Dalton's Law- Partial Pressures Explained
What Dalton's Law Actually Is
Dalton's Law states that the total pressure exerted by a mixture of non-reacting gases equals the sum of the partial pressures of each individual gas. That's it. One sentence explains the whole thing.
The law works because gases behave independently. They don't form compounds under normal conditions, so each gas contributes its own pressure as if the others weren't there.
Partial Pressure: The Core Concept
Partial pressure is the pressure a single gas would exert if it occupied the container alone. Think of it this way: if you have a container with oxygen and nitrogen mixed together, the oxygen pushes against the walls just as hard as it would if nitrogen weren't present.
Each gas molecule bounces around and hits the walls. All those collisions add up. The total pressure is just the sum of all collisions from every gas species.
The Formula
Ptotal = P1 + P2 + P3 + ... + Pn
Where Pn represents the partial pressure of each gas. You can also calculate partial pressure using mole fraction:
Pgas = (mole fraction of that gas) × (total pressure)
Why This Matters
Dalton's Law isn't theoretical. It shows up in real situations:
- Scuba diving — Decompression sickness happens because of partial pressures of gases in your blood, not just the total pressure
- Medicine — Anesthesia gases are dosed based on partial pressures, not concentrations
- Atmospheric science — Weather patterns depend on water vapor partial pressure
- Industrial processes — Chemical reactors use partial pressures to control reaction rates
Gas Properties Comparison
| Gas | Symbol | Approx. Mole Fraction in Air | Partial Pressure at 1 atm |
|---|---|---|---|
| Nitrogen | Nâ‚‚ | 0.7808 | 0.78 atm |
| Oxygen | Oâ‚‚ | 0.2095 | 0.21 atm |
| Argon | Ar | 0.0093 | 0.009 atm |
| Carbon Dioxide | COâ‚‚ | 0.0004 | 0.0004 atm |
How To Calculate Partial Pressures
Method 1: Using Mole Fractions
Step 1: Find the mole fraction of your gas
Step 2: Multiply by total pressure
Example: A container holds helium and neon at 2 atm total pressure. If the mole fraction of helium is 0.3, the partial pressure of helium is 0.3 × 2 = 0.6 atm.
Method 2: Using Boyle's Law
If you know the volume and temperature, and the gas alone would exert a certain pressure:
Partial pressure of gas A = (Volume of gas A / Total volume) × Total pressure
This works when gases are at the same temperature, which is the standard assumption.
Common Mistakes
People mess this up constantly. Here's what to avoid:
- Assuming equal pressures — Partial pressures aren't equal just because you have equal volumes. They depend on mole fractions, which depend on the number of molecules
- Ignoring temperature — All gases in the mixture must be at the same temperature for the law to apply directly
- Confusing concentration with pressure — A gas can have high concentration but low partial pressure if total pressure is low
- Forgetting non-ideal behavior — At high pressures or low temperatures, real gases deviate from this simple model
Getting Started With Problems
When you see a Dalton's Law problem:
- Identify all gases in the mixture
- Determine total pressure (often given)
- Find mole fractions or volumes for each gas
- Apply the formula Pi = (mole fractioni) × (Ptotal)
- Verify: sum of all partial pressures should equal total pressure
The verification step catches most calculation errors. If your partial pressures don't add up to the total, something went wrong.
The Bottom Line
Dalton's Law is straightforward: total pressure equals the sum of individual gas pressures. No complexity, no hidden tricks. Master the mole fraction calculation, verify your sums, and you won't have problems with it.