# Lecture 2 - VLE Calculations by gjjur4356

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```									VLE Calculations

Purpose of lecture:
To demonstrate how Raoult’s law is used to predict VLE behaviour of
ideal mixtures

Highlights
• Phase rules gives the number of variables needed to determine the
intensive state of a system at equilibrium
• Saturation pressures can be calculated by means of the Antoine Eqn.
• Raoult’s law can be used for constructing Pxy, Txy diagrams and
performing dew point and bubble point calculations

Reading assignment: Section 10.4, pp. 347-357 (7th edition), or
Section 10.4, pp. 338-348 (6th edition)

CHEE 311                       Lecture 2                    1
Gibbs Phase Rule for Intensive Variables                  SVNA-10.2

For a system of π phases and N species, the degree of freedom is:
F=2-π+N
F = # of variables that must be specified to fix the intensive
state of the system at equilibrium
Phase Rule Variables:
The system is characterized by T, P and (N-1) mole fractions for
each phase
2 + (N-1)π variables must be specified

Phase Rule Equations:
At equilibrium            μiα = μi β = μi π     for all N species
(π-1)N independent equations can be written in terms of T, P
and compositions

Degrees of freedom:         F = 2 + (N-1)π - (π-1)N
= 2- π +N

CHEE 311                       Lecture 2                    2
Phase Rule in VLE: Single Component Systems
For a two phase (π=2) system of a single component (N=1):
F = 2- π + N
F = 2- 2 + 1 = 1
Therefore, for the single component system, specifying either T or
P fixes all intensive variables. List some of them.

800
VLE for Pure Components

600
Pressure: kPa

400

200

0
270         320        370              420
Temperature: K

CHEE 311                               Acetonitrile 2 Nitromethane
Lecture                     3
Correlation of Vapour Pressure Data
Pisat, or the vapour pressure of component i, is commonly represented
by Antoine Equation (Appendix B, Table B.2, SVNA 7th ed.):

B
ln Pisat   =A−
T+C

For acetonitrile (Component 1):
2945 .47
ln P1sat / kPa = 14.2724 −
T / °C + 224
For nitromethane (Component 2):

2972 .64
sat
ln P2     / kPa = 14.2043 −
T / °C + 209
These functions are the only component properties needed to
characterize ideal VLE behaviour

CHEE 311                          Lecture 2                  4
Phase Rule in VLE: Ideal Binary Mixtures
(General Case)
For a two phase (π=2), binary system (N=2):
F =2-π+N=2
Therefore, for the binary case, two intensive variables must be
specified to fix the state of the system. How does this work?

CHEE 311                       Lecture 2                    5
Phase Rule in VLE: Binary Systems (Pxy diagrams)
Example: Acetonitrile (1) / Nitromethane (2) system

Acetonitrile(1) - Nitromethane(2) @ 75C
90

80
Pressure, kPa

70

60

50

40
0.0       0.2        0.4    x1,y1      0.6   0.8   1.0
y1         x1

Which component is more volatile?
What phases are present in each region?
CHEE 311                                              Lecture 2                     6
Phase Rule in VLE: Binary Systems (Txy diagrams)
Alternatively, we can specify a system pressure and examine the
VLE behaviour as a function of temperature and composition.
Acetonitrile(1) Nitromethane(2) @ 70kPa
90.0

85.0
Temp, deg C

80.0

75.0

70.0

65.0
0.00         0.20      0.40             0.60   0.80   1.00
x1,y1
y1         x1

What phases are present in each region?
What would this all look like in 3D?
CHEE 311                                                  Lecture 2                 7
VLE Calculations using Raoult’s Law
Raoult’s Law for ideal phase behaviour relates the composition of liquid
and vapour phases at equilibrium through the component vapour
pressure, Pisat.

yi P = xi Pi sat

Given the appropriate information, we can apply Raoult’s law to the
solution of 5 types of problems:
Dew Point:      Pressure or Temperature
Bubble Point: Pressure or Temperature
P,T Flash: calculation of equilibrium composition (P, T, zi given)

What is zi?

