — 327.8) = 172.2 F of superheat. Another new term you will find used frequently is the word quality. A wet vapor consists of saturated vapor and saturated liquid in equilibrium. The mass fraction of vapor is known as the quality. 

Liquids Vapor pressure is the most important of the basic thermodynamic properties of fluids. It is the pressure of equilibrium, coexisting liquicf and vapor phases at a specified temperature. The vapor pressure curve is a monotonic function of temperature from its minimum value (the triple point pressure) at the triple point temperature T, to its maximum value (the critical pressure) at T. ... 

It is well known that the vapor pressure curves of the solid and liquid phases of a given substance meet at the triple point thus, in Fig. 16 the curve AO represents solid-vapor equilibria, OB is for liquid-vapor, and OC for solid-liquid equilibria. The three curves meet at the triple point O where solid, liquid and vapor can coexist in equilibrium. It will be observed that near the triple point, at least, the slope of the curve AO on the pressure-temperature diagram is greater than that of OB , in other words, near the... 

For a maximum or minimum in the total vapor pressure curve, dP/dni must be zoro hence, by equation (35.4), either dps/dNi must be zero, or N pi must equal Nip. The former condition is unlikely, since it would mean that the partial vapor pressure would remain constant in spite of a change of composition, and so for a mairimum or minimum in the total vapor pressure curve NjPi = Nips or N1/N2 = pi/p. If the gases behave ideally, Pi/pt is equal to Ni/i, and the vapor will ve the same composition as the liquid in equilibrium with it, as stated above. 

The curved line from T to C in Figure 13-17a is a vapor pressure curve obtained experimentally by measuring the vapor pressures of water at various temperatures (Table 13-8). Points along this curve represent the temperature-pressure combinations for which liquid and gas (vapor) coexist in equilibrium. At points above AC, the stable form of water is liquid below the curve, it is vapor. 

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