Partial Pressures
Dalton's law
In ideal gas mixtures, total pressure equals the sum of component partial pressures. Each component contribution scales with its mole fraction.
P_i = χ_i × P_total
P_total = Σ P_i
This concept is essential for technical gases, breathing-gas calculations, gas-phase kinetics, and equilibrium estimation under pressure.
- Air composition and oxygen partial pressure
- Pressure effects in closed systems
- Safety and process calculations for gas mixtures
Formulas
P_i = χ_i × P_total
χ_i = P_i / P_total
P_total = ΣP_i
Detailed examples
Example 1: Air at 1 bar
χ(O₂)=0.21; P_total=1.00 bar
P(O₂)=0.21 bar
χ(O₂)=0.21; P_total=1.00 bar
P(O₂)=0.21 bar
Example 2: Elevated pressure
χ(O₂)=0.21; P_total=5.00 bar
P(O₂)=1.05 bar (5× higher)
χ(O₂)=0.21; P_total=5.00 bar
P(O₂)=1.05 bar (5× higher)
Example 3: Mole fraction from measurement
P_i=0.35 bar; P_total=2.00 bar
χ_i=0.175
P_i=0.35 bar; P_total=2.00 bar
χ_i=0.175
Interpretation
Same mole fraction does not mean same partial pressure: changing total pressure scales all components proportionally.
Same mole fraction does not mean same partial pressure: changing total pressure scales all components proportionally.
Technical Background
Model limits
Dalton's law is most accurate for ideal gases. At high pressure or with strongly interacting species, real-gas deviations can become relevant.
Laboratory accuracy and practice
For precise gas analysis, pressure unit consistency, temperature control, and pressure-sensor calibration are critical. Small errors in P_total directly affect all derived P_i values.
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