# 5.2.2 Ideal Gas Equation

## Ideal Gas Equation

• An ideal gas is a specific type of gas which:
• Has molecules with negligible volume
• Collisions which are elastic
• Cannot be liquified
• Has no interactions between the molecules (except during collisions)
• Obeys the (ideal) gas laws (Boyles law, Charles’ law and Pressure law)

• All of these can occur at any temperature or pressure

• The ideal gas equation for number of moles can be expressed as:

• The ideal gas equation for number of molecules can also be written in the form:

• An ideal gas is therefore defined as:

A gas which obeys the equation of state pV = nRT at all pressures, volumes and temperatures

#### Worked example

A storage cylinder of an ideal gas has a volume of 8.3 × 103 cm3. The gas is at a temperature of 15 °C and a pressure of 4.5 × 107 Pa.

Calculate the amount of gas in the cylinder, in moles.

Step 1: State the known quantities

• Pressure, P = 4.5 × 107 Pa
• Volume, V = 8.3 × 103 cm3 = 8.3 × 103 × 10−6 = 8.3 × 103 m3
• Temperature, T = 15 °C = 15 + 273 = 288 K

Step 2: Write down the ideal gas equation

pV = nRT

Step 3: Rearrange for the number of moles n

Step 4: Substitute in values and calculate number of moles of gas

#### Exam Tip

Don’t worry about remembering the values of R and k, they will both be given in the equation sheet in your exam.

### Get unlimited access

to absolutely everything:

• Unlimited Revision Notes
• Topic Questions
• Past Papers