14 ◾  Distillation Control, Optimization, and Tuning
energy consumed, that is, boilup and reflux flow rates, relative
to the feed rate. The relative volatility in a single stage originates thermodynamically from the ratio of pure component
vapor pressures and the ratio of activity coefficients in the liquid phase (Equation 3.1). The separation power is the ratio of
component 1 to component 2 in the vapor phase divided by
the ratio of component 1 to component 2 in the liquid phase.
Nonidealities in the vapor phase are often insignificant below
about 2 atm of pressure.
α = γ 1 p 1 /γ 2 p 2 = (y 1 /y 2 )/(x 1 /x 2 )
(3.1)
where:
α = relative volatility, alpha
γ = activity coefficient in liquid phase, gamma
p = pure component vapor pressure
x = mole fraction in liquid phase
y = mole fraction in vapor phase
subscript 1 = component 1
subscript 2 = component 2
For example, when 4.88 wt% ethanol in water is in equilibrium with 35.58 wt% ethanol in water vapor at atmospheric
pressure, the relative volatility, α, is equal to (35.58/64.42)/
(4.88/95.12) = 10.77.
When a binary system is ideal with no interaction, the
activity coefficients in the liquid phase are 1.0 and the system obeys Raoult’s law. One rough rule of thumb is that the
ratio of pure component vapor pressures is equal to 1.036
raised to the power of the difference in boiling points in
degrees Celsius. Komori and Ohe 1 reported a complete set of
vapor–liquid equilibrium data for cyclohexane/n-heptane at
atmospheric pressure as shown in Table 3 .1. The atmospheric
boiling point of n-heptane is 98.4°C, and the atmospheric boiling point of cyclohexane is 80.7, so the difference in boiling
point is 17.7°C. The rough rule of thumb suggests that the ratio