CHEE 311                        Lecture 2                     8
Dew and Bubble Point Calculations
Dew Point Pressure:
Given a vapour composition at a specified temperature, find the
composition of the liquid in equilibrium
Given T, y1, y2,... yn find P, x1, x2, ... xn
Dew Point Temperature:
Given a vapour composition at a specified pressure, find the composition
of the liquid in equilibrium
Given P, y1, y2,... yn find T, x1, x2, ... xn
Bubble Point Pressure:
Given a liquid composition at a specified temperature, find the composition
of the vapour in equilibrium
Given T, x1, x2, ... xn find P, y1, y2,... yn
Bubble Point Temperature:
Given a vapour composition at a specified pressure, find the composition
of the liquid in equilibrium
Given P, x1, x2, ... xn find T, y1, y2,... yn

Why these names?
CHEE 311                          Lecture 2                       9
VLE Calculations - Introduction

• For now, we will do calculations only for binary and ideal mixtures
• Multicomponent nonideal situations later

• The calculations use two key equations:
1) Raoult’s law for ideal phase behaviour:

Pi = yi P = xi Pi           sat

2) Antoine Equation for vapour pressures of pure components (1)

Bi
ln( P ) = Ai −
sat
(2)
T + Ci
i

CHEE 311                          Lecture 2                  10
BUBL P Calculation (T, x1 known)

• What do we want to find out?
• How do we do it?

What about BUBL T, DEW P, DEW T?

CHEE 311                    Lecture 2     11
Example

Assuming Raoult’s Law to be valid, prepare
(a) a Pxy diagram for T=90oC, and
(b) a Txy diagram for P=90 kPa
for a mixture of 1-chlorobutane (1) /chlorobenzene (2)

Antoine Coefficients:
A             B        C

1-chlorobutane (1)   13.9600     2826.26     224.10

Chlorobenzene (2)    13.9926     3295.12     217.55

Let’s list the steps required.
How could we do it using a spreadsheet?
CHEE 311                         Lecture 2               12
Example – Generation of Txy Diagram

P            90.00   kPa                   A1            13.96     A2          13.99
T1sat        74.65   degC                  B1          2826.26     B2        3295.12
T2sat       129.57   degC                  C1           224.10     C2         217.55

T
(degC)     P1sat     P2sat     x1          x2          y1
74.65     90.00     15.12        1.00        0.00        1.00
80.00    106.29     18.51        0.81        0.19        0.96
85.00    123.53     22.23        0.67        0.33        0.92
90.00    142.88     26.54        0.55        0.45        0.87
95.00    164.52     31.50        0.44        0.56        0.80
100.00    188.61     37.18        0.35        0.65        0.73
105.00    215.33     43.67        0.27        0.73        0.65
110.00    244.86     51.04        0.20        0.80        0.55
115.00    277.39     59.38        0.14        0.86        0.43
120.00    313.10     68.77        0.09        0.91        0.30
125.00    352.18     79.30        0.04        0.96        0.15
129.57    391.01     90.00        0.00        1.00        0.00

CHEE 311                                    Lecture 2                    13
Example – (b) Construction of a Txy Plot

Txy diagram for 1-chlorobutane (1) and chlorobenzene (2) at
P = 90 kPa (assuming validity of Raoult's law )

140.00
vapor
120.00
VLE
100.00
T (degC)

80.00                                                                      x1
liquid
60.00                                                                      y1

40.00

20.00

0.00
0.00     0.20        0.40           0.60           0.80   1.00
x1,y1

CHEE 311                                           Lecture 2                            14
VLE Calculations - Summary
• Why?
• How?
• Who cares?
• Which type is the most difficult?

Specified/Known   Unknown       Calculation
Variables      Variables
T, x           P, y         BUBL P
T, y           P, x         DEW P
P, x           T, y         BUBL T
P, y           T, x         DEW T
P, T           x, y        P, T Flash

CHEE 311                       Lecture 2                 15

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