Ideal Gas Equation (DP IB Physics: HL)

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 = nN_A

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

N = 5.5 mol × (6.02 × 10²³) mol^–1

N = 3.3 × 10²⁴