101.9 VLE

Material Balances in Multiphase Systems

ChE 101 Fundamentals of Chemical Engineering

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Outline

¤ Vapor-Liquid Equilibrium

– Phase diagrams

– Raoult’s Law

¤ Gas-Liquid Equilibrium

– Henry’s Law

– Psychrometric charts

¤ Liquid-Liquid Equilibrium

¤ Solid-Liquid Equilibrium

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Recall: Separation Processes

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How do we determine these compositions?

Phase Diagrams

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Phase Diagrams

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Phase Diagrams

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𝑃𝑠𝑎𝑡 𝑇

Phase Diagrams

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¤ Equations for vapour/saturation pressure

– Clapeyron equation

– Antoine equation

ln 𝑃𝑠𝑎𝑡 = 𝐴 −𝐵

𝑇 + 𝐶

Phase Diagrams

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¤ Graphs for vapour/saturation pressure (Cox chart)

Phase Diagrams

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Phase Diagrams

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Gibbs Phase Rule

¤ Applicable to systems at equilibrium with no reaction– F: degrees of freedom, number of independent intensive variables

needed to fix all other intensive variables

– P: number of phases

– C: number of independent components𝐹 = 2 − 𝑃 + 𝐶

¤ Ex. How many number of phases in:– A solution of salt in water

– Saturated salt solution with salt crystals settling

– A system of CaCO3 decomposing to CaO and CO2

– Oil and water

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Vapor-Liquid Equilibrium

¤ Ex. Alcohol solution

– NBP of water: 100oC

– NBP of ethanol: 78.4oC

– How many degrees of freedom?

– Composition in vapour: 𝑦𝑖– Composition in liquid: 𝑥𝑖– Recall: partial pressure

𝑃𝑖 = 𝑦𝑖𝑃

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¤ Raoult’s Law: 𝑃𝑖 ∝ 𝑥𝑖

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𝑦𝑖𝑃 = 𝑥𝑖𝑃𝑖𝑠𝑎𝑡 𝑇


¤ Non-ideal solutions

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¤ P-xy Diagram

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Tota

lTota

l

Liquid region

Vapor region

Tie line


¤ T-xy diagram

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Liquid region

Vapor region


¤ Recall: ILAR

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L

V

F 𝐹 = 𝐿 + 𝑉𝑧𝑖𝐹 = 𝑥𝑖𝐿 + 𝑦𝑖𝑉


Ex. Based on the T-xy diagram for toluene and benzene (x-axis is for benzene),

• Which is the more volatile component?

• What are the vapor pressures of each component at 100oC?

• What are the normal boiling points of each component?

• Equal amounts of toluene at 85oC and benzene at 110oC are mixed at atmospheric conditions

• What it the final temperature?

• What are the final compositions?

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Ex. A 70% toluene mixture in a closed isothermal piston cylinder at 100oC and 1000 mmHg is depressurized to 600 mmHg

• What is the initial state of the system?

• At what P will the first bubble form? What is its composition?

• At what P will the last drop of liquid evaporate? What is its composition?

• What are the liquid and vaporcompositions at 750 mmHg? What is the vapor-liquid ratio at this point?

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¤ Bubble-P calculation

– Given: T, 𝑥𝑖

𝑖𝑦𝑖𝑃 =

𝑖𝑥𝑖𝑃𝑖𝑠𝑎𝑡 𝑇 = 𝑃

¤ Dew-P calculation

– Given: T, 𝑦𝑖

𝑖

𝑦𝑖

𝑃𝑖𝑠𝑎𝑡 𝑇

= 𝑖

𝑥𝑖𝑃=1

𝑃

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Ex. A 70% toluene mixture in a closed isothermal piston cylinder at 100oC and 1000 mmHg is depressurized to 600 mmHg

• What is the initial state of the system?

• At what P will the first bubble form? What is its composition?

• At what P will the last drop of liquid evaporate? What is its composition?

• What are the liquid and vapor compositions at 750 mmHg? What is the vapor-liquid ratio at this point?

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¤ Bubble-T calculation– Given: P, 𝑥𝑖

𝑃 − 𝑖𝑦𝑖𝑃 = 𝑃 −

𝑖𝑥𝑖𝑃𝑖𝑠𝑎𝑡 𝑇 = 0

– For binary solutions,𝑃 = 𝑥1𝑃1

𝑠𝑎𝑡 + 𝑥2𝑃2𝑠𝑎𝑡

– Let 𝛼 =𝑃1𝑠𝑎𝑡

𝑃2𝑠𝑎𝑡 = exp 𝐴1 − 𝐴2 −

𝐵1

𝑇+𝐶1−𝐵2

𝑇+𝐶2

𝑃2𝑠𝑎𝑡 =

𝑃

𝑥1𝛼 + 𝑥2

𝑇 =𝐵2

𝐴2 − ln𝑃2𝑠𝑎𝑡 − 𝐶2

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¤ Bubble-T calculation

– Given: P, 𝑥𝑖

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Guess T Calc 𝛼 Calc 𝑃2𝑠𝑎𝑡

Calc new T

Converge


¤ Dew-T calculation

– Given: P, 𝑦𝑖

𝑖

𝑦𝑖

𝑃𝑖𝑠𝑎𝑡 𝑇

= 𝑖

𝑥𝑖𝑃=1

𝑃

– For binary solutions,1

𝑃=𝑦1

𝑃1𝑠𝑎𝑡 +

𝑦2

𝑃2𝑠𝑎𝑡 → 𝑃1

𝑠𝑎𝑡 = 𝑃 𝑦1 + 𝑦2𝛼

𝑇 =𝐵1

𝐴1 − ln𝑃1𝑠𝑎𝑡 − 𝐶1

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¤ Dew-T calculation

– Given: P, 𝑦𝑖

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Guess T Calc 𝛼 Calc 𝑃1𝑠𝑎𝑡

Calc new T

Converge

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101.9 VLE