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Figure 8.1 Apparatus used to explore the p, V, and T properties of water.

ˆ

8.2 Phase Diagrams and the Phase Rule


Figure 8.2 Results of the experiment of heating at constant volume shown on a phase

diagram (p versus T at constant V).̂


Figure 8.3 Various common processes as represented on a p*-T diagram.


Figure 8.4 Experiments to obtain a p-V phase diagram. The dashed lines are measurements

made at constant temperatures T1 and T2. The dots represent the points at which

vaporization, or condensation, respectively, of the saturated liquid, or vapor, occurs; they

form an envelope about the two-phase region.

ˆ


Figure 8.5 Representation of quality on a p-V phase diagram. A is saturated liquid and C is

saturated vapor. The compound at B is part liquid and part vapor, and the fraction vapor is

called the quality.

ˆ


Figure 8.6 The p-V -T surface for water (a compound that expands on freezing) in three

dimensions showing also two-dimensional projections for sequential pairs of the three

variables.

ˆ


Figure 8.7 The surface of the solid-liquid-vapor phases of water with the coordinates of p, V,

and T.ˆ


8.3 Single-Component Two-Phase Systems (Vapor Pressure)

8.3.1 Prediction via Equations


Figure 8.8 Portion of the p-V phase diagram for water (note that the axes are logarithmic

scales).

ˆ


Figure 8.9 Cox chart. The vapor pressure of compounds other than water can be observed

to fall on straight lines.

8.3.3 Predicting Vapor Pressures from Reference Substance Plots


8.4 Two-Component Gas/Single-Component Liquid Systems

8.4.1 Saturation


Figure 8.10 Instrumentation for stack gas analysis.

8.4.2 condensation


Figure 8.11 Cooling of an air-water mixture at constant total pressure. The lines and curves

for the water are distorted for the purpose of illustration—the scales are not arithmetic units.


Figure 8.12 Effect of an increase of pressure on saturated air, removal of condensed water,

and a return to the initial pressure at constant temperature.


Figure 8.13 Change of partial and total pressure during the vaporization of water into initially

dry air (a) at constant temperature and total pressure (variable volume); (b) at constant

temperature and volume (variable pressure).

8.4.3 Vaporization


Figure 8.14 Evaporation of water at constant pressure and temperature of 65ºC.


8.5 Two-Component Gas/Two-Component Liquid Systems

8.5.1 Ideal Solution Relations


Figure 8.15 Application of Raoult’s law to an ideal solution of benzene and toluene (like

species) to get the total pressure as a function of composition. The respective vapor

pressures are shown by points A and B at 0 and 1.0 mole fraction benzene.


Figure 8.16 Plot of the partial pressures and total pressure (solid lines) exerted by a solution

of carbon disulfide (CS2)– methylal (CH2(OCH3)2) as a function of composition. The dashed

lines represent the pressures that would exist if the solution were ideal.


Figure 8.17 Phase diagram for a mixture of benzene and toluene at 80ºC. At 0 mol fraction

of benzene (point A) the pressure is the vapor pressure of toluene at 80ºC. At a mole fraction

of benzene of 1 (point B) the pressure is the vapor pressure of benzene at 80ºC. The tie line

shows the liquid and vapor compositions that are in equilibrium at a pressure of 0.62 atm

(and 80ºC).

8.5.2 Vapor-Liquid Equilibria Phase Diagrams


Figure 8.18 Phase diagram for a mixture of benzene and toluene at 0.50 atm. At 0 mole

fraction of benzene (point A) the temperature is that when the vapor pressure of toluene is

0.50 atm. At a mole fraction of benzene of 1 (point B) the temperature is that when the vapor

pressure of benzene is 0.50 atm. The tie line shows the liquid and vapor compositions that

are in equilibrium at a temperature of 80ºC (and 0.50 atm).


Figure 8.19 Phase diagram for a nonideal mixture of isopropanol and water at 1 atm.


8.5.3 K-value (Vapor-Liquid Equilibrium Ratio)


Figure 8.20 Change of K of water with composition at p = 1 atm.


Figure 8.21 K-values for isobutane as a function of temperature and pressure. From Natural

Gasoline Association of America Technical Manual, 4th ed. (1941), with permission (based on

data provided by George Granger Brown)


8.5.4 Bubble Point and Dew Point Calculations


8.6 Multicomponent Vapor-Liquid Equilibrium

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