Gas Laws and States of Matter: Pressure, Volume, and Kelvin Temperature

Compress the same amount of gas at a fixed temperature and its pressure rises. The particles have less volume available and strike the container walls more frequently. A gas-law equation expresses that relationship, provided its assumptions fit the situation.

Gas laws relate pressure, volume, temperature, and amount of gas. The ideal gas model neglects particle volume and intermolecular attractions. It gives useful approximations when gases are sufficiently dilute and far from condensation. Gas-law temperatures use kelvin, while pressure and volume units must match the chosen gas constant or ratio.

Which quantities are held constant?

For a fixed amount of gas at constant temperature, Boyle’s law gives \(P_1V_1=P_2V_2\). At constant pressure, volume is proportional to absolute temperature. For a fixed amount with both pressure and temperature changing, use

\[ \frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}. \]

Convert Celsius to kelvin with \(T_K=T_C+273.15\). A ratio of Celsius temperatures does not represent the required absolute-temperature ratio.

Worked example: pressure after compression

A sealed gas sample occupies 2.00 L at 1.20 atm. It is compressed to 0.800 L while temperature remains constant. Assuming ideal behavior,

\[ P_2=\frac{P_1V_1}{V_2}=\frac{(1.20)(2.00)}{0.800}=3.00\,\mathrm{atm}. \]

The volume falls to 40.0% of its original value, so pressure rises by a factor of 2.50. That direction agrees with the particle model.

When do you use the ideal gas equation?

Use \(PV=nRT\) when amount in moles is part of the calculation. For liters and atmospheres, a suitable rounded constant is \(R=0.08206\,\mathrm{L\,atm\,mol^{-1}\,K^{-1}}\). For SI pressure in pascals and volume in cubic meters, use a compatible value of \(R\).

High pressure and conditions near condensation can make particle volume and attractions significant. Under those conditions, the ideal-gas prediction may need a real-gas correction.

How do phase changes differ from gas expansion?

During evaporation, particles leave a liquid’s surface. Boiling occurs throughout a liquid when its vapor pressure reaches the external pressure. The boiling temperature therefore depends on the surrounding pressure.

1. Identify the initial and final states.
2. Write which quantities stay constant.
3. Convert temperatures to kelvin and align units.
4. Solve, then check whether the direction of change makes sense.

Can you apply the idea?

1. What temperature scale must be used in gas-law ratios?

   Check your answer

   Kelvin, the absolute-temperature scale.

2. At constant temperature, what happens to pressure when a fixed gas amount doubles its volume?

   Check your answer

   Pressure halves under the ideal model.

3. Convert \(25.00\,^{\circ}\mathrm{C}\) to kelvin.

   Check your answer

   \(298.15\,\mathrm{K}\).

4. At fixed pressure and amount, absolute temperature doubles. What happens to ideal-gas volume?

   Check your answer

   It doubles.

5. When does boiling occur in relation to vapor pressure?

   Check your answer

   When the liquid’s vapor pressure reaches the external pressure.

6. Why can the ideal model become inaccurate at very high pressure?

   Check your answer

   The finite volume of particles and their interactions can no longer be neglected.

Watch the idea explained

The Ideal Gas Law: Crash Course Chemistry #12 — CrashCourse.

This selected excerpt runs from 0:50 to 1:35. Boyle law at fixed temperature and gas amount.

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