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Multiphase Systems
Phase Diagrams for Pure Substances
See Fig. 6.1-1 on p. 241 for reference. Learn the definitions of the following terms, and their location on a phase diagram:
critical point triple point vapor pressure curve melting curve sublimation curve normal boiling point normal melting point saturated liquid saturated vapor solid, liquid, and gas regions supercritical region
Vapor Pressures
Clausius-Clapeyron equation
Relates slope of vapor pressure curve to enthalpy change and volume change on vaporization.
In approximate, integrated form (Eqn. 6.1-3) predicts that ln p* vs 1/T is a straight line, which is the basis for interpolation of vapor pressures.
Cox chart
Plot log p* versus log p* (^) ref for any number of substances, then replace the scale on the x-axis with a temperature scale (using experimental data for the reference substance).
The result is a Cox chart (Fig. 6.1-4, p. 247), which will turn out to give nearly straight lines for all substances. Become familiar with this chart and the species for which vapor pressures are represented on it.
Test yourself. 1. What are the triple point conditions for CO 2?
- Why does dry ice sublime at atmospheric pressure?
- What is the normal boiling point for mercury?
- What is the vapor pressure of methanol at 250 o^ F?
- What is the vapor pressure of propane at 250 o^ F?
Antoine equation:
3-parameter fits to data - see Table B.4, p. 640 for constants for some species.
better than Clausius-Clapeyron equation.
more accurate than reading information off the Cox chart.
stay within the specified ranges for good accuracy
Gibbs Phase Rule
F = degrees of freedom = number of phase equilibrium variables (T, P, mole fraction compositions in each phase) which can be independently specified
m = number of components
= number of phases
F = m + 2 -
Example. In a system containing two components (m = 2, e.g., water and carbon dioxide) and two phases ( = 2, e.g., vapor and liquid phases present), two of the phase equilibrium variables must be given (F = 2) to fix all the others, for example, P and T can be fixed, or P and x (^) A, or T and y (^) B , etc.
If r = the number of independent chemical reactions at equilibrium in the system, then the phase rule must be modified to become
F = m + 2 - - r
Gas-Liquid Systems with One Condensable Component
Two components: 1) a volatile liquid A (e.g., water) 2) a non-condensable gas B (e.g., air)
m = 2
Two phases: 1) liquid 2) vapor
No reactions: r = 0
Degrees of freedom: F = 2 + 2 - 2 = 2
Absolute humidity = 0.0087 kg water/kg dry air
Multicomponent Gas-Liquid Systems
Use of tabulated vapor-liquid equilibrium data
Example. Ammonia gas is absorbed from an air stream by use of liquid water as a solvent. Conditions in the absorber are 100. o^ F and 50. psia. The liquid solution entering the top of the tower is 10.0 mole % ammonia. What is the composition of the gas stream leaving the top of the absorber, if it can be assumed to be in equilibrium with the liquid phase? If the inlet gas contained 30.0 mole % ammonia, what fraction was removed in the absorber?
From Perry’s Handbook, at these conditions, the equilibrium partial pressures of the two liquid components over a 10.0 mole % solution are 1.98 psia for ammonia and 0.45 psia for water. Thus, the mole fractions are
y(NH 3 ) = 1.98/50. = 0.
y(H 2 O) = 0.45/50. = 0.
y(air) = 1 - 0.040 - 0.010 = 0.
The fraction ammonia removed can be found by (in - out)/in:
frac removed = (0.300-0.040*0.700/0.950)/0. = 0.
Raoult’s and Henry’s laws
Raoult’s law – ideal liquid solution, ideal gas
Py (^) A = p (^) A*xA
Component A must be below its critical temperature.
Henry’s law – ideal dilute solution, ideal gas
Py (^) A = HAxA
Component A must be in low concentration (solute). Component A may be above its critical temperature.
Component B (solvent -- binary mix) must obey Raoult’s law.
xA = solubility of A in the solvent (B) HA = Henry’s law constant (must be found experimentally)
Important terms: bubble point dew point Pxy diagram (at constant T) Txy diagram (at constant P)
Question: How do you use Raoult’s law to calculate dew and bubble points for mixtures?
Solutions of Solids in Liquids
Phase diagrams
Pressure is not usually important for solid-liquid systems. Temperature is almost always important.
If both the liquid and solid phases are completely miscible (very unusual), then the phase diagram will look exactly like a liquid-vapor Txy diagram (Fig. 6.4-1), but it would be a Tx (^) LxS diagram.
If the liquid phase is miscible, but the two solids are completely immiscible, then a eutectic point results.
Liquid (L)
L + S 1 C D E
P T
Saturated Liquid
Solid Phase
T
Liquid + Pure Solid 1
Liquid + Pure Solid 2
