**
Ideal Gas Law
**

The combined gas law shows that the pressure of a gas is inversely proportional to volume and directly proportional to temperature. Avogadro’s law shows that volume or pressure is directly proportional to the number of moles of gas. Putting these together leaves us with the following equation:

As with the other gas laws, we can also say that is equal to a constant. The constant can be evaluated provided that the gas being described is considered to be ideal.

The
**
ideal gas law
**
is a single equation which relates the pressure, volume, temperature, and number of moles of an ideal gas. If we substitute in the variable
for the constant, the equation becomes:

The ideal gas law is conventionally rearranged to look this way, with the multiplication signs omitted:

The variable
in the equation is called the
**
ideal gas constant
**
.

#### Sample Problem: Ideal Gas Law

What volume is occupied by 3.760 g of oxygen gas at a pressure of 88.4 kPa and a temperature of 19°C? Assume the oxygen is ideal.

*
Step 1: List the known quantities and plan the problem.
*

Known

Unknown

In order to use the ideal gas law, the number of moles of O
_{
2
}
must be found from the given mass and the molar mass. Then, use
to solve for the volume of oxygen.

*
Step 2: Solve
*
.

Rearrange the ideal gas law and solve for .

*
Step 3: Think about your result
*

The number of moles of oxygen is far less than one mole, so the volume should be fairly small compared to molar volume (22.4 L/mol) since the pressure and temperature are reasonably close to standard. The result has three significant figures because of the values for and . Since a joule (J) = kPa • L, the units cancel correctly, leaving a volume in liters.