Partial Pressure & Dalton's Law
Partial pressure is the pressure a gas component would exert if it alone occupied the volume. Dalton's Law: Pi = xi·Ptotal for gas mixtures. Each gas contributes independently to total pressure.
Why This Chemistry Calculation Matters
Why: Partial pressure calculations are essential for diving gas mixtures, breathing air safety, industrial gas analysis, and atmospheric science. Dalton's Law enables prediction of gas behavior in mixtures.
How: Enter mole fractions (summing to 1) and total pressure for each gas. The calculator applies Pi = xi·Ptotal. Alternatively, enter partial pressures to derive mole fractions.
- ●In ideal gas mixtures, each gas behaves as if others were absent.
- ●Mole fraction equals volume fraction for ideal gases at constant T and P.
- ●Oxygen partial pressure limits drive diving gas mixture design (e.g., Nitrox).
Sample Gas Mixtures
🌍 Dry Air (Sea Level)
Standard atmospheric composition at 1 atm
🤿 Heliox (Diving Gas)
Helium-oxygen mixture for deep diving
🏊 Nitrox (Enriched Air)
Nitrogen-oxygen mixture for extended diving
🔥 Natural Gas
Typical natural gas composition
🚗 Exhaust Gas
Automotive exhaust composition
🌊 Trimix (Deep Diving)
Helium-nitrogen-oxygen for technical diving
💨 Breathing Air (SCBA)
Self-contained breathing apparatus air
Calculate Partial Pressure
Gas Components
📚 Official Data Sources
⚠️ Disclaimer: This calculator uses IUPAC definitions for partial pressure and Dalton's Law of Partial Pressures. For precise work, consult IUPAC Gold Book, NIST Chemistry WebBook for gas properties, and authoritative physical chemistry references for gas mixture data.
⚠️For educational and informational purposes only. Verify with a qualified professional.
🔬 Chemistry Facts
Dalton's Law: Ptotal = P₁ + P₂ + ... + Pn for ideal gas mixtures.
— IUPAC
Partial pressure Pi = χi × Ptotal; mole fractions must sum to 1.
— IUPAC
Diving: PO₂ > 1.6 atm risks oxygen toxicity; PN₂ causes narcosis.
— NIST
Dry air: 78% N₂, 21% O₂ → PN₂ ≈ 0.78 atm, PO₂ ≈ 0.21 atm at 1 atm.
— NIST
What is Partial Pressure?
Partial pressure is the pressure that a single gas component in a mixture would exert if it alone occupied the entire volume at the same temperature. In a gas mixture, each gas contributes independently to the total pressure according to its mole fraction.
Key Concept
In a mixture of ideal gases, each gas behaves as if the other gases weren't present. This is the foundation of Dalton's Law of Partial Pressures.
How to Calculate Partial Pressure
Method 1: From Mole Fraction
Where Pi is the partial pressure of gas i, Xi is its mole fraction, and Ptotal is the total pressure of the mixture.
Method 2: From Partial Pressures
Ptotal = ΣPi
The mole fraction can be calculated from partial pressures, and the total pressure is the sum of all partial pressures.
Example Calculation
For dry air at 1 atm with 78% N₂ and 21% O₂:
PO₂ = 0.21 × 1.0 atm = 0.21 atm
Ptotal = 0.78 + 0.21 + ... = 1.0 atm
When to Use Partial Pressure Calculations
Diving & Breathing Gases
Critical for calculating safe oxygen partial pressures in scuba diving, medical breathing mixtures, and hyperbaric chambers.
- Oxygen toxicity limits
- Nitrogen narcosis prevention
- Decompression planning
Industrial Processes
Essential for chemical reactions, gas separation, combustion analysis, and process optimization in industrial settings.
- Reaction kinetics
- Gas solubility
- Emissions monitoring
Atmospheric Science
Understanding air composition, altitude effects, and atmospheric pressure variations for weather and climate studies.
- Altitude calculations
- Weather patterns
- Climate modeling
Laboratory Research
Critical for gas chromatography, mass spectrometry, and controlled atmosphere experiments in research laboratories.
- Gas analysis
- Reaction conditions
- Quality control
Dalton's Law Formulas
Dalton's Law of Partial Pressures
Pi = Xi × Ptotal
The total pressure of a gas mixture equals the sum of the partial pressures of each component gas.
Mole Fraction
Xi = Pi / Ptotal
The mole fraction is the ratio of moles of a component to total moles, or the ratio of partial pressure to total pressure.
Volume Fraction (for Ideal Gases)
For ideal gases at constant temperature and pressure, volume fraction equals mole fraction equals pressure fraction.
Average Molar Mass
The average molar mass of a gas mixture is the mole-fraction-weighted average of component molar masses.
Common Gas Mixtures
| Mixture | Components | Application |
|---|---|---|
| Dry Air (Sea Level) | Nitrogen (78.08%), Oxygen (20.95%), Argon (0.9299999999999999%), Carbon Dioxide (0.04%) | Atmospheric science, breathing |
| Medical Air | Nitrogen (78%), Oxygen (21%), Argon (1%) | Hospitals, respiratory therapy |
| Heliox (Helium-Oxygen) | Helium (79%), Oxygen (21%) | Deep-sea diving, respiratory distress |
| Nitrox (Nitrogen-Oxygen) | Nitrogen (68%), Oxygen (32%) | Scuba diving, extended bottom time |
| Trimix (Helium-Nitrogen-Oxygen) | Helium (50%), Nitrogen (30%), Oxygen (20%) | Technical diving, deep sea exploration |
| Natural Gas (Typical) | Methane (85%), Ethane (9%), Propane (4%), Nitrogen (2%) | Fuel, heating, power generation |
Practical Examples
Example: Dry Air at Sea Level
Given:
- P_total = 1.0 atm
- χ_N₂ = 0.78, χ_O₂ = 0.21
Solution:
P_N₂ = 0.78 × 1.0 = 0.78 atm
P_O₂ = 0.21 × 1.0 = 0.21 atm
Sum = 0.99 atm (+ trace gases = 1.0)
Example: Diving Gas (Nitrox 32)
Given:
- 32% O₂, 68% N₂ at 2 atm (10 m depth)
Solution:
P_O₂ = 0.32 × 2.0 = 0.64 atm
P_N₂ = 0.68 × 2.0 = 1.36 atm
PO₂ < 1.6 atm (safe)
📚 Official Data Sources
Safety Considerations
Critical Safety Warnings
- • Oxygen Partial Pressure: PO₂ above 1.6 atm can cause oxygen toxicity. Above 2.0 atm is dangerous.
- • Nitrogen Narcosis: High PN₂ at depth causes narcosis. Limit exposure based on depth.
- • Hypoxia: PO₂ below 0.16 atm (equivalent to ~8% at sea level) causes hypoxia.
- • Flammability: High oxygen partial pressures increase fire risk significantly.
- • Gas Mixtures: Always verify gas composition before use in breathing or industrial applications.
⚠️ Disclaimer: This calculator uses IUPAC definitions for partial pressure and Dalton's Law of Partial Pressures. For precise work, consult IUPAC Gold Book, NIST Chemistry WebBook, and authoritative physical chemistry references.