25 Models for activity coefficient - Pennsylvania State University · 2016. 2. 11. · 25 Models for activity coefficient • today.Raoult’s law example activity coefficients from

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

15

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?