Dalton's Law Formula- Complete Explanation and Examples
What Is Dalton's Law?
Dalton's Law, also called Dalton's Law of Partial Pressures, states that the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of each individual gas in the mixture.
John Dalton figured this out in 1801. He was studying gas mixtures and realized something simple but important: gases in a mixture act independently. They don't know the other gases are there.
This is a fundamental concept in chemistry and physics. You'll use it whenever you deal with gas mixtures, whether you're calculating atmospheric pressure, designing a gas collection system, or working with respiratory gases.
The Dalton's Law Formula
Here's the mathematical expression:
Ptotal = P1 + P2 + P3 + ... + Pn
Where:
- Ptotal = Total pressure of the gas mixture
- P1, P2, P3... = Partial pressure of each gas component
- n = Total number of gases in the mixture
The partial pressure of any gas in a mixture follows this relationship:
Pgas = (mole fraction of gas) × Ptotal
Or equivalently:
Pgas = Ptotal × (moles of gas / total moles)
Understanding Partial Pressure
Partial pressure is the pressure that a single gas would exert if it occupied the container alone, at the same temperature, occupying the same volume.
Think of it this way: imagine you have a container with three different gases. Gas A molecules bounce around, Gas B molecules bounce around, and Gas C molecules bounce around. Each type of molecule contributes to the total pressure based on how many molecules are present.
The molecules don't care about the other gases. Each gas behaves exactly as it would in its own container. The total pressure is just the sum of all these independent contributions.
Why Does This Work?
Gas molecules are so far apart from each other in most conditions that they essentially don't interact. They're like tiny billiard balls bouncing around independently. This is why Dalton's Law works for ideal gases and is a good approximation for real gases at normal temperatures and pressures.
Dalton's Law Examples
Example 1: Simple Two-Gas Mixture
Problem: A container holds a mixture of oxygen (O₂) and nitrogen (N₂). The partial pressure of oxygen is 0.21 atm and the partial pressure of nitrogen is 0.79 atm. What is the total pressure?
Solution:
Ptotal = PO₂ + PN₂
Ptotal = 0.21 atm + 0.79 atm = 1.00 atm
This is exactly how atmospheric air behaves. The air you breathe is roughly 21% oxygen and 79% nitrogen by volume, giving partial pressures of about 0.21 atm and 0.79 atm respectively at sea level.
Example 2: Finding Partial Pressure from Mole Fraction
Problem: A gas mixture contains 2 moles of helium and 3 moles of neon at a total pressure of 5 atm. What is the partial pressure of each gas?
Solution:
First, calculate the mole fraction of each gas:
Total moles = 2 + 3 = 5 moles
Mole fraction of He = 2/5 = 0.40
Mole fraction of Ne = 3/5 = 0.60
Now calculate partial pressures:
PHe = 0.40 × 5 atm = 2.0 atm
PNe = 0.60 × 5 atm = 3.0 atm
Check: PHe + PNe = 2.0 + 3.0 = 5.0 atm ✓
Example 3: Gas Collected Over Water
Problem: You collect oxygen gas over water at 25°C. The total pressure is 755 mmHg and the vapor pressure of water at 25°C is 24 mmHg. What is the partial pressure of the oxygen?
Solution:
The total pressure includes both the oxygen and water vapor. Remove the water vapor pressure to get the partial pressure of oxygen:
PO₂ = Ptotal - Pwater vapor
PO₂ = 755 mmHg - 24 mmHg = 731 mmHg
This is why you must subtract water vapor pressure when collecting gases over water in lab experiments.
Comparing Gas Pressures in Common Mixtures
| Gas Mixture | Components | Typical Composition | Application |
|---|---|---|---|
| Atmospheric Air | N₂, O₂, Ar, CO₂ | 78%, 21%, 0.9%, 0.04% | Breathing, weather |
| Natural Gas | CH₄, C₂H₆, CO₂ | 70-90%, 0-20%, 0-8% | Heating, cooking |
| Exhaled Breath | N₂, O₂, CO₂, H₂O | 75%, 15%, 4%, 6% | Medicine, diving |
| Scuba Tank (Air) | N₂, O₂ | 79%, 21% | Diving |
| Anesthetic Gas | N₂O, O₂, Halothane | Variable mixture | Surgery |
Getting Started: How to Solve Dalton's Law Problems
Here's a step-by-step approach for any partial pressure calculation:
Step 1: Identify Known Values
List what you know: total pressure, individual partial pressures, moles of each gas, or mole fractions. Know which values you're given and which you need to find.
Step 2: Determine What Formula to Use
If you need total pressure from partial pressures:
Ptotal = Σ Pi
If you need partial pressure from mole fraction:
Pi = Xi × Ptotal
If you need mole fraction from moles:
Xi = ni / ntotal
Step 3: Calculate and Verify
Plug in your values and solve. Always verify by checking that the sum of all partial pressures equals the total pressure. If it doesn't, you made an error somewhere.
Common Mistakes to Avoid
- Forgetting to subtract water vapor when working with collected gases
- Confusing mole fraction with percentage by volume (they're the same for ideal gases, but not for liquids or solids)
- Using partial pressure where total pressure is needed or vice versa
- Rounding too early in calculations—keep extra digits until the final answer
Real-World Applications of Dalton's Law
Respiratory Physiology
Your lungs work on Dalton's Law principles. When you inhale, oxygen moves into your blood because its partial pressure in the alveoli is higher than in your blood. Carbon dioxide moves out because its partial pressure is higher in your blood.
At high altitudes, atmospheric pressure drops, which means all partial pressures drop proportionally. This is why breathing becomes difficult at elevation—there's less oxygen available even though the percentage remains constant.
Scuba Diving
Divers must understand Dalton's Law to avoid decompression sickness. As depth increases, pressure increases. More nitrogen dissolves into the bloodstream. If a diver ascends too quickly, the nitrogen comes out of solution as bubbles, causing "the bends."
This is also why technical divers use gas mixtures with reduced oxygen and nitrogen percentages at extreme depths.
Gas Collection in Labs
When collecting a gas over water in a graduated cylinder, you measure the total pressure of the gas plus water vapor. You must subtract the water vapor pressure (which depends on temperature) to get the partial pressure of your collected gas.
Industrial Gas Mixtures
Manufacturing processes often require specific gas mixtures with precise partial pressures. Gas welding, pharmaceutical production, and food packaging all rely on controlling partial pressures of specific gases.
Limitations of Dalton's Law
Dalton's Law assumes gases behave ideally. At high pressures or low temperatures, real gas behavior deviates from this ideal model because gas molecules start interacting with each other.
The law also breaks down for gases that react with each other. If gases chemically combine or undergo reactions, the pressure relationships change because the number of gas molecules changes.
For most practical purposes at normal conditions, Dalton's Law works well enough. Engineers build entire industries around these calculations without running into major problems.
The Bottom Line
Dalton's Law is straightforward: total pressure equals the sum of partial pressures. Gas molecules behave independently in a mixture. Use mole fractions to convert between partial and total pressure.
Master the basic formula, understand mole fraction, and practice the three common problem types (finding total from partials, finding partials from mole fractions, and water vapor corrections). That's all you need for most chemistry and physics applications.