1. Evaluation of
The value of
at some temperature can be computed from values of
along with expressions for the ideal heat capacities.
2. Exact Equilibrium Composition for gases.
The equilibrium constant is defined as
. The left hand side
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are observed in a giant plasma membrane vesicle (GPMV) prepared as described in reference  and
fluorescently labeled with the fluorescent dye diIC12. The vesicle's critical temperature is 24.3 C. The
scale bar is 5 m.
The Thermodynamic web (Koretsky, Engineering and Chemical Thermodynamics, Wiley, 2004)
Measured properties: P, v and T
Fundamental properties: U and S are derived from the fundamental postulates of thermodynamics
First law-energy is conserved
Handling Heat Capacity-follows development in Sandler
From the previous sets of equations it is apparent that we need to have data on C p and Cv. So it would
seem that we need Cp=Cp(T,P) and Cv=Cv(T,v). This situation can be relaxed if we have PvT data or
Since we know the power, the problem
boils down to calculating the enthalpy change. We also know two intensive variables for the inlet and
outlet so all properties are constrained. Since the pressure is 10 bar, we cannot
Measurement of Intermolecular/Surface Forces
There are both direct and indirect methods of measuring intermolecular forces.
1) Thermodynamic data give info on the nature of short range interactions. It is relatively easy to
collect PVT data, boiling point
ethanol and water the ethanol molecules have an average of 1 hydrogen bond per molecule,
whereas the water molecules have 2. The ethanol molecules interfere with the hydrogen bonds
and therefore make the liquid more volatile.
ethanol and benzene the hydro
Phase Equilibria-Single component
There are a number of important questions to ask:
Why do different phases coexist for a pure species or mixtures?
What are the criteria for chemical equilibria?
How do I solve phase equilibria problems?
The Clapeyron equation
The equilibrium condition stataes that the Gibbs energy is equal in two coexisting phases (gas, liquid,
Each Gibbs energy for each phase is dependent on T and P and can be plotted as a surface. At each T and
P there is only
Free Energy of Mixing
Entropy of Mixing
nA atoms of A
nB atoms of B
Total atoms N = nA + nB
Then Smix = k ln W= k lnN!/nA!nb!
This can be rewritten in terms of
the two types of atoms:
nA/N = cA nB/N = cB
and using Stirlings approximation
B.1. Thermodynamics of Phase Transitions
In most cases a critical point is the terminal point of a line representing transi—
tions which are discontinuous or “1st order” transitions. This end point exhibits
many singularities arising from the continuous c
Combining the first and second law we found the THERMODYNAMIC POTENTIAL
which is powerful because it directly gives
As well as
So it is clear that the function E(S,V) is powerful. At the same time, the variable S is not convenient as it
cannot be measured
Intermolecular Interactions-result from the distribution of electrons in atoms and molecules
(Recommended reading: Israelachvili, J., Intermolecular and Surface Forces 1992, 2nd ed., Academic
Press, Note many of the figures and tables in this section are
1. The Gibbs Phase Rule for Reacting Systems.
Recall that the phase rule for non-reacting systems was given by
is the number of degrees of freedom, is the number of phases in
is the number of components in the mixture. This equation
The Gibbsian Equations
1. Who can tell me the equation for
the change in the total internal
energy? Equation (6.1) of your text is
The intensive relation is
2. There are at least three other functions. What are they?
The set of equations for , , , and
1. There are two main classes of functions for fitting
1. Rational functions are empirical models that express
as a ratio of
polynomials. They provide flexibility in fitting VLE data. They have
very little theoretical meaning, and as a result cannot
from the Lee-Kesler correlations. The Lee-Kesler correlations
are an empirical three-parameter corresponding states treatment for pure fluid
properties. The correlations are typically valid over the entire range of the data
listed in the tabl
from an equation of state.
The fugacity coefficient of a mixture can be calculated from
We can then compute
from the partial property relations presented.
But, most EOS are pressure explicit (i.e.,
as a function of
), so the
Generalization to multicomponents:
The generalized equation for multicomponent mixtures is
You have to explicitly account for the fact that you can't hold all mole
fractions but one constant. Equation (5) reduces to Eqns. (3) and (4) for a
1. Notation of chemical reactions:
Consider the chemical reaction
The numbers in front of the chemical formulae are the stoichiometric
coefficients, . By convention we take the sign to be positive for products
(terms on the right), negative for reactants
We are going to talk about partial properties. We will start by showing that the
chemical potential is a partial property.
1. Definition of Chemical Potential.
Recall that we wrote the Fundamental Property Relation as
This is extensive.
1. Exact expressions for phase equilibrium.
What are the equations for phase equilibrium?
These expressions are exact.
We can eliminate the chemical potentials in favor of fugacities. Which
fugacities do we use?
. These equations are also exact! Now w
1. Raoult's Law
1. Raoult's Law is a simple model for describing VLE. It is not a `Law' at
all, but just an approximation to real behavior.
There are two assumptions involved in Raoult's Law:
The vapor phase is an ideal gas.
What does thi
1. Review of the laws of thermodynamics
1. Zeroth Law: Temperature
2. First Law: Energy
3. Second Law: Entropy
For the combined First & Second Laws:
4. Third Law: Absolute zero of entropy
2. The Gibbs Phase rule
We observe that there