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Ideal Gases (CIE AS Chemistry)

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Ideal Gas Law

Kinetic theory of gases

  • The kinetic theory of gases states that molecules in gases are constantly moving
  • The theory makes the following assumptions:
    • The gas molecules are moving very fast and randomly
    • The molecules hardly have any volume
    • The gas molecules do not attract or repel each other (no intermolecular forces)
    • No kinetic energy is lost when the gas molecules collide with each other (elastic collisions)
    • The temperature of the gas is related to the average kinetic energy of the molecules

  • Gases that follow the kinetic theory of gases are called ideal gases
  • However, in reality, gases do not fit this description exactly but may come very close and are called real gases

Ideal gases

  • The volume that an ideal gas occupies depends on:
    • Its pressure
    • Its temperature
    • See section Changing gas volume on 1.4.1 Gas Pressure

  • When a gas is heated (at constant pressure) the particles gain more kinetic energy and undergo more frequent collisions with the container wall
  • To keep the pressure constant, the molecules must get further apart and therefore the volume increases
  • The volume is therefore directly proportional to the temperature (at constant pressure)

How the volume of a gas increases upon heating 

States of Matter Volume and Temperature, downloadable AS & A Level Chemistry revision notes

The volume of a gas increases upon heating to keep a constant pressure (a); volume is directly proportional to the temperature (b)

Limitations of the ideal gas law

  • At very high pressures and low temperatures real gases do not obey the kinetic theory as under these conditions:
    • Molecules are close to each other
    • There are instantaneous dipole- induced dipole or permanent dipole- permanent dipole forces between the molecules
    • These attractive forces pull the molecules away from the container wall
    • The volume of the molecules is not negligible

  • Real gases therefore do not obey the following kinetic theory assumptions at high temperatures and pressures:
    • There is zero attraction between molecules (due to attractive forces, the pressure is lower than expected for an ideal gas)
    • The volume of the gas molecules can be ignored (volume of the gas is smaller than expected for an ideal gas)

Ideal Gas Equation

Ideal gas equation

  • The ideal gas equation shows the relationship between pressure, volume, temperature and number of moles of gas of an ideal gas:

pV = nRT

   p = pressure (pascals, Pa)

   V = volume (m3)

   n = number of moles of gas (mol)

   R = gas constant (8.31 J K-1 mol-1)

   T = temperature (kelvin, K)

  • The ideal gas equation can also be used to calculate the molar mass (Mr) of a gas

Worked example

Calculating the volume of a gas

Calculate the volume occupied by 0.781 mol of oxygen at a pressure of 220 kPa and a temperature of 21 °C.

Answer

  • Step 1: Rearrange the ideal gas equation to find the volume of gas:
    • V = fraction numerator n R T over denominator p end fraction
  • Step 2: Check that values have the correct units:
    • p = 220 kPa = 220 000 Pa
    • n = 0.781 mol
    • R = 8.31 J K-1 mol-1
    • T = 21 oC = 294 K
  • Step 2: Calculate the volume the oxygen gas occupies:
    • V = table row blank blank cell fraction numerator 0.781 space mol space cross times space 8.31 space straight J space straight K to the power of negative 1 end exponent space mol to the power of negative 1 end exponent space cross times space 294 space straight K over denominator 220 space 000 space Pa end fraction end cell end table
    • V = 0.00867 m3 
    • V = 8.67 dm3  

Worked example

Calculating the molar mass of a gas

A flask of volume 1000 cm3 contains 6.39 g of a gas. The pressure in the flask was 300 kPa and the temperature was 23 °C.

Calculate the relative molecular mass of the gas.

Answer

  • Step 1: Rearrange the ideal gas equation to find the number of moles of gas:
    • n = begin mathsize 14px style fraction numerator p V over denominator R T end fraction end style
  • Step 2: Check that values have the correct units:
    • p = 300 kPa = 300 000 Pa
    • V = 1000 cm3 = 0.001 m3
    • R = 8.31 J K-1 mol-1
    • T = 23 oC = 296 K
  • Step 3: Calculate the number of moles of gas:
    • n = fraction numerator 300 space 000 space Pa space cross times space 0.001 space straight m cubed over denominator 8.31 space straight J space straight K to the power of negative 1 end exponent space mol to the power of negative 1 end exponent space cross times space 296 space straight K end fraction
    • = 0.12 mol
  • Step 4: Calculate the molar mass using the number of moles of gas:
    • n = begin mathsize 14px style fraction numerator mass over denominator molar space mass end fraction end style
    • molar mass = fraction numerator 6.39 over denominator 0.12 space mol end fraction
    • molar mass = 53.25 g mol-1

Examiner Tip

Ideal gases have zero particle volume (the particles are really small) and no intermolecular forces of attraction or repulsion.

To calculate the temperature in Kelvin, add 273 to the Celsius temperature, eg. 100 oC is 373 Kelvin.

Remember: an ideal gas will have a volume that is directly proportional to the temperature and inversely proportional to the pressure.

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Caroline

Author: Caroline

Expertise: Physics Lead

Caroline graduated from the University of Nottingham with a degree in Chemistry and Molecular Physics. She spent several years working as an Industrial Chemist in the automotive industry before retraining to teach. Caroline has over 12 years of experience teaching GCSE and A-level chemistry and physics. She is passionate about creating high-quality resources to help students achieve their full potential.