The ideal gas law connects pressure, volume, temperature, and amount of gas in one useful equation: PV = nRT. It matters because it lets scientists and engineers predict how gases behave in containers, engines, balloons, lungs, and weather systems. The law is a model, so it works best for gases at low pressure and high temperature where particles are far apart.
It gives a simple way to turn observations of a gas into quantitative predictions.
The equation combines Boyle's law, Charles's law, Avogadro's law, and Gay-Lussac's law into one relationship. In the ideal gas model, gas particles move randomly, collide elastically, and take up negligible volume compared with the container. Temperature must be measured in kelvin because particle kinetic energy is proportional to absolute temperature.
For example, if a sealed gas is heated while its volume stays constant, particle collisions become stronger and the pressure increases.
Key Facts
- Ideal gas law: PV = nRT.
- P is pressure, V is volume, n is moles of gas, R is the gas constant, and T is absolute temperature.
- Use T in kelvin: K = °C + 273.15.
- Common gas constant: R = 8.314 J/(mol·K) when pressure is in pascals and volume is in cubic meters.
- Boyle's law at constant n and T: P1V1 = P2V2.
- Combined gas law at constant n: P1V1/T1 = P2V2/T2.
Vocabulary
- Pressure
- Pressure is the force exerted per unit area by gas particle collisions with the walls of a container.
- Volume
- Volume is the amount of space occupied by the gas and its container.
- Mole
- A mole is an amount of substance equal to 6.022 × 10^23 particles.
- Absolute temperature
- Absolute temperature is temperature measured in kelvin, where 0 K represents the lowest possible thermal energy.
- Ideal gas
- An ideal gas is a simplified model of a gas whose particles have negligible size and no intermolecular forces except during collisions.
Common Mistakes to Avoid
- Using Celsius in PV = nRT is wrong because the ideal gas law requires absolute temperature in kelvin.
- Mixing units for R is wrong because the value of R must match the pressure, volume, and temperature units used in the problem.
- Forgetting that n must stay constant in the combined gas law is wrong because adding or removing gas changes the relationship between P, V, and T.
- Assuming the ideal gas law works perfectly for every gas is wrong because real gases deviate most at high pressure and low temperature.
Practice Questions
- 1 A 2.00 mol sample of gas is in a 0.0500 m^3 container at 300 K. Using R = 8.314 J/(mol·K), what is the pressure in pascals?
- 2 A gas at 1.20 atm occupies 3.00 L at constant temperature. If the volume is compressed to 1.50 L and the amount of gas does not change, what is the new pressure?
- 3 A sealed rigid container of gas is heated from 300 K to 600 K. Explain what happens to the pressure and why, using particle motion and collisions.