CHEMICAL THERMODYNAMICS
By
Jorge Omar Gil Posada
CH9: An Introduction to Mixtures.
Binary Interaction Parameters (kij)
1. Values for the interaction coefficient are obtained from experimental data
involving a mixture of compounds i and j.
2. kij values are small, typically between 0.0 and 0.2 for nonpolar or weakly
polar systems, and can be larger - or even negative - for polar ones.
3. The values vary from one EoS to the other.
4. For hydrocarbons that are not very different in size, zero values for the
interaction coefficient can be used.
5. For systems containing CO2 and n-paraffins, kij values for the Peng-Robinson
(PR) EoS are given by Kato et al (1981).
6. For systems containing CO2, H2S, N2, and CO with hydrocarbons, kij values for
the SRK EoS are given by Graboski and Daubert (1978).
7. For H2-hydrocarbons, see Lin (1980), and Tsonopoulos and Heidman (1986).
8. For the volumetric properties of gaseous water with some nonpolar gases,
see De Santis et al (1974).
Homework: Find Binary Interaction Parameters (kij)
REVIEW
REVIEW
REVIEW
The chemical potential (μi) of a compound i is defined as the partial
derivative of Gibbs free energy with respect to the number of moles
of compound i:
Thus, chemical potential indicates the change in Gibbs energy of a
system when a small amount of compound i is added, if everything
else (T, P, and the amount of all compounds other than i) is held
constant. For a pure compound, this is simply the molar Gibbs energy
REVIEW
Applying the chain rule gives
The derivative of any variable with respect to itself is simply one, so
the first term on the right-hand side simplifies to G. But G for a pure
compound is an intensive property; its value is independent of the
number of moles, so (∂G/∂ni ) is 0, so
Thus, for a pure compound, it matters little whether we express the
equilibrium criterion in terms of molar Gibbs free energy (GL = G V)
or chemical potential (μiL = μiV); since they are identical
EXAMPLE 8.5. ESTIMATING A VAPOR PRESSURE FOR
FREON USING THE VAN DER WAALS EOS
EXAMPLE 8.5. ESTIMATING A VAPOR PRESSURE FOR
FREON USING THE VAN DER WAALS EOS
Thus, the vapor pressure is approximately 105.2 psia
EXAMPLE 8.5. ESTIMATING A VAPOR PRESSURE FOR
FREON USING THE VAN DER WAALS EOS
Home work: Python program that uses VDW EOS to built previous table
Varies P from 1 to 120 psi using step = 0,1 psi
Calculate molar volumen for each P and T= 15 oF (for both phases)
Calculate Z for both phases
Calculate fugacity coefficients and fugacities of phases
Determine P at which fugacities are equal
RESIDUAL PROPERTIES
Methane enters a turbine at T = 600 K and P = 10 bar and leaves at
T = 400 K and P = 2 bar. How much work is produced for each mole
of gas? a(Vd W) = 0.2303 Pa-m6/mol2,and b(Vd W) = 4.306x10-5 m3/mol
RESIDUAL PROPERTIES
Methane enters a turbine at T = 600 K and P = 10 bar and leaves at
T = 400 K and P = 2 bar. How much work is produced for each mole
of gas? a(Vd W) = 0.2303 Pa-m6/mol2,and b(Vd W) = 4.306x10-5 m3/mol
RESIDUAL PROPERTIES
Step 1: Define a system and write an energy balance
RESIDUAL PROPERTIES
Step 2: Write a total derivative expression for molar enthalpy
RESIDUAL PROPERTIES
The quantity CP dT cannot be integrated unless CP is known as a
function of temperature. It is indeed known for the ideal gas state,
but assuming that methane behaves as an ideal gas is questionable
at P = 10 bar.
RESIDUAL PROPERTIES
Solution 1.
RESIDUAL PROPERTIES
Solution 1I.
RESIDUAL PROPERTIES
Solution 1II.
RESIDUAL PROPERTIES
RESIDUAL PROPERTIES
RESIDUAL PROPERTIES
RESIDUAL PROPERTIES
RESIDUAL PROPERTIES
RESIDUAL PROPERTIES
RESIDUAL PROPERTIES
RESIDUAL PROPERTIES
RESIDUAL PROPERTIES
Which indeed goes to zero as the ideal gas is approached. In
other words, even if VR in the ideal-gas state is not zero, it
represents an infinitesimal fraction of the molar volume and
thus its contribution is negligible.
RESIDUAL PROPERTIES
RESIDUAL PROPERTIES
RESIDUAL PROPERTIES
RESIDUAL PROPERTIES
RESIDUAL PROPERTIES
RESIDUAL PROPERTIES
RESIDUAL PROPERTIES
RESIDUAL PROPERTIES
RESIDUAL PROPERTIES
RESIDUAL PROPERTIES
RESIDUAL PROPERTIES
RESIDUAL PROPERTIES
RESIDUAL PROPERTIES
Homework: Calculate the residual enthalpy and entropy at
220 K, 20 bar assuming the validity of the truncated virial
equation. Hint: Find B = B(T)
T [K] -B [cm3/mol]
108,45 364,99
125,2 267,97
149,1 188,04
186,4 126,20
223,6 82,62
249,3 68,53
RESIDUAL PROPERTIES –VAN DEER WAALS
RESIDUAL PROPERTIES –VAN DEER WAALS
HR Deduction
HR Deduction
HR Deduction
RESIDUAL PROPERTIES –SOAVE-REDLICH-KWONG
RESIDUAL PROPERTIES –PENG-ROBINSON
REVIEW
REVIEW
Van Deer Waals EOS
REVIEW –SOAVE-REDLICH-KWONG
REVIEW –PENG-ROBINSON
Peng-Robinson EOS
Binary Interaction Parameters (kij)
1. Values for the interaction coefficient are obtained from experimental data
involving a mixture of compounds i and j.
2. kij values are small, typically between 0.0 and 0.2 for nonpolar or weakly
polar systems, and can be larger - or even negative - for polar ones.
3. The values vary from one EoS to the other.
4. For hydrocarbons that are not very different in size, zero values for the
interaction coefficient can be used.
5. For systems containing CO2 and n-paraffins, kij values for the Peng-Robinson
(PR) EoS are given by Kato et al (1981).
6. For systems containing CO2, H2S, N2, and CO with hydrocarbons, kij values for
the SRK EoS are given by Graboski and Daubert (1978).
7. For H2-hydrocarbons, see Lin (1980), and Tsonopoulos and Heidman (1986).
8. For the volumetric properties of gaseous water with some nonpolar gases,
see De Santis et al (1974).
Homework: Find Binary Interaction Parameters (kij)
EOS AND FUGACITY COEFFICIENT
EOS AND FUGACITY COEFFICIENT
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EOS AND FUGACITY COEFFICIENT
EOS AND FUGACITY COEFFICIENT
EOS AND FUGACITY COEFFICIENT
EOS AND FUGACITY COEFFICIENT
