The ideal gas equation: Putting it all together

If you take Boyle’s law, Charles’s law, Gay-Lussac’s law, and  Avogadro’s law and throw them into a blender, turn the blender on high for a minute, and then pull them out, you get the ideal gas equation — a way of working in volume, temperature, pressure, and amount of a gas. The ideal gas equation has the following form:

PV = nRT

The P represents pressure in atmospheres (atm), the V represents volume in liters (L), the n represents moles of gas, the T represents the temperature in Kelvin (K), and the R represents the ideal gas constant, which is 0.0821 liters atm/K-mol.

Using the value of the ideal gas constant, the pressure must be expressed in atm, and the volume must be expressed in liters. You can calculate other ideal gas constants if you really want to use torr and milliliters, for example, but why bother? It’s easier to memorize one value for R and then remember to express the pressure and volume in the appropriate units.

Naturally, you’ll always express the temperature in Kelvin when working any kind of gas law problem.  The ideal gas equation gives you an easy way to convert a gas from a mass to a volume if the gas is not at STP. For instance, what’s the volume of 50.0 grams of oxygen at 2.00 atm and 27.0°C? The first thing you have to do is convert the 50.0 grams of oxygen to moles using the molecular weight of O₂: (50.0 grams) • (1 mol/32.0 grams) = 1.562 mol

Now take the ideal gas equation and rearrange it so you can

solve for V:

PV = nRT

V = nRT/P

Add your known quantities to calculate the following answer:

V = [(1.562 mol) • (0.0821 L atm/K-mol) • (300 K)]/ 2.00 atm = 19.2 L