VLE Calculations

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# VLE Calculations - PowerPoint PPT Presentation

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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Presentation Transcript
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
• 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
• 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
• 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
• (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)
• 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)
• 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
• 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 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
• 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, 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
• 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
• Why?
• How?
• Who cares?
• Which type is the most difficult?

Lecture 2