The gas laws: use Boyle's law, Charles's law, Gay-Lussac's law and the combined gas law to relate the pressure, volume and temperature of a gas.

What this topic is asking

Standard CH.4 asks you to relate the pressure, volume and temperature of a gas using the gas laws. Virginia expects you to apply Boyle's law, Charles's law, Gay-Lussac's law and the combined gas law to calculate an unknown quantity. The recurring rule is that temperature must be in kelvin, and the calculations are one-step rearrangements.

Boyle's law

This makes sense from kinetic molecular theory: squeezing the gas into a smaller volume makes the particles hit the walls more often, raising the pressure. Doubling the pressure halves the volume. Boyle's law has no temperature term because temperature is held constant.

Charles's law

Heating a gas makes its particles move faster and push outward, so the gas expands to keep the pressure constant. Because the relationship is direct, doubling the Kelvin temperature doubles the volume. This is why temperature must be in kelvin: using Celsius would give a wrong ratio (and absurd results near $0\,^{\circ}\text{C}$).

Gay-Lussac's law and the combined gas law

Gay-Lussac's law holds the volume constant and relates pressure to Kelvin temperature directly: $\dfrac{P_1}{T_1} = \dfrac{P_2}{T_2}$. Heating a gas in a rigid container raises the pressure as the particles strike the walls harder and more often.

The combined gas law merges all three into one relationship for a fixed amount of gas:

If one of pressure, volume or temperature is held constant, it cancels from both sides and the combined law reduces to Boyle's, Charles's or Gay-Lussac's law. This makes the combined gas law the one formula to remember: write it out, cross out whatever the question holds constant, and solve the rest. The subscript $1$ values are the starting conditions and the subscript $2$ values are the final conditions, so a common, safe routine is to list $P_1$, $V_1$, $T_1$, $P_2$, $V_2$ and $T_2$, convert any Celsius temperatures to kelvin, identify the unknown, and rearrange for it before substituting.

Try this

Q1. A gas at $1.0$ atm and $4.0$ L is compressed to $2.0$ L at constant temperature. Find the new pressure. [2 points]

• Cue. Boyle's law: $P_2 = \dfrac{(1.0)(4.0)}{2.0} = 2.0$ atm.

Q2. Why must temperature be in kelvin for the gas laws? [1 point]

• Cue. The laws use absolute temperature; the Kelvin scale starts at absolute zero, so ratios of temperature are only meaningful in kelvin.