Ideal gas laws, Dalton's law, Raoult's law, Henry's law

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

2. Ideal gas law
• Ideal gas law describes the behaviour of
ideal gases. It also works quite well with
other gases at high temperatures and low
pressures.
• With this law, you can calculate the missing
value of pressure, volume, temperature and
amount of substance, if you know three other
values.
• If you use another unit for pressure, you have
to choose the correct value for ideal gas
constant and other units.
𝑃𝑉 = 𝑛𝑅𝑇
𝑃 = pressure (Pa)
𝑉 = volume m3
n = amount of substance mol
𝑇 = temperature (K)
𝑅 = ideal gas constant
= 8.31451
Pa ∙ m3
mol ∙ K

3. 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 = 𝑝 𝑎 + 𝑝 𝑏 + … + 𝑝 𝑛 =
𝑖=1
𝑛
𝑝𝑖
𝑃 = total pressure
𝑝𝑖 = partial pressure of component 𝑖
𝑝𝑖 = 𝑦𝑖 𝑃
𝑦𝑖 = mole fraction of component 𝑖
Ideal gas law can also be used with one
component:
𝑝 𝐴 𝑉 = 𝑛 𝐴 𝑅𝑇
𝑝 𝐴 = partial pressure of component 𝐴
nA = amount of substance 𝐴 mol
Picture: Andrew Jarvis CC BY-SA 4.0

4. Raoult's law
• Raoult's law says that the partial
pressure can be calculated with the
vapor pressure of pure component
and its mole fraction in liquid. 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 = 𝑥𝑖 𝑝′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
𝑥𝑖 𝑝′𝑖
𝑝𝑖 = 𝑦𝑖 𝑃 ⇒ 𝑦𝑖 =
𝑝 𝑖
𝑃
⇒ 𝑦𝑖 = 𝑥𝑖
𝑝 𝑖′
𝑃

5. Antoine equation
• Raoult's law requires value for the vapor
pressure. Those can be found from
literature or they can be calculated e.g.
with the Antoine equation.
• Example: Find out the vapor pressure
of benzene at the temperature of 50 °C.
• Coefficents for benzene are
A = 13.8594, B = 2773.78, C = 220.07
• Unit for temperature is °C and for
pressure kPa.
ln 𝑝′𝑖 = 𝐴 −
𝐵
𝑇 + 𝐶
𝑝′𝑖 = 𝑒 𝐴−
𝐵
𝑇+𝐶
𝑝′𝑖 = 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 same units in temperature.
𝑝′𝑖 = 𝑒13.8594−
2773.78
50+220.07 ≈ 36.2 kPa

6. Henry's law
• Henry's law is an alternative to
Raoult's law. Instead of partial
pressure, there is an empirical
constant, called Henry's law
constant H.
• Henry’s law constant is determined
to the specific gas-liquid
combination.
• It is temperature dependent. The
value increases with increasing
temperature.
• Mixtures which obey Henry's law are
called ideal-dilute solutions.
𝑝𝑖 = 𝐻𝑖 𝑥𝑖
𝑝𝑖 = partial pressure of component 𝑖
𝐻𝑖 = Henry′
s law constant
𝑥𝑖 = mole fraction of component 𝑖
𝐢𝐧 𝐥𝐢𝐪𝐮𝐢𝐝 (dissolved gas)
Another form for Henry’s law
𝑝𝑖 = 𝐾 𝐻 𝑐𝑖
𝑝𝑖 = partial pressure of component 𝑖
𝐾 𝐻 = Henry′s law constant
𝑐𝑖 = concentration of component 𝑖
𝐢𝐧 𝐥𝐢𝐪𝐮𝐢𝐝 (dissolved gas)
Be careful to choose correct values for constants!
They are different in different equations.

7. Comparison of Raoult’s law and Henry’s law
• Raoult's law is much more theory-based.
• Henry’s law is more practical, because it is
based on empirical data.
• Raoult’s law applies to the solvent and Henry’s
law applies to the solute.
• In ideal solutions, both the solute and the
solvent obey the Raoult's law.
• In ideal dilute solutions, the solute obeys
Henry’s law. The solvent obeys Raoult’s law.
• Both of the laws have their own benefits and
restrictions. In the next graphic, the comparison
of these two laws is in the graphical form. Differences between Henry’s law and
Rapoult’s law. Picture: Hipple (2017, 60).

8. This project has received funding from the European Union’s Horizon 2020
research and innovation programme under grant agreement No 869993.
References
• Hipple, J. 2017. Chemical Engineering for Non‐Chemical Engineers. John Wiley & Sons, Inc, pp.
105-106.
• Theodore, L. & Ricci, F. 2010. Mass Transfer Operations for the Practicing Engineer. John Wiley
& Sons, Inc, pp. 31-34, 46-65.
Videos:
• Dalton’s law and partial pressures: https://youtu.be/jbmOcH1fFKs
• Ideal gas laws: https://youtu.be/robEY-idcLU
• Raoult’s law with an example: https://youtu.be/8n3_bZzoG1o