The ideal gas law is the most important gas law for you to know: it combines all of the laws you learned about in this chapter thus far, under a set of standard conditions. The four conditions used to describe a gas—pressure, volume, temperature, and number of moles (quantity)—are all related, along with R, the universal gas law constant, in the following formula:
PV = nRT
where P = pressure (atm), V = volume (L), n = number of moles (mol), R = 0.08206 L · atm/mol · K, and T = temperature (K).
Now try an example using the ideal gas law equation.
Example
A 16.0 g sample of methane gas, CH4, the gas used in chemistry lab, has a volume of 5.0 L at 27ºC. Calculate the pressure.
Explanation
Looking at all the given, you have a mass, a volume, and a temperature, and you need to find the pressure of the system. As always, start by checking your units. You must first convert 16.0 g of CH
4 into moles: 16.0 g CH
4
1 mol CH
4/16.0 g CH
4 = 1 mol of methane. The volume is in the correct units, but you must convert the temperature into Kelvins: 27 + 273 = 300K. Now you’re ready to plug these numbers into the ideal gas law equation:
PV = nRT
(P) (5.0 L) = (1.0 mol) (0.0821 L
atm/mol
K) (300K), so P = 4.9 atm
Don't let the math scare you. Remember that your test will be all multiple choice. You may be asked for proper setup, or at least you will have answers to choose from, and you won't have to do these lengthy calculations without a calculator. These examples are only meant to give you practice using the gas law equations.
