# **The Ideal Gas Law **

The ideal gas law is a combination of the other gas laws which shows the relationship of all four properties simultaneously. The law is stated mathematically:

**PV=nRT**** **

where P is pressure, V is volume, n is amount, and T is the temperature. R is a constant that makes the mathematical relationship work.This constant is called the universal gas constant and has a value of 0.08206 L atm/K mol. This value, of course, only works if the volume is in liters, the pressure in atmospheres, the temperature in Kelvin and the amount in moles.

Converting into standard metric units (kPa instead of atm) gives a value of 8.314 L kPa/K mol.

There are, in fact, lots of values possible for R, depending on the units you wish to use in the problem, but keep in mind that they are all mathematically equal, in the same way that 1 foot is the same thing as 12 inches. The numbers appear different, but the value (including the units) is exactly the same.

Ideal gas law problems are, therefore, different from IF problems in a very important way. In an IF problem, the pressure, amount and volume can be in any unit at all (as long as the initial and final values use the same unit). In an ideal gas law problem, the units MUST match the units for the value of R being used. You should, therefore, memorize the units with the number. In other words, knowing 0.0826 is useless if you don't know that pressure must be atmospheres, volume must be liters, amount must be in moles and temperature must be Kelvin.

The ideal gas law (often pronounced piv-nert) is used to find one of the four gas properties when given the other three. Here is an example: