John Dalton noticed something strange back in 1801: when you mix different gases together that don't chemically react, they don't crowd each other out. Instead, each gas acts as if it occupies the entire container all by itself. Dalton's law of partial pressures states that the total pressure exerted by a mixture of unreacting gases equals the sum of the partial pressures of each individual gas. If you've ever wondered why scuba divers monitor gas mixes closely or how weather systems track atmospheric pressure, you're looking at this exact principle in action.
The core formula is straightforward. If you have three gases—let's call them A, B, and C—mixed in a rigid container, the total pressure ($P_{total}$) is simply:
$$P_{total} = P_A + P_B + P_C$$
Each individual pressure value ($P_A$, $P_B$, etc.) represents the partial pressure, which is the pressure that specific gas would exert if it filled the container completely on its own. Because gas molecules are mostly empty space and don't attract or repel each other under ideal conditions, they strike container walls independently.
Why Partial Pressures Matter in the Real World
You don't just use this law to pass high school chemistry exams. Understanding how gases contribute to a shared mixture governs safety in extreme environments.
Scuba diving provides a striking example. Pure oxygen becomes toxic to human tissue under high pressures found deep underwater. To prevent oxygen poisoning, technical divers breathe trimix or nitrox—mixtures containing oxygen, nitrogen, and helium. Dive computers calculate the partial pressure of oxygen at every depth to ensure it stays within safe limits (typically below 1.4 atmospheres). If the total pressure at depth increases, the partial pressure of every gas in the tank scales up proportionally.
Medical ventilators rely on the same math. When hospitals deliver precise oxygen therapy, clinicians calculate partial pressures to ensure a patient's lungs absorb enough oxygen without risking hyperoxia.
The Mole Fraction Method
Often, you won't be given the individual partial pressures directly. Instead, you'll know the total pressure and the amount of each gas present. That's where the mole fraction comes in.
The mole fraction ($\chi$) tells you what percentage of the total gas mixture belongs to a specific component. You find it by dividing the moles of one gas ($n_A$) by the total moles of all gases combined ($n_{total}$):
$$\chi_A = \frac{n_A}{n_{total}}$$
Once you have the mole fraction, you can isolate the partial pressure of that specific gas by multiplying it by the total pressure:
$$P_A = \chi_A \times P_{total}$$
For a practical breakdown of how this works, see the Chemistry LibreTexts guide on gas laws.
Step-by-Step Example Calculation
Let's walk through a standard problem. Imagine a 10-liter steel tank holding a mixture of 2.0 moles of nitrogen gas ($N_2$) and 1.0 mole of oxygen gas ($O_2$) at 300 Kelvin. What is the partial pressure of each gas, and what is the total pressure?
Find total moles: Combine the individual moles together. $$n_{total} = 2.0\text{ mol} + 1.0\text{ mol} = 3.0\text{ moles}$$
Calculate mole fractions:
- Nitrogen: $\chi_{N_2} = \frac{2.0}{3.0} = 0.67$
- Oxygen: $\chi_{O_2} = \frac{1.0}{3.0} = 0.33$
Calculate total pressure: Use the ideal gas law ($PV = nRT$), where $R = 0.08206\text{ L}\cdot\text{atm}/(\text{mol}\cdot\text{K})$. $$P_{total} = \frac{n_{total}RT}{V} = \frac{(3.0\text{ mol})(0.08206)(300\text{ K})}{10.0\text{ L}} = 7.39\text{ atmospheres}$$
Determine partial pressures: Multiply each mole fraction by the total pressure.
- $P_{N_2} = 0.67 \times 7.39\text{ atm} = 4.95\text{ atm}$
- $P_{O_2} = 0.33 \times 7.39\text{ atm} = 2.44\text{ atm}$
- Check your work: $4.95 + 2.44 = 7.39\text{ atm}$. The math checks out.
For additional practice problems and automated checks, you can explore the Khan Academy gas laws tutorial.
Dealing with Gases Collected Over Water
A classic chemistry lab trap involves collecting a gas by bubbling it through water. When you do this, the gas isn't pure—it traps water vapor along the way.
According to Dalton's law, the total pressure inside your collection flask is equal to the pressure of the dry gas plus the vapor pressure of the water at that specific temperature:
$$P_{total} = P_{gas} + P_{water}$$
To find the pressure of just the gas you care about, look up the water vapor pressure on a standard reference table for that temperature, then subtract it from the total room pressure. Ignoring this step is one of the most common reasons students mess up lab calculations.
Common Mistakes to Avoid
- Mixing up units: Always ensure your pressure units match before adding them together. If one value is in kilopascals (kPa) and another is in atmospheres (atm), convert them first.
- Assuming gases react: Dalton's law only applies when gases do not chemically react with each other. If hydrogen and oxygen react to form water, the pressure drops dramatically because the molecules bind into a liquid.
- Forgetting temperature and volume dependence: If you change the volume of the container, every partial pressure changes, even though the mole fractions stay identical.
Frequently Asked Questions
Does Dalton's law work for real gases?
It works exceptionally well for ideal gases, but real gases deviate under high pressures or very low temperatures. Under those extreme conditions, intermolecular forces and the actual physical volume of the gas molecules themselves cause slight discrepancies.
What happens to partial pressure if temperature increases?
If volume stays constant, raising the temperature increases the kinetic energy of the molecules. They hit the container walls harder and more frequently, which raises both the individual partial pressures and the total pressure.
How do I convert Torr to Atmospheres?
Divide your pressure value in Torr by 760, since 1 standard atmosphere equals 760 Torr.
Why don't heavier gases sink to the bottom of a container?
Gas molecules possess high thermal kinetic energy that constantly keeps them in random motion, overcoming gravity in standard container sizes. They mix uniformly rather than settling by weight.
