Dalton's Law of Partial Pressures
Learn Dalton's Law of Partial Pressures formula P_total = P1 + P2 + ... + Pn for calculating total gas mixture pressure.
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. This law was formulated by the English chemist and physicist John Dalton in 1801. A partial pressure is the pressure that a gas would exert if it alone occupied the entire volume of the mixture at the same temperature.
This law is a direct consequence of the ideal gas assumption that gas molecules do not interact with each other. Each gas in a mixture behaves independently, contributing to the total pressure in proportion to its mole fraction. The partial pressure of any component can be calculated as Pi = xi times Ptotal, where xi is the mole fraction of gas i.
Dalton's Law is fundamental in many practical applications. In respiratory physiology, it explains how oxygen and carbon dioxide are exchanged in the lungs. The air we breathe is a mixture of nitrogen (about 78 percent), oxygen (about 21 percent), and trace gases. At sea level atmospheric pressure of 101.3 kPa, the partial pressure of oxygen is approximately 21.3 kPa. At high altitudes where total pressure drops, the partial pressure of oxygen decreases proportionally, which is why breathing becomes difficult.
In chemistry laboratories, this law is essential when collecting gases over water. The collected gas is always mixed with water vapor, so the pressure of the dry gas equals the total pressure minus the vapor pressure of water at that temperature. Industrial applications include designing gas storage systems, scuba diving gas mixtures, and anesthesia delivery in medicine.
The law works best for ideal gases and at moderate pressures. At very high pressures or low temperatures, intermolecular forces become significant and real gas behavior deviates from the ideal prediction. In those cases, more sophisticated equations of state are needed.
Variables
| Symbol | Meaning |
|---|---|
| Ptotal | Total pressure of the gas mixture (Pa, atm, or kPa) |
| P1, P2, ... Pn | Partial pressures of individual gas components |
| xi | Mole fraction of gas i (dimensionless, between 0 and 1) |
| n | Number of different gas components in the mixture |
Example 1
Problem: A container holds nitrogen at 250 kPa and oxygen at 150 kPa. What is the total pressure?
Apply Dalton's Law: Ptotal = PN2 + PO2
Ptotal = 250 kPa + 150 kPa
Ptotal = 400 kPa
Example 2
Problem: A gas is collected over water at 25 degrees C. The total pressure is 101.3 kPa and the vapor pressure of water at 25 degrees C is 3.17 kPa. What is the pressure of the dry gas?
Ptotal = Pgas + Pwater, so Pgas = Ptotal - Pwater
Pgas = 101.3 kPa - 3.17 kPa
Pgas = 98.13 kPa
When to Use It
Dalton's Law is used whenever you work with mixtures of gases.
- Collecting gases over water in laboratory experiments
- Calculating oxygen partial pressure at different altitudes
- Designing breathing gas mixtures for scuba diving (nitrox, trimix)
- Determining gas composition in industrial chemical processes
- Understanding respiratory gas exchange in physiology and medicine