The ideal gas law and molar volume: use the ideal gas law to relate pressure, volume, temperature and moles, and use the molar volume of a gas at STP.

What this topic is asking

Standard CH.4 completes the gas section with the ideal gas law and the molar volume. Virginia expects you to use $PV = nRT$ to relate pressure, volume, temperature and the number of moles of a gas, and to use the fact that one mole of any gas occupies $22.4$ L at STP. The ideal gas law is the tool to reach for whenever the amount of gas (in moles) is part of the problem.

The ideal gas law

The combined gas law ($\dfrac{P_1 V_1}{T_1} = \dfrac{P_2 V_2}{T_2}$) compares the same gas under two sets of conditions and assumes the amount is fixed. The ideal gas law describes a single state and explicitly includes moles, so it is the right choice when a problem gives or asks for a number of moles (or a mass you can convert to moles).

The gas constant and units

Because $R$ carries units, the ideal gas law only gives the right answer when the data match those units. Convert Celsius to kelvin, milliliters to liters, and other pressure units to atmospheres as needed before solving. A pressure given in kilopascals or millimeters of mercury, or a volume in milliliters, will give a wildly wrong answer if substituted directly, so always reconcile the units with $R$ first. If a problem instead gives a mass of gas rather than a number of moles, convert the mass to moles with the molar mass before using the equation, since $n$ in $PV = nRT$ is always in moles.

Molar volume at STP

At standard temperature and pressure (STP), $0\,^{\circ}\text{C}$ ($273$ K) and $1$ atm, one mole of any ideal gas occupies $22.4$ L. This molar volume is the same for every gas, because kinetic molecular theory treats the particle volume and the forces between particles as negligible, so only the number of particles sets the volume. You can confirm it from the ideal gas law: $V = \dfrac{nRT}{P} = \dfrac{(1)(0.0821)(273)}{1} = 22.4$ L. The $22.4$ L value lets you convert quickly between moles of a gas and its volume at STP without the full equation.

Try this

Q1. What volume does $0.50$ mol of nitrogen gas occupy at STP? [1 point]

• Cue. $0.50 \times 22.4 = 11.2$ L.

Q2. Which equation would you use to find the pressure of a $3.0$ mol gas sample at a known volume and temperature? [1 point]

• Cue. The ideal gas law, $PV = nRT$, because the number of moles is involved.