STATES OF MATTER - properties of gases and liquids (fluids) and solids

22. Dalton's Law of Partial Pressures and calculations and use in solving gaseous equilibrium expression problems - exam practice questions

22. Dalton's law of partial pressures and calculations

• DALTON'S LAW

• Dalton's Law of partial pressures states that at constant temperature the total pressure exerted by a mixture of gases in a definite volume is equal to the sum of the individual pressures which each gas would exert if it alone occupied the same total volume.

• For a mixture of gases 1, 2, 3 that are NOT reacting ...

• P_tot = p₁ + p₂ + p₃ etc.

• where p₁, p₂ etc. represent the partial pressures.

• The partial pressure ratio is the same as the % by volume ratio and the same as the mole ratio of gases in the mixture.

• This means for a component gas z, the partial pressure is expressed as:

  • p_z = P_tot x %z/100

  • for % of volume of gases or in terms of moles of gases:

  • p_z = P_tot x mol z/total mol (e.g. in a given system volume)

  • p_z= P_tot x mol fraction z (e.g. for any system volume)

Examples of partial pressure calculations

• Ex. Q4d.1

  • In the manufacture of ammonia a mixture of nitrogen : hydrogen in a 1 : 3 ratio is passed over an iron/iron oxide catalyst at high temperature and high pressure.

    • N_2(g) + 3H_2(g) 2NH_3(g)

  • What are the partial pressures of nitrogen and hydrogen if the total pressure of the gases is 200 atm prior to reaction? So P_tot = 200 atm.

    • The 1 : 3, N₂ :H₂ ratio means that nitrogen forms ¹/₄ of the mixture, therefore

    • p_N2 = ¹/₄ x 200 = 50 atm and

    • p_H2 = p_tot – p_N2 = 150 atm (or from ³/₄ x 200)

    • -

• Ex. Q4d.2

  • Methanol can be synthesised by combining carbon monoxide and hydrogen in a 1 : 2 ratio.

    • CO_(g) + 2H_2(g) CH₃OH_(g)

  • In an experimental reactor experiment, 300^oC at a total pressure of 400kPa, the final equilibrium gaseous mixture contained 10% carbon monoxide.

  • (a) Calculate the % of hydrogen gas and % methanol vapour in the final mixture.

    • Whatever hydrogen is left, its % must be double that of carbon monoxide since they were both mixed and react in a 1 : 2 ratio, so there will 20% hydrogen left in the equilibrium mixture.

    • Therefore there will be 100 – 10 – 20 = 70% methanol vapour in the final mixture.

  • (b) Calculate the partial pressures of the three gases in the mixture.

    • p_CO = 0.1 x 400 = 40 kPa

    • p_H2 = 0.2 x 400 = 80 kPa

    • p_CH3OH = 0.7 x 400 = 280 kPa

    • (useful to check 40 + 80 + 280 = 400)

  • (c) From the partial pressure data in (b) calculate the value of the equilibrium constant, K_p, under these reaction conditions (use Pa pressure units).

    • Kp =	pCH3OH
      	–––––––––––
      	pCO pH22

    • Kp =	280 000
      	–––––––––––––––––   = 1.09 x 10–9 Pa–2
      	40 000 x 80 0002

    • Note that although the equilibrium constant seems small for the 70% methanol, its to do with the relatively large numbers on the bottom line and a power of 2 as well.

• –

Some key points

Dalton’s law of partial pressures states that the total pressure of a mixture of non‑reacting gases is equal to the sum of the pressures each gas would exert if it occupied the container alone.

In other words, each gas contributes its own “partial pressure,” and adding them together gives the overall pressure.

Dalton’s Law of Partial Pressures

The Concept

• John Dalton (1801–1802) observed that gases in a mixture behave independently.
• Each gas exerts a partial pressure proportional to its amount (mole fraction).
• The total pressure is the sum of all partial pressures: P_tot = p₁ + p₂ + p₃ etc.

Formulae used

• This means for a component gas z, the partial pressure is expressed as:

  • p_z = P_tot x %z/100 (can be % of theoretical volume or % moles)

  • for % of volume of gases or in terms of moles of gases:

  • p_z = P_tot x mol z/total mol (e.g. moles in a given system volume)

  • p_z= P_tot x mol fraction z (e.g. for any system volume)

Applications of Dalton's law of partial pressures

• Explains air composition: total atmospheric pressure is the sum of nitrogen, oxygen, carbon dioxide, etc.
• Used in scuba diving: oxygen partial pressure must be monitored to avoid toxicity.
• Important in industrial gas mixtures and respiratory physiology.

Student Exam Tips for Dalton's law of partial pressures

• Always state that gases are non‑reacting when applying Dalton’s law.
• Use Kelvin temperatures if calculations involve the ideal gas law alongside Dalton’s law.
• Remember: partial pressure depends on mole fraction, not mass fraction.
• In multiple-choice, check whether the question asks for total pressure or individual partial pressure.

Typical Misconceptions

•  Thinking heavier gases exert more pressure — pressure depends on number of particles, not mass.
•  Forgetting that Dalton’s law applies only to non‑reacting gases.
•  Mixing up mole fraction with mass fraction.
•  Assuming partial pressures change with container size independently — they scale with total pressure and mole fraction.

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