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:

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. It is important to learn this value WITH the units, since the constant only works if the volume is in liters, the pressure in atmospheres, the temperature in Kelvin and the amount in moles.

It is possible to solve Ideal Gas Law problems in other units using different numerical values for R. For instance, converting into standard metric units for pressure (kPa instead of atm) gives a value of 8.314 L kPa/K mol.Using Torr (or mm Hg) instead of atm gives a value of 62.4 L Torr/K mol.

Keep in mind that all of these versions of R are 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.

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:
A 2.78 L balloon holds helium at 1.28 atm and 38 ^oC. How many moles of helium are in the balloon? 

We can recognize that this is NOT an IF problem, because there are no final conditions -- in other words, nothing is changing.

So, in this case, we know the following:

Pressure	1.28 atm
volume	2.78 L
amount	?
temperature	38oC

Assuming that we are using 0.08206 L atm/K mol, all of the units are fine except temperature. Converting to Kelvin (by adding 273.15) gives us:

Pressure	1.28 atm
volume	2.78 L
amount	?
temperature	311 K

 Starting with the ideal gas law:

We can rearrange it to solve for amount:

then substitute in our values and solve: