Gas Laws
Apply Boyle, Charles, Gay-Lussac, combined gas law, ideal gas law, and partial pressure relationships to solve gas problems.
A lesson of Chemistry, in Energy, States of Matter, and Solutions, about 35 minutes.
By the end of this lesson, you will be able to explain each gas law from particle motion, choose the right one for a problem, use the ideal gas law, and say where the ideal model breaks down.
Four Variables, One Model
A gas is described by pressure, volume, temperature and amount, and the gas laws are all statements about how those four trade against each other.
Kinetic molecular theory is the picture behind all of them:
- Particles are in constant random motion
- They are tiny compared with the space between them, so a gas is mostly empty
- Collisions are perfectly elastic, losing no energy
- Their average kinetic energy is proportional to the absolute temperature
Pressure is collisions. Gas particles striking a wall and bouncing off exert force; more collisions, or harder ones, means more pressure. Every law below is that sentence applied to a different change.
Temperature must be in KELVIN, always.
$$K = °C + 273$$
This is not a convention. Kelvin is proportional to average kinetic energy, and Celsius is not: doubling from $10°C$ to $20°C$ does not double the energy, while doubling from $283$ K to $566$ K does. Using Celsius in a gas law gives wrong answers, and at negative temperatures it gives absurd ones.
The Three Simple Laws
Each holds two variables fixed and relates the other two.
Boyle's law: $P$ and $V$ are inverse, at constant $T$.
$$P_1V_1 = P_2V_2$$
Halve the volume and the particles hit the walls twice as often, so the pressure doubles. Squeezing a sealed syringe demonstrates it directly.
Charles's law: $V$ and $T$ are direct, at constant $P$.
$$\frac{V_1}{T_1} = \frac{V_2}{T_2}$$
Warm the gas and the particles move faster, so the container must expand to keep the pressure constant. A balloon in a freezer shrinks.
Gay-Lussac's law: $P$ and $T$ are direct, at constant $V$.
$$\frac{P_1}{T_1} = \frac{P_2}{T_2}$$
A rigid container cannot expand, so faster particles simply hit harder. This is why aerosol cans warn against heating, and why car tire pressure reads higher after a long drive.
Combining all three gives the form that covers any change:
$$\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$$
Whichever quantity is constant cancels from both sides, so the combined law reduces to whichever simple law you need, and there is no reason to memorize all four separately.