Dalton's Law of Partial Pressures
Dalton's Law states total gas pressure equals the sum of partial pressures.
Learn the formula P_total = P₁ + P₂ + ... with examples.
The Formula
Dalton's Law of Partial Pressures states that the total pressure exerted by a mixture of non-reacting gases equals the sum of the partial pressures of each individual gas. Each gas in a mixture behaves independently and contributes to the total pressure as if it occupied the container alone.
This law was proposed by English chemist John Dalton in 1801. It is widely used in chemistry, respiratory physiology, and atmospheric science. The partial pressure of each gas can be calculated using the mole fraction: Pᵢ = xᵢ × P_total, where xᵢ is the mole fraction of gas i.
Variables
| Symbol | Meaning |
|---|---|
| P_total | Total pressure of the gas mixture (in atm, Pa, mmHg, etc.) |
| P₁, P₂, ... Pₙ | Partial pressure of each individual gas |
| xᵢ | Mole fraction of gas i (dimensionless, between 0 and 1) |
Example 1
A container holds oxygen at 0.4 atm, nitrogen at 0.5 atm, and carbon dioxide at 0.1 atm. What is the total pressure?
Identify partial pressures: P_O₂ = 0.4 atm, P_N₂ = 0.5 atm, P_CO₂ = 0.1 atm
Apply Dalton's Law: P_total = P_O₂ + P_N₂ + P_CO₂
P_total = 0.4 + 0.5 + 0.1
P_total = 1.0 atm
Example 2
At sea level (P_total = 760 mmHg), air is approximately 78% nitrogen and 21% oxygen. What are the partial pressures?
Convert percentages to mole fractions: x_N₂ = 0.78, x_O₂ = 0.21
P_N₂ = x_N₂ × P_total = 0.78 × 760 = 592.8 mmHg
P_O₂ = x_O₂ × P_total = 0.21 × 760 = 159.6 mmHg
P_N₂ ≈ 593 mmHg, P_O₂ ≈ 160 mmHg
When to Use It
Dalton's Law is essential whenever you work with gas mixtures.
- Calculating the composition of atmospheric air
- Determining oxygen partial pressure for scuba diving and altitude medicine
- Analyzing gas mixtures in industrial chemistry
- Understanding respiratory gas exchange in the lungs