Avogadro's Law

• Avogadro's Law states:

For a gas at constant temperature and pressure, the number of?moles?n?is directly proportional to the volume?V?of the gas

• This can be expressed in equation form as:

• This means that two different gases of equal temperatures, pressures and volumes have the same number of particles?N
  • Note that the number of particles?N?is directly proportional to the number of?moles?n

Equation of State for an Ideal Gas

• Boyle's Law,?Charles's Law?and?Gay-Lussac's?law can be combined with Avogadro's law to give a single constant, known as the?ideal gas constant,?R
• Combining the four equations leads to the?equation of state of an ideal gas

• Where:
  • p?= pressure in pascals (Pa)
  • V?= volume in metres cubed (m³)
  • T?= temperature in kelvin (K)
  • n?= number of moles in the gas (mol)
  • R?= 8.31 J K^–1?mol^–1?(ideal gas constant)

Step 1: Write down the known quantities

• • Temperature,?T?= –55°C = 218 K
  • Pressure,?p?= 0.5 MPa = 0.5 × 10⁶?Pa
  • Volume,?V?= 0.02 m³

Note the conversions:

• • The pressure?p?must be converted from megapascals (MPa) into pascals (Pa)
  • The temperature must be converted from degrees Celsius (°C) into kelvin (K)

Step 2: Write down the equation of state of ideal gases

Step 3: Rearrange the above equation to calculate the number of moles?n

Step 4: Substitute numbers into the equation

• • From the data booklet,?R?= 8.31 J K^–1?mol^–1

n?= 5.5 mol

Step 5: Calculate the number?of particles?N

• • Write down the relationship between number of particles and number of moles

N?=?nNA

• • From the data booklet,?NA?= 6.02 × 1023?mol^–1?(Avogadro constant)

N?= 5.5 mol × (6.02 × 10²³) mol^–1

N?= 3.3 × 10²⁴