Dalton's Law Calculator

Calculate total and partial pressures in gas mixtures using Dalton's Law of Partial Pressures

Dalton's Law Calculator

Dalton's Law: P_total = P₁ + P₂ + P₃ + ...
Total pressure of a gas mixture equals the sum of partial pressures

Partial Pressures of Gases

All pressures must be in the same units (atm, kPa, mmHg, etc.)

Example: Air Composition (1 atm):

• N₂: 0.78 atm (78%)

• O₂: 0.21 atm (21%)

• Ar: 0.009 atm (0.9%)

• CO₂: 0.0004 atm (0.04%)

Understanding Dalton's Law

Dalton's Law states that the total pressure of a gas mixture is equal to the sum of the partial pressures of each individual gas component.

P_total = P₁ + P₂ + P₃ + ...

P_total = total pressure of mixture
P₁, P₂, P₃ = partial pressures of each gas
Each gas behaves independently

Partial Pressure

The partial pressure is the pressure a gas would exert if it occupied the entire volume alone:

P_i = χ_i × P_total

χ_i = n_i / n_total

The mole fraction (χ) equals the pressure fraction in an ideal gas mixture.

Where It's Used

•Scuba Diving: Calculating nitrogen and oxygen partial pressures at depth
•Atmospheric Science: Analyzing air composition and weather patterns
•Gas Storage: Managing compressed gas cylinders and tanks
•Industrial Processes: Chemical reactions involving gas mixtures

Example Calculation

Problem:

A gas mixture contains nitrogen at 0.70 atm, oxygen at 0.20 atm, and argon at 0.05 atm. What is the total pressure?

Step 1: List partial pressures

P_N₂ = 0.70 atm
P_O₂ = 0.20 atm
P_Ar = 0.05 atm

Step 2: Apply Dalton's Law

P_total = 0.70 + 0.20 + 0.05
P_total = 0.95 atm

Step 3: Calculate mole fractions

χ_N₂ = 0.70 / 0.95 = 0.737 (73.7%)
χ_O₂ = 0.20 / 0.95 = 0.211 (21.1%)
χ_Ar = 0.05 / 0.95 = 0.053 (5.3%)

Result:

Total pressure is 0.95 atm, with N₂ comprising 73.7% of the mixture.

Atmospheric Air Composition

At sea level (1.00 atm), dry air consists of:

Gas	Mole %	Partial Pressure
Nitrogen (N₂)	78.08%	0.7808 atm
Oxygen (O₂)	20.95%	0.2095 atm
Argon (Ar)	0.93%	0.0093 atm
Carbon Dioxide (CO₂)	0.04%	0.0004 atm

Note:

Partial pressures change with altitude. At 10,000 ft (0.69 atm), oxygen partial pressure drops to ~0.14 atm, causing altitude sickness in some people.

Scuba Diving Application

Depth and Pressure

Depth	P_total	P_O₂	P_N₂
Surface	1.0 atm	0.21 atm	0.79 atm
10 m (33 ft)	2.0 atm	0.42 atm	1.58 atm
20 m (66 ft)	3.0 atm	0.63 atm	2.37 atm
30 m (99 ft)	4.0 atm	0.84 atm	3.16 atm

Safety Concerns

Nitrogen Narcosis

High P_N₂ (>3.2 atm) causes impaired judgment. Occurs below ~30 m.

Oxygen Toxicity

P_O₂ > 1.4 atm can cause seizures. Limits depth for air diving to ~57 m.

Decompression Sickness

Dissolved N₂ forms bubbles if pressure drops too quickly during ascent.

Gas Collection Over Water

When a gas is collected over water, the total pressure includes the vapor pressure of water:

P_total = P_gas + P_H₂O

P_gas = P_total - P_H₂O

Must subtract water vapor pressure to get the actual pressure of the collected gas.

Water Vapor Pressure (P_H₂O)

Temperature (°C)	P_H₂O (mmHg)
15	12.8
20	17.5
25	23.8
30	31.8

Dalton's Law Calculator