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

The gas laws are four short relationships, and the trick to using them is not memorizing four formulas but spotting what stays constant. Each law and its symbols:

Here $P$ is pressure, $V$ is volume, $T$ is absolute temperature in Kelvin, and $n$ is the amount of gas in moles. Subscripts $1$ and $2$ mark the initial and final states. Each law isolates one trade-off by holding the rest fixed: Boyle's law keeps $T$ and $n$ constant so pressure and volume trade off, Charles's law keeps $P$ and $n$ constant so volume tracks absolute temperature, Avogadro's law keeps $P$ and $T$ constant so volume tracks moles, and the combined law keeps only $n$ fixed while $P$, $V$, and $T$ all change. Reading the formula starts with reading which quantities are pinned.

Why each relation holds

A gas pushes on its container because its particles move and collide with the walls. That single picture produces all four laws:

• Shrink the container at constant temperature and the same particles hit the walls more often, so pressure rises as volume falls. That is Boyle.
• Heat the gas at constant pressure and the particles move faster, so the gas must expand to keep the same wall pressure. Volume tracks absolute temperature. That is Charles.
• Add particles at constant pressure and temperature and the gas needs more room. Volume tracks moles. That is Avogadro.
• Let pressure, volume, and temperature all change with no gas added or removed and the combined law bundles Boyle and Charles into one before-and-after relation.

The formula follows from the condition, which is why naming what is constant comes first.

Worked example: combined gas law, step by step

A 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 $360\ \mathrm{K}$, with no gas escaping. Find the new pressure.

The amount is fixed and all three variables change, so use the combined gas law and solve for $P_2$:

Substitute:

The result, $1.92\ \mathrm{atm}$, makes sense: compression raises pressure and heating raises pressure, so a higher final value is expected. Notice the structure of the work: initial values stayed grouped on the left, final values on the right, the equation was rearranged once for the unknown, and the substitution kept consistent units throughout. That ordering is what keeps before-and-after problems from going wrong.

Try it yourself, then check

Rework the example but hold the temperature at $300\ \mathrm{K}$ instead of heating to $360\ \mathrm{K}$. With no heating the combined law reduces to Boyle's law:

Compare $1.6\ \mathrm{atm}$ with the $1.92\ \mathrm{atm}$ above. The $0.32\ \mathrm{atm}$ difference is exactly what heating to $360\ \mathrm{K}$ contributed.

Calculation pitfalls

• Using Celsius in ratios. Charles's law and the combined law need absolute temperature, so convert to Kelvin first.
• Picking a law before checking the condition. Start from what is constant, not from the formula you remember best.
• Forgetting Avogadro's law needs constant $P$ and $T$. If either also changes, the simple moles-to-volume ratio is not enough.
• Mixing states and units. Keep all initial values together and all final values together, and watch temperature conversions.

Gas laws apply in introductory chemistry, lab calculations, syringe and piston problems, and weather-balloon reasoning, working best when the gas is roughly ideal and the problem states which quantities are fixed. Near high pressure or condensation a fuller real-gas model may be needed. The natural next step is the ideal gas law, which unifies pressure, volume, temperature, and moles in one equation and handles problems where the amount of gas matters directly.