Gas Laws — Boyle's, Charles's, Avogadro's & Combined

Gas laws are a small set of relationships that tell you how a gas changes when you compress it, heat it, or change how much of it is present. The key is not memorizing four disconnected formulas. The key is noticing what stays constant.

If temperature stays constant, pressure and volume trade off. If pressure stays constant, volume tracks absolute temperature. If pressure and temperature stay constant, volume tracks the number of moles. When a fixed amount of gas changes pressure, volume, and temperature at the same time, the combined gas law is usually the cleanest tool.

The Main Gas Laws At A Glance

Boyle's Law

Boyle's law applies when temperature and amount of gas stay constant:

$$P_1V_1 = P_2V_2$$

Under that condition, pressure is inversely related to volume. If you squeeze a gas into half the volume at the same temperature, the pressure doubles.

Charles's Law

Charles's law applies when pressure and amount of gas stay constant:

$$\frac{V_1}{T_1} = \frac{V_2}{T_2}$$

Here temperature must be in Kelvin. If the absolute temperature doubles and pressure stays constant, the volume doubles.

Avogadro's Law

Avogadro's law applies when pressure and temperature stay constant:

$$\frac{V_1}{n_1} = \frac{V_2}{n_2}$$

This means volume is directly proportional to the amount of gas. If you double the number of moles while keeping pressure and temperature fixed, the volume doubles.

Combined Gas Law

The combined gas law is useful when the amount of gas is fixed but pressure, volume, and temperature can all change:

$$\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$$

It bundles Boyle's and Charles's law into one relationship. You can think of it as the right choice for a before-and-after state change when no gas is added or removed.

The Intuition That Makes Gas Laws Click

A gas pushes on the walls of its container because its particles are moving and colliding with those walls.

If you make the container smaller without changing temperature, the same particles hit the walls more often, so pressure rises. If you heat the gas, the particles move faster, so either pressure rises or, if the pressure is allowed to stay constant, the gas expands. If you add more gas particles while keeping pressure and temperature fixed, the gas needs more volume to accommodate them.

That is why gas-law problems are mostly about conditions. The formula follows from the condition.

One Worked Example

A sample of gas occupies $2.0\ \mathrm{L}$ at $1.2\ \mathrm{atm}$ and $300\ \mathrm{K}$. It is compressed to $1.5\ \mathrm{L}$ and heated to $360\ \mathrm{K}$. No gas escapes. What is the new pressure?

Because the amount of gas stays fixed and all three variables change, use the combined gas law:

$$\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$$

Solve for $P_2$:

$$P_2 = \frac{P_1V_1T_2}{T_1V_2}$$

Substitute the values:

$$P_2 = \frac{(1.2)(2.0)(360)}{(300)(1.5)} = \frac{864}{450} = 1.92\ \mathrm{atm}$$

So the new pressure is $1.92\ \mathrm{atm}$.

The result makes physical sense. The gas was compressed, which tends to raise pressure, and it was also heated, which also tends to raise pressure. A higher final pressure is exactly what you should expect.

Common Mistakes

Using Celsius In Gas-Law Ratios

For Charles's law and the combined gas law, temperature must be absolute temperature. Use Kelvin, not Celsius.

Picking A Law Before Checking The Condition

Do not start from the formula you remember best. Start from what is constant. That tells you which law applies.

Forgetting That Avogadro's Law Needs Constant $P$ And $T$

Volume is proportional to moles only under those conditions. If pressure or temperature also changes, that simple ratio is not enough by itself.

Mixing States And Units Carelessly

Initial values must stay grouped together, and final values must stay grouped together. Unit conversions also matter, especially for temperature.

When Gas Laws Are Used

Gas laws show up in introductory chemistry, lab calculations, syringe and piston problems, weather-balloon style reasoning, and any setup where a gas changes state without requiring a full real-gas model.

They are most useful when the gas is treated approximately as ideal and the problem clearly tells you which quantities are fixed. If the gas is far from ideal behavior, especially at high pressure or near condensation, you may need a more detailed model.

Try Your Own Version

Take the same example but keep the temperature at $300\ \mathrm{K}$ instead of heating to $360\ \mathrm{K}$. Solve it again and compare the final pressure. That is a quick way to see exactly what heating contributed.

If you want the next step after these relationships, explore the ideal gas law. It unifies pressure, volume, temperature, and moles in one equation and makes it easier to handle problems where the amount of gas matters directly.