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S1.5Structure 1 — Models of the particulate nature of matter

Ideal gases — IB Chemistry SL Revision Notes & Topical Questions

5 min read 11 parts Lesson 5 of 6 1 quiz

📚 IB Chemistry 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

S1.5 Ideal gases — IB CHEMISTRY SL notes: State the ideal gas assumptions, apply the gas laws and pV = nRT, and explain why real gases deviate from ideal behaviour.Motion — gas particles are in constant, rapid, random motion.Volume — the volume of the particles is negligible comp…

  • Collisions
  • Temperature
  • Smaller volume
  • Extrapolation
  • Avogadro's law
  • Molar volume

Part 1 of 8Kinetic theory assumptions for an ideal gas

Motion
  • Motion gas particles are in constant, rapid, random motion.
Volume
  • Volume the volume of the particles is negligible compared with the volume of the container.
Forces
  • Forces there are no intermolecular forces between particles, which neither attract nor repel.
Collisions
  • Collisions all collisions are perfectly elastic, so no kinetic energy is lost.
Temperature
  • Temperature average kinetic energy is directly proportional to the absolute temperature.
Ideal gas
  • Ideal gas a gas that follows all these assumptions and obeys pV = nRT under all conditions.

Part 2 of 8Origin of gas pressure

Pressure
  • Pressure the force per unit area, p = F/A, arising from particles colliding with the container walls.
    What the symbols mean: p = pressure (Pa = N m−2) · F = force acting at right angles to the surface (N) · A = area (m2)
Unit
  • Unit the pascal (Pa), equal to N m−2, with 1 kPa = 1000 Pa and standard pressure 100 kPa.
Higher temperature
  • Higher temperature gives greater average kinetic energy, so collisions are more frequent and more forceful and pressure rises at constant volume.
Smaller volume
  • Smaller volume means more collisions per unit area per unit time, so pressure rises at constant temperature.

Part 3 of 8The gas laws

LawConstantRelationshipGraph
Boylen, Tp ∝ 1/V; p1V1 = p2V2p against V is a curve; p against 1/V is a straight line through the origin
Charlesn, pV ∝ T; V1/T1 = V2/T2V against T (K) is a straight line through the origin
Gay-Lussacn, Vp ∝ T; p1/T1 = p2/T2p against T (K) is a straight line through the origin
Combinednp1V1/T1 = p2V2/T2—
Temperature
  • Temperature must always be in kelvin.
Extrapolation
  • Extrapolation graphs of V or p against °C extrapolate to −273 °C.

Part 4 of 8Molar gas volume

Avogadro's law
  • Avogadro's law equal volumes of gases at the same T and p contain equal numbers of moles.
Molar volume
  • 22.7 dm3 mol−1 at STP (273 K, 100 kPa), so n = V/Vm.
Reacting gases
  • Reacting gases volume ratios equal mole ratios in the balanced equation.
Standard conditions
  • STP is 273.15 K (0 °C) and 100 kPa.

Part 5 of 8The ideal gas equation

Equation
Equation pV = nRT.
What the symbols mean: p = pressure (Pa) · V = volume (m3) · n = amount of gas (mol) · R = 8.31 J mol−1 K−1 · T = temperature (K = °C + 273)
p
p pressure in Pa.
  • V — volume in m3.
  • n — amount in mol.
  • R — gas constant, 8.31 J K−1 mol−1.
  • T — temperature in K.
Origin
  • Origin combining pV = constant, V/T = constant and p/T = constant gives pV/T = constant, which equals nR.
Unit conversions
  • Unit conversions kPa × 1000 gives Pa, dm3 ÷ 1000 gives m3, cm3 ÷ 106 gives m3, and K = °C + 273.
Data booklet
  • Data booklet the equation and R are given in the IB Data Booklet.

Part 6 of 8Using the ideal gas equation

1
Write down the known quantities and identify the unknown.
2
Convert pressure to Pa, volume to m3 and temperature to K.
3
Rearrange pV = nRT for the unknown.
4
Substitute R = 8.31 J K−1 mol−1 and calculate.
5
State the answer with the correct unit and significant figures.
Molar mass
  • Molar mass using n = m/M gives M = mRT/(pV), with m in g, p in Pa and V in m3.
Density form
  • M = ρRT/p, where ρ = m/V.

Part 7 of 8Real gases and deviation from ideal behaviour

Cause 1
  • Cause 1 particles have a finite volume, so at high pressure the free space is less than the container volume.
Cause 2
  • Cause 2 particles attract each other, so at low temperature collisions with the walls are softer and the pressure is lower than predicted.
Compression factor
  • Compression factor pV/(nRT) equals 1 for an ideal gas, and a real gas deviates from 1.
Very high pressure
  • Very high pressure pV/nRT rises above 1 because particle volume dominates.
Most ideal
  • Most ideal high temperature and low pressure, and small non-polar particles with weak London dispersion forces such as He and H2.
Greater deviation
  • Greater deviation gases with strong intermolecular forces, such as polar or hydrogen-bonding NH3.

Part 8 of 8More from the specification

More from the specification
Kinetic molecular theory of gases
  • Postulates that ideal gas particles have negligible volume and zero intermolecular attraction, undergoing continuous random elastic collisions.
Temperature and collision pressure
  • Increasing temperature raises average particle kinetic energy,
    • causing increased collision frequency and higher momentum transfer with container walls.
Combined gas equation applications
  • Rearranging (P1 V1)/T1 = (P2 V2)/T2 to calculate changing properties of a fixed amount of gas.
Molar volume of ideal gas
  • At standard temperature and pressure, one mole of any ideal gas occupies 22.7 dm3.
    • (STP: 273.15 K, 100 kPa)
Formula
  • Symbols and numbers showing the atoms in a compound.
Theory
  • A tested hypothesis that is widely accepted.
Kinetic theory
  • The model that matter consists of particles in constant motion.

Key terms

TermMeaning
Ideal gasA theoretical gas with negligible particle volume, no intermolecular forces and elastic collisions.
PressureThe force per unit area, produced in gases by particle collisions with the walls.
Molar volumeThe volume of one mole of gas, 22.7 dm3 mol−1 at STP.
Boyle's lawAt constant temperature, pressure is inversely proportional to volume.
Charles's lawAt constant pressure, volume is proportional to absolute temperature.
Real gasA gas whose particles have volume and attract each other, so it deviates from ideal behaviour.

Avoid these mistakes

1
Using °C or cm3 in pV = nRT — temperature must be in K and volume in m3.
2
Saying real gases are ideal at low temperature and high pressure — they are most ideal at high temperature and low pressure.
3
Treating pressure as caused by particles attracting the walls — it comes from collisions with the walls.
4
Forgetting to use kelvin in the gas laws — ratios of Celsius temperatures give wrong answers.

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