IB Physics SL

Revision Notes

3.2.2 Ideal Gas Equation

Ideal Gas Equation

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 of an Ideal Gase

  • 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)

Worked Example

A gas has a temperature of –55°C and a pressure of 0.5 MPa. It occupies a volume of 0.02 m3.

Calculate the number of gas particles.

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

Exam Tip

When using the equation of state of ideal gases, always remember to convert temperatures from degrees Celsius (°C) to kelvin (K).

Note that the number of moles n is not the same as the number of particles N:

  • When a question asks to calculate the number of particles in a sample of gas, you should first use the equation of state to determine the number of moles n of the gas, and then calculate the number of particles using N = nNA
  • If a question gives the number of particles in a sample of gas instead of the number of moles, you should first use n = N/NA to calculate the number of moles of the gas, and then use the equation of state to perform any further calculation (e.g. volume, pressure, etc.)
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