Q.A closed vessel contains $2\ \text{mol}$ of $\text{N}_2$ and $3\ \text{mol}$ of $\text{O}_2$ at a total pressure of $5\ \text{atm}$. Using Dalton's law of partial pressures, calculate the partial pressure of each gas.

Dalton's Law of Partial Pressures

Imagine you're in a room full of people talking. Each person contributes to the overall noise. If you could somehow measure the sound from just one person, that's their "partial noise." The total noise is just the sum of everyone's individual contributions. Gases behave the same way.

When you have a mixture of gases — say oxygen, nitrogen, and carbon dioxide — each gas behaves as if it were alone in the container. It doesn't care about the other gases. It bounces around, hits the walls, and exerts its own pressure. That pressure is called its partial pressure.

The Precise Statement

Dalton's Law of Partial Pressures says:

The total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of each individual gas.

Mathematically:

where $P_1$, $P_2$, $P_3$, etc. are the partial pressures of each gas.

What Exactly Is a Partial Pressure?

The partial pressure of a gas in a mixture is the pressure that gas would exert if it alone occupied the entire container at the same temperature.

Think of it this way: if you have a 1-litre flask containing oxygen and nitrogen at room temperature, the oxygen molecules don't know the nitrogen molecules exist. They just keep hitting the walls. The pressure from oxygen alone is its partial pressure. The pressure from nitrogen alone is its partial pressure. Add them up, and you get the total pressure.

Here $n_i$ is the number of moles of gas $i$, and $n_{\text{total}}$ is the total number of moles. This formula lets you find a gas's partial pressure if you know its mole fraction and the total pressure.

Why Does This Work?

Gases are mostly empty space. The molecules are far apart and move independently. In an ideal gas, there are no attractive or repulsive forces between molecules. So each gas in a mixture behaves exactly as it would alone. The pressure each gas exerts depends only on its own number of molecules, not on what other gases are present.

A Simple Example …