Slides for the eLearning course Separation and purification processes in biorefineries (https://open-learn.xamk.fi) in IMPRESS project. Section: Distillation Subject: 0.3 Basic concepts of distillation

1. This project has received funding from the European Union’s Horizon 2020
research and innovation programme under grant agreement No 869993.
Basic concepts
in distillation

2. Vapor pressure
• Vapor pressure is an important property of liquids.
It indicates how easily the liquid is evaporating.
• Vapor pressure is strongly dependent on the
temperature. The weaker the intermolecular forces
are, the higher is the vapor pressure. The amount of
liquid does not affect the vapor pressure.
• When the vapor pressure is equal to the pressure
surrounding the liquid, the liquid boils.
• Vapor pressures can be found in databases, or they
can be calculated by Antoine’s equation. Picture: HellTchi CC BY-SA 3.0

3. Antoine equation
• The Antoine equation is a class of semi-
empirical correlations describing the
relation between vapor pressure and
temperature for pure substances.
• Example: Find out the vapor pressure
of benzene at the temperature of 50 °C.
• Coefficents for benzene at 50 °C are
A = 4.01814, B = 1203.835, C = -53.226
• Units: temperature K and pressure bar.
log10 𝑃𝑖
′
= 𝐴 −
𝐵
𝑇 + 𝐶
𝑃𝑖
′
= 10𝐴−
𝐵
𝑇+𝐶
𝑃𝑖
′
= vapor pressure of pure 𝑖
T = temperature
A, B and C are coefficients of a specific
substance. They can be found in literature.
It is crucial to check the units used and use
the correct units in temperature, too.
Parameters can be found e.g. from here:
https://webbook.nist.gov/chemistry/
𝑃𝑖
′
= 104.01814−
1203.835
323.15−53.226
≈ 0.362 bar = 36.2 kPa

4. Dalton's law
• In the mixture of gases, the pressure
of each component is called a partial
pressure (pi).
In the ideal gases pi = yiP
• Dalton’s law says that the total
pressure is the sum of partial
pressures.
𝑃 = 𝑝𝑎 + 𝑝𝑏 + … + 𝑝𝑛 =
𝑖=1
𝑛
𝑝𝑖
𝑃 = total pressure
𝑝𝑖 = partial pressure of component 𝑖
𝑝𝑖 = 𝑦𝑖𝑃
𝑦𝑖 = mole fraction of component 𝑖
Ideal gas law can also be used with one
component:
𝑝𝐴𝑉 = 𝑛𝐴𝑅𝑇
𝑝𝐴 = partial pressure of component 𝐴
nA = amount of substance 𝐴 mol
Picture: Andrew Jarvis CC BY-SA 4.0

5. Raoult's law
• Raoult's law states that the partial
pressure of each component of an ideal
mixture of liquids is equal to the vapor
pressure of the pure component
multiplied by its mole fraction in the
mixture. pi = xi p'i
• When you combine the Dalton’s law
and the Raoult’s law, you will get
useful expressions for total pressure
and the mole fraction in vapor.
• Raoult’s law has many limitations. It
only applies to ideal solutions and the
vapor should act like ideal gas.
𝑝𝑖 = 𝑥𝑖𝑝′𝑖
𝑝𝑖 = partial pressure of component 𝑖
𝑝′𝑖 = vapor pressure of pure 𝑖
at the same temperature
𝑥𝑖 = mole fraction of component 𝑖
𝐢𝐧 𝐥𝐢𝐪𝐮𝐢𝐝
Combination of Raoult’s law and
Dalton’s law:
𝑃 =
𝑖=1
𝑛
𝑥𝑖𝑝′𝑖
𝑝𝑖 = 𝑦𝑖𝑃 ⇒ 𝑦𝑖 =
𝑝𝑖
𝑃
⇒ 𝑦𝑖 = 𝑥𝑖
𝑝𝑖′
𝑃

6. Relative volatility
• Relative volatility is a measure comparing the vapor pressures of two
components in a liquid mixture of chemicals.
• Common symbol for relative volatility is α. It is a unitless quantity.
𝛼 =
vapor pressure of more volatile component
vapor pressure of less volatile component
• When α = 1, separation by distillation would be impossible. The greater
the value, the easier is the separation by distillation.
• In ideal solutions, the relative volatility can be expressed in different forms
by using Raoult’s law and Dalton’s law.
𝛼𝐴𝐵 =
𝑝𝐴
′
𝑝𝐵
′ =
𝑝𝐴/𝑥𝐴
𝑝𝐵/𝑥𝐵
=
𝑝𝐴𝑥𝐵
𝑝𝐵𝑥𝐴
=
𝑦𝐴𝑃𝑥𝐵
𝑦𝐵𝑃𝑥𝐴
=
𝑦𝐴(1 − 𝑥𝐴)
𝑥𝐴(1 − 𝑦𝐴)

7. Vapor-liquid equilibrium (VLE)
• Vapor-liquid equilibrium (VLE) describes
the distribution of a chemical species
between the vapor phase and a liquid
phase under a given set of conditions.
• A binary system has two degrees of
freedom. In distillation, the pressure is
usually fixed. If we fix also the liquid
composition, the temperature and vapor
composition will be automatically fixed.
• VLE data can be expressed in tables or in
diagrams. These are discussed more
detailed in next chapters.
VLE diagram of ethanol and water at
1 atm. (http://www.vle-
calc.com/phase_diagram.html)

8. This project has received funding from the European Union’s Horizon 2020
research and innovation programme under grant agreement No 869993.
References
Dutta, B. K. 2007. Principles of mass transfer and separation processes. New Delhi: Prentice-Hall,
pp. 321-322.
Hipple, Jack. 2017. Chemical Engineering for Non-Chemical Engineers. American Institute of
Chemical Engineers, pp. 146-147.
Vapor-Liquid Equilibrium calculator. Available at: http://www.vle-calc.com/phase_diagram.html
[Assessed: 14 June, 2021].
Videos:
• Partial pressure vs. vapor pressure: https://youtu.be/QVK0yKJx6FM (3:56)
• Distillation, vapor pressure and volatility: https://youtu.be/sNUYVvXGhjg (4:03)
• Vapor Liquid equilibrium for binary systems: https://youtu.be/hLzqt2Mfnoc (7:08)