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Theme B — The Particulate Nature of Matter

B.3 Gas Laws — IB Physics SL Revision Notes & Topical Questions

5 min read 10 parts Lesson 24 of 44 1 quiz

📚 IB Physics SL Hub / Topical Revision
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Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
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Lesson summary

B.3 Gas Laws — IB SL Notes — IB PHYSICS SL notes: Describe pressure, the mole and the ideal gas model, apply the gas laws and the equation of state, and link gas pressure and internal energy to molecular motion.Pressure — P = F/A, with unit the pascal (Pa).What the symbols mean: …

  • Boyle's law
  • Charles's law
  • Pressure (Gay-Lussac) law
  • Macroscopic form
  • Molecular form
  • Many identical molecules

Part 1 of 8Pressure and the mole

Pressure
  • P = F/A, with unit the pascal (Pa).
    What the symbols mean: p = pressure (Pa = N m−2) · F = force acting at right angles to the surface (N) · A = area (m2)
Mole
  • Mole one mole contains NA = 6.02 × 1023 particles, so n = N/NA = mass / molar mass.

Part 2 of 8Empirical gas laws

Empirical gas laws
Boyle's law
  • PV = constant at constant temperature.
Charles's law
  • V/T = constant at constant pressure.
Pressure (Gay-Lussac) law
  • P/T = constant at constant volume.
Combined
  • PV/T = constant for a fixed mass of gas.
Kelvin
  • T must be in kelvin.

Part 3 of 8Equation of state

Macroscopic form
  • PV = nRT with R = 8.31 J K−1 mol−1.
Molecular form
  • PV = NkBT with kB = R/NA = 1.38 × 10−23 J K−1.

Part 4 of 8Kinetic model assumptions

Many identical molecules
  • Many identical molecules they are in random motion.
Negligible volume
  • Negligible volume the molecular volume is negligible compared with the container.
No intermolecular forces
  • No intermolecular forces except during collisions.
Elastic collisions
  • Elastic collisions collisions are elastic and of negligible duration.

Part 5 of 8Pressure and energy

Pressure from collisions
  • Pressure from collisions a molecule rebounding from a wall changes momentum, the wall exerts a force on it and by the third law it exerts a force on the wall.
  • Summing over all molecules gives P = ⅓ρ⟨v2⟩, with ⟨v2⟩ the mean square speed.
Mean kinetic energy
  • Ēk = (3/2)kBT per molecule.
Internal energy
  • Internal energy an ideal gas has no intermolecular potential energy, so U = (3/2)NkBT = (3/2)nRT for a monatomic gas, depending only on temperature.

Part 6 of 8Ideal and real gases

FeatureIdeal gasReal gas
Intermolecular forcesNonePresent
Molecular volumeNegligibleFinite
Obeys PV = nRTAlwaysApproximately, at low P and high T
Can be liquefiedNoYes
  • Deviations
    • they are largest at high pressure and low temperature, where the gas may liquefy.

Part 7 of 8Solving gas problems

1
Convert temperatures to kelvin and volumes to m3.
2
Decide what is constant: mass, temperature, pressure or volume.
3
Use P1V1/T1 = P2V2/T2 for a fixed mass, or PV = nRT for a single state.
4
Use N = nNA when the number of molecules is required.

Part 8 of 8More from the specification

More from the specification
Kinetic collision frequency of gas atoms
  • Kinetic collision frequency of gas atoms thermal motion of gas atoms colliding against container walls provides a microscopic means to understand pressure.
Gas laws
  • Gas laws for a fixed amount of gas, pV is constant at constant temperature (Boyle), p/T at constant volume and V/T at constant temperature in kelvin
Ideal gas equation
  • Ideal gas equation pV = nRT, where n is the amount of substance in moles and R is the molar gas constant 8.31 J per mol per K
Mole
  • Mole the amount of substance containing 6.02 x 1023 particles, N = nN_A
Kinetic theory
  • Kinetic theory pressure comes from molecular collisions, and average kinetic energy equals 3/2 kT, so it is proportional to temperature
Initial and final states
  • Initial and final states use p1V1/T1 = p2V2/T2 to compare states when the amount of gas is equal
Helium
  • Product of the fusion of hydrogen in stars.
Boltzmann constant
  • K = R/NA, the gas constant per molecule
Avogadro constant
  • The number of particles per mole, 6.02 × 10²³ mol⁻¹
Average speed
  • Total distance divided by total time.
Thermodynamic temperature
  • The absolute temperature in kelvin.
Theory
  • A well-tested, wide-ranging explanation supported by evidence.
Proportional
  • Changing by the same factor as another quantity.

Key terms

TermMeaning
PressureForce per unit area acting normally on a surface
MoleThe amount of substance containing 6.02 × 1023 elementary entities
Ideal gasA gas that obeys PV = nRT at all pressures, volumes and temperatures
Boltzmann constantkB = R/NA; relates temperature to energy per molecule
Mean square speedThe average of the squares of the molecular speeds
Equation of stateThe relation PV = nRT linking the macroscopic variables of an ideal gas

Avoid these mistakes

1
Using °C in gas equations — always use kelvin.
2
Thinking an ideal gas can be liquefied — real gases can, ideal gases cannot.
3
Using the mean speed instead of the mean square speed in P = ⅓ρ⟨v2⟩ — use the mean of the squares.
4
Applying (3/2)kBT to a whole gas without multiplying by N — it is per molecule.
5
Using volume in cm3 with SI pressure — convert to m3.

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