• 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
  • NA?=?Avogadro’s 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:

P?∝?T

• 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)

   

Step 1: Write down the ideal gas equation

Since the number of moles (n) is required, use the equation:

Step 2: Rearrange the equation for the number of moles n

Step 3: Substitute in values