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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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