Short Answer:
Dalton’s law of partial pressures states that in a mixture of non-reacting gases, the total pressure exerted by the mixture is equal to the sum of the partial pressures of each individual gas. A partial pressure is the pressure a gas would exert if it occupied the container alone.
This law is very useful in thermodynamics and gas analysis. For example, in atmospheric air (a mix of nitrogen, oxygen, carbon dioxide, etc.), the total pressure is the sum of the pressures of each gas as if it acted independently.
Detailed Explanation:
Dalton’s law of partial pressures
Dalton’s law is an important gas law named after the scientist John Dalton, who proposed it in the early 1800s. It helps us understand how gases behave in a mixture, especially when they do not chemically react with each other. According to this law, each gas in a mixture contributes to the total pressure as if it were the only gas present in the container.
This concept is widely used in engineering, chemistry, medical sciences, and atmospheric studies.
Statement of Dalton’s Law
“In a mixture of non-reacting gases, the total pressure is equal to the sum of the partial pressures of all individual gases.”
Mathematically:
P_total = P₁ + P₂ + P₃ + … + Pn
Where:
- P_total = total pressure of the gas mixture
- P₁, P₂, P₃, …, Pn = partial pressures of each gas in the mixture
Each partial pressure depends on the amount (moles) of that gas and the volume and temperature of the container.
Partial Pressure Formula
If we know the mole fraction of a gas in the mixture, we can calculate its partial pressure using:
P_gas = X_gas × P_total
Where:
- P_gas = partial pressure of a gas
- X_gas = mole fraction of that gas
- P_total = total pressure of the gas mixture
Mole fraction is:
X_gas = n_gas / n_total
Where:
- n_gas = number of moles of a specific gas
- n_total = total number of moles in the mixture
Real-Life Example
Example – Air Composition:
Air is a mixture of gases like nitrogen (78%), oxygen (21%), and small amounts of carbon dioxide and others.
Suppose total atmospheric pressure = 1 atm
Then:
- Partial pressure of nitrogen = 0.78 × 1 atm = 0.78 atm
- Partial pressure of oxygen = 0.21 × 1 atm = 0.21 atm
- Remaining gases = 0.01 atm
Total = 0.78 + 0.21 + 0.01 = 1 atm
This shows how Dalton’s law works in calculating individual gas pressures.
Applications of Dalton’s Law
- Breathing and respiratory systems
- Oxygen and carbon dioxide partial pressures help in lung gas exchange.
- Scuba diving and high-altitude conditions
- Gas mixtures are designed based on partial pressures.
- Gas cylinders and mixtures in industry
- Used in welding, laboratories, and chemical plants.
- Thermodynamic cycle analysis
- Used in gas mixture behavior in engines.
- Meteorology and climate science
- Helps in analyzing air composition and pressure distribution.
Important Points
- Gases must be non-reacting; the law does not apply to chemically reacting gases.
- Works best for ideal gas mixtures.
- Total pressure depends only on total number of moles, not the type of gases.
- At constant volume and temperature, the pressure is directly proportional to number of moles (from ideal gas law).
Limitations
- Dalton’s law assumes ideal gas behavior.
- Not accurate for gases at very high pressures or low temperatures.
- Cannot be applied when chemical reactions occur between the gases in the mixture.
Still, under normal conditions, Dalton’s law gives highly accurate results.
Conclusion
Dalton’s law of partial pressures explains how the total pressure in a gas mixture is the sum of the pressures contributed by each individual gas. Each gas behaves independently and adds to the total pressure based on its amount. This law is very useful in real-world applications such as air composition, breathing systems, industrial gas handling, and thermodynamic analysis. It is a key principle in understanding gas mixtures.