STATES OF MATTER - properties of gases and liquids (fluids) and solids and the origin of the Kelvin temperature scale - converting temperatures between Kelvin (K) and Celsius (^oC)

17. IDEAL GAS MODEL - IDEAL GAS BEHAVIOUR

 Also helpful for UK advanced level chemistry students aged ~16-18, IB chemistry courses and US grades 11-12 K12 AP honors courses

GCSE (~US grades 8-10) level multiple choice QUIZ on the states of matter: gases, liquids & solids

17. Ideal gas behaviour and the gas laws and explaining the origin of the Kelvin scale of temperature and comparing it with the Celsius scale of temperature

Introduction – the kinetic particle model of an ideal gas

• The (advanced) kinetic theory of gases is founded on the following six fundamental postulates:

  1. Gases are composed of minute discrete particles (usually molecules) and considered to have zero volume (which isn't true).

  2. There are no attractive forces between the gas particles (which isn't true, however weak the intermolecular forces are in gases).

  3. The particles are in continuous chaotic motion moving in straight lines between very frequent collisions with each other and the sides of the container (approximately 10⁹/s).

  4. The bombardment of the container walls by the particles causes the phenomenon we call pressure (i.e. force of impacts/unit area).

  5. The greater the force of collision and the more frequent the collisions the greater the gas pressure exerted by the gas on the container surface.

  6. The collisions are perfectly elastic i.e. no energy loss on collision due to friction.

  7. At relatively low pressures the average distance between particles is large compared to the diameter of the particles and therefore the inter–molecular forces between the particles is negligible (only ~true at relatively low pressures).

  8. The average kinetic energy of the particles is directly proportional to their absolute temperature on the Kelvin scale (K) i.e. average KE(J) T(K)

     • This means if you heat up a gas the average thermal kinetic energy of the particles increases, therefore the average speed increases too.

     • The Kelvin scale of temperature is explained below.

  9. The increase in the average particle kinetic energy with increase in temperature will cause the pressure to increase in fixed volume because the particle-surface impacts will be more forceful and more frequent or cause an increase the volume at constant pressure.

• When a gas behaves according to this model, the gas laws described in sections 18 to 21 are obeyed.

• However in real gases things are not so simple, so see ...

• non–ideal behaviour is discussed in section 24 (for advanced level students only).

Key points about Ideal Gas Model & Behaviour

The Ideal Gas Model

• Definition: A simplified model describing how gases behave under certain conditions.
• Assumptions:
  • Gas particles are in constant random motion.
  • Collisions between particles and container walls are perfectly elastic (no energy lost).
  • Particles have negligible volume compared to the container.
  • No intermolecular forces act between particles.
• Ideal gases obey the P-V-T laws relating gas pressure, volume and temperature

• See Parts 18-20 for calculations using ....

• 18. Particle model and gas pressure-volume calculations using Boyle's Law P₁V₁ = P₂V₂

• 19. Particle model relate to gas pressure-volume-temperature calculations using Charles's & Gay-Lussac Law V₁/V₂ = T₁/T₂  and  P₁T₁ =P₂T₂

• 20. Combined gas law equation - more complicated calculations involving P₁V₁/T₁ = P₂V₂/T₂

Ideal Gas Behaviour

• When gases behave ideally:
  • At low pressure (particles far apart, negligible forces).
  • At high temperature (kinetic energy overcomes attractions).
• When gases deviate:
  • At high pressure (particle volume matters).
  • At low temperature (intermolecular forces cause condensation).

Real-life example:
Carbon dioxide deviates from ideal behaviour near its liquefaction point because intermolecular forces become significant.

Origin of the Kelvin Scale

• Proposed by Lord Kelvin (William Thomson) in 1848.
• Based on absolute zero: the theoretical temperature where particles have minimum kinetic energy.
• Conversion:
  • ( T(K) = T(°C) + 273 )
  • Example: 25 °C = 298 K

Student Exam Tips

• Always convert °C to K before using gas equations.
• Remember room conditions: 25 °C (298 K), 100 kPa, molar volume ≈ 24 dm³.
• Show units clearly in calculations (Pa, m³, K).
• Use scientific notation for large/small numbers.
• In multiple-choice questions, check if the answer requires Kelvin not Celsius.

Typical Misconceptions

•  Thinking particles stop moving at absolute zero — they have minimum kinetic energy, not none.
•  Forgetting to convert °C to K in calculations.
•  Assuming gases always behave ideally — real gases deviate under certain conditions.
•  Mixing up molar gas volume (24 dm³ at RTP) with molar mass.
•  Believing pressure is caused by particle collisions only with each other — it’s collisions with container walls.

Quick Recap

• Ideal gas model = simplified assumptions about gas particles.
• Ideal gas behaviour = P-V-T equations are accurate at high T, low P; deviations at low T, high P.
• Kelvin scale = absolute temperature, starting at absolute zero.
• Exam boards require knowledge of molar gas volume, gas laws, and particle theory.
• Exam success depends on careful unit handling, avoiding misconceptions, and applying theory to calculations.

