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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 neede to determine the intensive state of a system at equilibrium

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vle calculations
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 neede 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)

Lecture 2

gibbs phase rule for intensive variables svna 10 2
Gibbs Phase Rule for Intensive Variables SVNA-10.2
  • For a system of  phases and N species, the degree of freedom is:
  • F = 2 -  + 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) variables must be specified
  • Phase Rule Equations:
  • At equilibrium i = i  = i  for all N species
    • (-1)N independent equations can be written in terms of T, P and compositions
  • Degrees of freedom: F = 2 + (N-1) - (-1)N
  • = 2-  +N

Lecture 2

phase rule in vle single component systems
Phase Rule in VLE: Single Component Systems
  • For a two phase (p=2) system of a single component (N=1):
  • F = 2-  + 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.

Lecture 2

correlation of vapour pressure data
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.):
  • For acetonitrile (Component 1):
  • For nitromethane (Component 2):
  • These functions are the only component properties needed to characterize ideal VLE behaviour

Lecture 2

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

Lecture 2

phase rule in vle binary systems pxy diagrams
Phase Rule in VLE: Binary Systems (Pxy diagrams)
  • Example: Acetonitrile (1) / Nitromethane (2) system

Which component is more volatile? What phases are present in each region?

Lecture 2

phase rule in vle binary systems txy diagrams
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.

What phases are present in each region? What would this all look like in 3D?

Lecture 2

vle calculations using raoult s law
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.
  • 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?

Lecture 2

dew and bubble point calculations
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?

Lecture 2

vle calculations introduction
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:
  • 2) Antoine Equation for vapour pressures of pure components

(1)

(2)

Lecture 2

bubl p calculation t x 1 known
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?

Lecture 2

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

Let’s list the steps required.

How could we do it using a spreadsheet?

Lecture 2

vle calculations summary
VLE Calculations - Summary
  • Why?
  • How?
  • Who cares?
  • Which type is the most difficult?

Lecture 2