# Ideal Gas Equation(Edexcel A Level Physics)

Expertise

Physics

## Ideal Gas Equation

• When calculating for gases, assume that the gas is an ideal gas
• The three gas laws (explained below) can be combined to create one equation in terms of pressure, volume, temperature and amount of gas.

#### The Boltzmann Constant, k

• The Boltzmann constant k is used in the ideal gas equation and is defined as:

• Where:
• R = molar gas constant

• Boltzmann’s constant therefore has a value of

• The Boltzmann constant relates the properties of microscopic particles (e.g. kinetic energy of gas molecules) to their macroscopic properties (e.g. temperature)
• This is why the units are J K-1

• Its value is very small because the increase in kinetic energy of a molecule is very small for every incremental increase in temperature

#### The Gas Laws

• The ideal gas laws are the experimental relationships between pressure (P), volume (V) and temperature (T) of an ideal gas
• The mass and the number of molecules of the gas is assumed to be constant for each of these quantities

#### Boyle’s Law

• If the temperature T of an ideal gas is constant, then Boyle’s Law is given by:

• This means the pressure is inversely proportional to the volume of a gas

Pressure increases when a gas is compressed

• The relationship between the pressure and volume for a fixed mass of gas at constant temperature can also be written as:

P1V1 = P2V2

• Where:
• P1 = initial pressure (Pa)
• P2 = final pressure (Pa)
• V1 = initial volume (m3)
• V2 = final volume (m3)

#### Charles's Law

• If the pressure P of an ideal gas is constant, then Charles’s law is given by:

V ∝ T

• This means the volume is proportional to the temperature of a gas
• The relationship between the volume and thermodynamic temperature for a fixed mass of gas at constant pressure can also be written as:

• Where:
• V1 = initial volume (m3)
• V2 = final volume (m3)
• T1 = initial temperature (K)
• T2 = final temperature (K)

#### Pressure Law

• If the volume V of an ideal gas is constant, the Pressure law is given by:

PT

• This means the pressure is proportional to the temperature
• The relationship between the pressure and thermodynamic temperature for a fixed mass of gas at constant volume can also be written as:

• Where:
• P1 = initial pressure (Pa)
• P2 = final pressure (Pa)
• T1 = initial temperature (K)
• T2 = final temperature (K)

#### Worked example

A storage cylinder of an ideal gas has a volume of 8.3 × 103 cm3. The gas is at a temperature of 15oC and a pressure of 4.5 × 107 Pa. Calculate the number of molecules of gas in the cylinder.

Step 1: Write down the ideal gas equation

Step 2: Rearrange the equation for the number of molecules, N

Step 3: Substitute in values

#### Exam Tip

After you solve a problem using any of the gas laws (or all of them combined), always check whether your final result makes physical sense - e.g. if you are asked to calculate the final pressure of a fixed mass of gas being heated at constant volume, your result must be greater than the initial pressure given in the problem (since Gay- Lussac's law states that pressure and absolute temperature are directly proportional at constant volume).

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