25 Models for activity coefficient
• today. Raoult’s law exampleactivity coefficients from data
Margules, van Laar models
Wilson model
NRTL
• announce. Exam 03, Wed 04nov2009, 8 am.
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• announce. Exam 03, Wed 04nov2009, 8 am.Final, Wed 16dec2009, 8-9:50 (101 CHAM)
Velegol out of town Wed 11nov2009
make NOTES in your books for extra eqs!
• assignments. no HW assignment; put notes in bookreading: Ch 07
Example. Raoult’s law
A solution of pentane (1) / heptane (2) at P = 4.3
bar has K1 = 2.2. Find the temperature of the
system, and the mol fraction x1.
answer: T = 122.5 C, x1 = 0.313
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When does nonideality matter?
Assumptions of Raoult’s law- ideal gas (relatively low p and high T), to give little interaction or vol effect
- ideal solutions (similar intermolecular forces, similar volume/molecule)
Causes of nonideality …- high p or low T (especially relative to critical values)
- great differences in intermolecular forces A-A, A-B, B-B
- size differences (VDW forces)
- lone pairs or hydrogen bonding (S or N or O)
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- lone pairs or hydrogen bonding (S or N or O)
- “If it has an oxygen, watch out!”- great differences in size and shape
What research has happened to solve this?- analytical theory for how intermolecular forces give models
- computation with molecular dynamics and quantum mech
- experiments
Activity coefficients from experimental data
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Example. Calculating γγγγ
Calculate the activity coefficients for ethyl-methyl
ketone (1) / toluene (2) at 50 C.
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Effect of T and P on activity coefficients
Matsoukas Example 7.23
(p 123)
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Changes in γi with T and P
are SMALL.
Excess Gibbs energy
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Story CENTER: Entrepreneurship
Character
Excellence
Ownership
Tenacity
10
Tenacity
Entrepreneurship
Relationship
Activity coefficient models
Margules equation (fit for A12 and A21)
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van Laar equation (fit for B12 and B21)
Wilson equation for activity coefficient
12
Non-random two liquid (NRTL) model
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Example. Fitting with more parameters
Say we have the data below. Find the best fit for
y = ax, y = a + bx, y = a + bx2, y = a + b/x + c/x2
x y
_________
1 4.1
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1 4.1
2 6.9
3 11.7
4 18.9
5 28.8
The best fit requires a sound model
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20
25
30y
y=ax
y=a+bx
y=a+bx^2
y=a+b/x+c/x^2
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0
5
10
15
0 2 4
Summary
C
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Character
Excellence
Ownership
Tenacity
Entrepreneurship
Relationship
Entrepreneurship – idea journal!
List of symbols for 25
Aij = fitting parameters for Margules model (activity coefficients)
Bij = fitting parameters for van Laar model
gij = interaction parameters for NRTL model
Gij = modified interactions for NRTL model
λij = interaction parameters for Wilson model
Λij = modified interactions parameters for Wilson model
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Λij = modified interactions parameters for Wilson model
τij = interaction differences for NRTL model
Vi = molar volumes of pure component i
Opinion Box
• Take out a sheet of paper.
• Keep your paper anonymous, without your name.
Let me know …
• What made sense?
• What was confusing?
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• What was confusing?
• Questions? Technical? Center? Personal? Fun?
• Suggestions?
• Comments?