Page 365 - Chemical engineering design

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CHEMICAL ENGINEERING
OL
D standard state fugacity of the pure liquid
f
i
i D liquid-phase activity coefficient
x i D concentration of component i in the liquid phase
Substitution from equations 8.29 and 8.30 into equation 8.28, and rearranging gives:
i f OL
y i i
K i D D 8.31
x i
i
where K i is the distribution coefficient (the K value).
i can be calculated from an appropriate equation of state (see Section 8.16.3).
f OL can be computed from the following expression:
i

P
o
i
o s
f OL D P exp L (8.32)
i i i i
RT
o
where P D the pure component vapour pressure (which can be calculated from the
i
Antoine equation, see Section 8.11), N/m 2
s
D the fugacity coefficient of the pure component i at saturation
i
L
3
D the liquid molar volume, m /mol
i
The exponential term in equation 8.32 is known as the Poynting correction, and corrects
for the effects of pressure on the liquid-phase fugacity.
s
is calculated using the same equation of state used to calculate i .
i
For systems in which the vapour phase imperfections are not significant, equation 8.32
reduces to the familiar Raoult’s law equation (see Volume 2, Chapter 11):
i P o i
K i D 8.33

Relative volatility
The relative volatility of two components can be expressed as the ratio of their K values:
K i
˛ ij D 8.34
K j
For ideal mixtures (obeying Raoult’s law):

P o i
K i D 8.35
P
and
K o i P o i
˛ ij D o D o 8.36
K P
j j
o
o
where K and K are the ideal K values for components i and j.
i j