lecture 3
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Fall 2008
ChE 545: Mass Transfer Operations I
Lecture 3: Thermodynamics and Equilibrium
Activity coefficient ( ) of a component is related to the partial molar excess Gibbs
free energy( ) for that component:
gE, molar excess Gibbs free energy, is a function of composition (xis), T, and P.
For a regular solution (no excess volume or entropy, vE = s
E = 0), the activity
coefficient is given by:
where, is the solubility parameter, is the volume fraction, and vL the molar
volume in the liquid phase.
Other expressions are available for the activity coefficients, based on the
functional relationship for the excess Gibbs free energy. These relationships are
based on various theories of solution (Wilson, NRTL, UNIQUAC, etc.).
Gibbs Phase rule stipulates the number of independent variables that need to be
specified for fixing the equilibrium state of the system consisting of C
components and P phases.
F = C – P + 2
The phase rule refers to intensive properties (independent of the system size).
The degree of freedom for a binary vapor-liquid system is 2, meaning only 2
variables need to be specified (out of P, T, x1 and y1) to fix the equilibrium
conditions. The two independent equations (assuming ideality, i.e., Raoult’s law)
are:
T-x-y, and x-y diagrams can be constructed using these equations. The region
enclosed by T-x and T-y lines on the T-x-y diagram comprises a two phase region.
Any point within this region denotes the overall composition of the system
(abscissa) at that temperature (ordinate). Horizontal line passing through this
point connecting the T-x and T-y curves is called a tie line. The intersections of
the tie line with the two curves represent the vapor and liquid concentrations at
equilibrium with each other. The relative amounts of liquid and vapor can be
determined using inverse lever rule.
Alternately,
Where, 2,1 is the separation factor (relative volatility) of component 2 with
respect to component 1, and is given by (for Raoult’s law case):
Azeotropes (constant boiling mixtures, x1 = y1) result due to the non-ideality of
the system.
o Minimum boiling azeotropes have the azeotrope boiling at a lower
temperature than the boiling point of the more volatile component (and
also the less volatile component). These result when activity coefficients
of the components are greater than 1.
o Maximum boiling azeotropes boil at a temperature higher than the boiling
point of the less volatile component (and also the more volatile
component). Activity coefficients are less than 1 in this case.
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