Dalton's Law of Partial Pressures

Dalton's Law states that the total pressure of a gas mixture equals the sum of the partial pressures of each individual gas. Each gas behaves independently.

Dalton's Law

Ptotal = P₁ + P₂ + P₃ + ...

Or in summation notation:

Ptotal = ΣPi

Variable Definitions

Ptotal = Total Pressure

Units: atm, kPa, mmHg, torr, Pa

Sum of all partial pressures in the mixture

Pi = Partial Pressure

Units: Same as Ptotal

Pressure each gas would exert alone

💡 Pi = χi × Ptotal (where χ = mole fraction)

χi = Mole Fraction

Formula: χi = ni / ntotal

Range: 0 to 1 (unitless)

Fraction of total moles that gas i represents

Key Relationships

Partial Pressure from Moles:

Pi = (ni/ntotal) × Ptotal

Using mole fraction

Using Ideal Gas Law:

Pi = niRT/V

Each gas independently

Mole Fractions Sum:

Σχi = 1

All fractions must add to 1

Percent by Pressure:

%Pi = (Pi/Ptotal) × 100

Same as mole percent

Step-by-Step Example

Problem: A mixture contains 2.0 mol N₂, 3.0 mol O₂, and 1.0 mol Ar at 5.0 atm total pressure. Find each partial pressure.

Given:

  • n(N₂) = 2.0 mol
  • n(O₂) = 3.0 mol
  • n(Ar) = 1.0 mol
  • Ptotal = 5.0 atm

Step 1: Calculate total moles

ntotal = 2.0 + 3.0 + 1.0 = 6.0 mol

Step 2: Calculate mole fractions

χ(N₂) = 2.0 / 6.0 = 0.333

χ(O₂) = 3.0 / 6.0 = 0.500

χ(Ar) = 1.0 / 6.0 = 0.167

Step 3: Calculate partial pressures

P(N₂) = 0.333 × 5.0 = 1.67 atm

P(O₂) = 0.500 × 5.0 = 2.50 atm

P(Ar) = 0.167 × 5.0 = 0.83 atm

Step 4: Verify (check sum)

1.67 + 2.50 + 0.83 = 5.00 atm ✓

Answers:

  • P(N₂) = 1.67 atm
  • P(O₂) = 2.50 atm
  • P(Ar) = 0.83 atm

Real-World Applications

🌬️ Atmospheric Pressure

Air pressure (1 atm) = P(N₂) + P(O₂) + P(Ar) + P(CO₂) + ...

🫁 Breathing & Diving

Oxygen partial pressure determines how much O₂ dissolves in blood

⚗️ Gas Collection

Collected gas over water: Pgas = Ptotal - PH₂O

🏭 Industrial Processes

Controlling reaction rates by adjusting partial pressures of reactants

Common Mistakes

❌ Forgetting water vapor pressure

When collecting gas over water, must subtract water vapor pressure: Pgas = Ptotal - PH₂O

❌ Using mass instead of moles

Partial pressure depends on MOLES, not mass. Heavier gases don't have higher partial pressures if moles are equal.

❌ Mismatched pressure units

All pressures must use the same units. Can't add atm and kPa directly!

❌ Assuming gases interact

Dalton's Law assumes ideal behavior - gases don't attract or repel each other. Not accurate for highly polar or reactive gases.

Related Calculators

Dalton's Law Calculator

Calculate partial pressures instantly

Partial Pressure Calculator

Find individual gas pressures

Ideal Gas Law

PV = nRT calculations

Mole Fraction

Calculate χ for mixtures

Frequently Asked Questions

What is Dalton's Law of Partial Pressures?

Ptotal = P₁ + P₂ + P₃ + ... The total pressure of a gas mixture equals the sum of the partial pressures of each component gas.

What is a partial pressure?

The pressure each gas in a mixture would exert if it alone occupied the entire volume. It depends on the mole fraction.

How do I find partial pressure from mole fraction?

Pi = χi × Ptotal, where χi = ni/ntotal. Multiply the mole fraction by total pressure.

Does Dalton's Law work for all gases?

It's most accurate for ideal gases that don't interact. Works well for common gases (N₂, O₂, etc.) at moderate T and P, less accurate for polar or reactive gases.

Why subtract water vapor when collecting gas over water?

Water evaporates into the container, contributing to total pressure. To get just the collected gas pressure: Pgas = Ptotal - PH₂O.

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