The Kelvin Scale of Temperature

In the past lots of measurements have been made to investigate:

(i) how the pressure and volume of a given mass of vary at constant temperature (left graph above)

(ii) how the pressure and volume gas of a fixed mass of gas varies with temperature (right graph above).

This resulted in the formulation of the laws of gases described in section 17. to 19. along with how to use them in calculations and problem solving.

18. Gas pressure-volume calculations using Boyle's Law

19. Gas pressure-volume-temperature calculations using Charles's and Gay-Lussac Law

20. The combined gas law equation - more complicated calculations involving P-V-T

However, before this, if you look at these two graphs of gas behaviour when changing pressure or volume with temperature, one thing becomes clear, when the graph lines are extrapolated back to the x axis they give a value of –273^oC. This gave rise to the idea that there was a minimum possible temperature of –273 ^oC and further experimentation has confirmed this time and time again. At –273^oC all substances are solid and in terms of the kinetic particle theory of matter, at –273 ^oC the particles have virtually no motion i.e. ~no vibration of the atoms in the solid.

Therefore as well as the established Celsius scale (centigrade scale), a new temperature scale was proposed in which the lowest value was 0 (known as absolute zero) rather than –273. This is called the Kelvin scale of temperature or the absolute temperature scale, denoted by the unit K.

Incidentally you don't say degrees Kelvin like you say degrees Celsius, you just say Kelvin.

The Kelvin temperature scale was also designed so that a 1 K temperature change or interval, exactly equals 1^oC Celsius change or interval. Therefore you can easily convert between the two temperature scale by a simple calculation

K = ^oC + 273   and  ^oC = K – 273 

and it is the temperature in K that you must use in gas law calculations (see calculations in Parts 18, 19 and 20.

Some examples are worked out below and a practice in reading a Celsius thermometer, which is what you use in the school or college laboratory!

–7oC –7 + 273 = 267 K

36oC 36 + 273 = 309 K

77oC 77 + 273 = 350 K

101.5oC 101.5 + 273.0 = 374.5 K

132oC 132 + 273 = 405 K

206oC 206 + 273 = 479 K

It seems a bit weird to say you body has a normal temperature of 310 K, which is why it is always important to state the units too!

Key points about Ideal Gas Model & Behaviour

The Ideal Gas Model

• Definition: A simplified model describing how gases behave under certain conditions.
• Assumptions:
  • Gas particles are in constant random motion.
  • Collisions between particles and container walls are perfectly elastic (no energy lost).
  • Particles have negligible volume compared to the container.
  • No intermolecular forces act between particles.
• Ideal gases obey the P-V-T laws relating gas pressure, volume and temperature

• See Parts 18-20 for calculations using ....

• 18. Particle model and gas pressure-volume calculations using Boyle's Law P₁V₁ = P₂V₂

• 19. Particle model relate to gas pressure-volume-temperature calculations using Charles's & Gay-Lussac Law V₁/V₂ = T₁/T₂  and  P₁T₁ =P₂T₂

• 20. Combined gas law equation - more complicated calculations involving P₁V₁/T₁ = P₂V₂/T₂

Ideal Gas Behaviour

• When gases behave ideally:
  • At low pressure (particles far apart, negligible forces).
  • At high temperature (kinetic energy overcomes attractions).
• When gases deviate:
  • At high pressure (particle volume matters).
  • At low temperature (intermolecular forces cause condensation).

Real-life example:
Carbon dioxide deviates from ideal behaviour near its liquefaction point because intermolecular forces become significant.

Origin of the Kelvin Scale

• Proposed by Lord Kelvin (William Thomson) in 1848.
• Based on absolute zero: the theoretical temperature where particles have minimum kinetic energy.
• Conversion:
  • ( T(K) = T(°C) + 273 )
  • Example: 25 °C = 298 K

Student Exam Tips

• Always convert °C to K before using gas equations.
• Remember room conditions: 25 °C (298 K), 100 kPa, molar volume ≈ 24 dm³.
• Show units clearly in calculations (Pa, m³, K).
• Use scientific notation for large/small numbers.
• In multiple-choice questions, check if the answer requires Kelvin not Celsius.

Typical Misconceptions

•  Thinking particles stop moving at absolute zero — they have minimum kinetic energy, not none.
•  Forgetting to convert °C to K in calculations.
•  Assuming gases always behave ideally — real gases deviate under certain conditions.
•  Mixing up molar gas volume (24 dm³ at RTP) with molar mass.
•  Believing pressure is caused by particle collisions only with each other — it’s collisions with container walls.

Quick Recap

• Ideal gas model = simplified assumptions about gas particles.
• Ideal gas behaviour = P-V-T equations are accurate at high T, low P; deviations at low T, high P.
• Kelvin scale = absolute temperature, starting at absolute zero.
• Exam boards require knowledge of molar gas volume, gas laws, and particle theory.
• Exam success depends on careful unit handling, avoiding misconceptions, and applying theory to calculations.

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