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

Ideal gases — IB Chemistry HL Revision Notes & Topical Questions

5 min read 11 parts Lesson 5 of 6 1 quiz

📚 IB Chemistry HL 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 HL notes: State the kinetic theory assumptions, apply the gas laws and PV = nRT, find molar mass and explain why real gases deviate from ideal behaviour.Constant motion — gas molecules are in constant, rapid, random motion.Negligible volume — the v…

  • Elastic collisions
  • Temperature
  • Elastic versus inelastic
  • Closest to ideal
  • Factors affecting volume
  • Smaller volume

Part 1 of 9Kinetic theory of gases

Constant motion
  • Constant motion gas molecules are in constant, rapid, random motion.
Negligible volume
  • Negligible volume the volume of individual molecules is negligible compared with the volume of the gas.
No forces
  • No forces there are no intermolecular forces, so particles neither attract nor repel one another.
Elastic collisions
  • Elastic collisions no kinetic energy is lost in collisions.
Temperature
  • Temperature it is directly proportional to the average kinetic energy of the particles.
Elastic versus inelastic
  • Elastic versus inelastic in an elastic collision particles bounce apart and kinetic energy is conserved,
  • whereas in an inelastic collision kinetic energy is lost and particles usually stick together.

Part 2 of 9Ideal and real gases

Ideal gas
  • Ideal gas a gas that follows all the assumptions of the kinetic theory.
Real gases
  • Real gases they do not follow the model perfectly.
Closest to ideal
  • Closest to ideal real gases behave most like ideal gases at low pressure and high temperature.
Factors affecting volume
  • Factors affecting volume the volume a gas occupies depends on pressure and temperature.

Part 3 of 9Pressure and volume: Boyle's law

Pressure
  • Pressure gas particles exert pressure by colliding with the walls of the container.
Smaller volume
  • Smaller volume at constant temperature, squashing the particles together makes collisions with the wall more frequent, so pressure rises.
Boyle's law
  • Boyle's law pressure is inversely proportional to volume at constant temperature, so PV is constant.
Graphs
  • P against 1/V is a straight line, P against V is a curve and PV against P is a straight line.

Part 4 of 9Temperature and volume or pressure

Charles' law
  • Charles' law at constant pressure, volume is directly proportional to temperature in kelvin, so V/T is constant.
  • Heating gives particles more kinetic energy and more frequent collisions.
  • To keep pressure constant, the gas expands.
  • A graph of V against T in kelvin is a straight line.
Pressure law
  • Pressure law at constant volume, pressure is directly proportional to temperature in kelvin, so P/T is constant.
  • Particles move faster and collide with the walls more often, so pressure rises.
Kelvin required
  • Kelvin required temperature must be in kelvin in all gas laws.

Part 5 of 9Combining the gas laws

Combining the gas laws
Combined relationship
  • PV = a constant, V/T = a constant and P/T = a constant combine to give PV/T = a constant.
Constant of proportionality
  • Constant of proportionality it depends on the number of moles n and the gas constant R, giving PV = nRT.
Fixed amount of gas
  • P1V1/T1 = P2V2/T2, with subscript 1 for initial and 2 for final conditions.
Ratios
  • Ratios the pressures or volumes can stay in any units because only their ratio is used, but temperatures must be in kelvin.
Constant quantity
  • Constant quantity a quantity that stays constant is left out of the equation.

Part 6 of 9The ideal gas equation

1Equation
  • 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)
2P
P pressure in pascals (Pa).
3V
V volume in m3.
4n
n amount in moles.
5R
R gas constant, 8.31 J K−1 mol−1.
6T
T temperature in kelvin (°C + 273).
7Data booklet
  • Data booklet the equation and R are given in the IB Data Booklet.
8Molar mass
  • Molar mass substituting n = m / M gives M = mRT / PV.

Part 7 of 9Unit conversions for gas calculations

1Pressure
  • 1 kPa = 1000 Pa.
2Volume
  • 1 m3 = 1000 dm3 = 106 cm3.
3To m3 from cm3
  • To m3 from cm3 divide by 106.
4To m3 from dm3
  • To m3 from dm3 divide by 1000.
5Temperature
  • Temperature add 273 to the Celsius value to get kelvin.
6Check first
  • Check first the equation requires volume in m3, so check units before substituting.

Part 8 of 9Real gases

Ideal assumptions
  • Ideal assumptions particles have negligible volume and there are no intermolecular forces.
Deviation
  • Deviation real gases deviate at low temperature and high pressure;
    • the higher the pressure and the lower the temperature, the greater the deviation.
High pressure
  • High pressure particles are close together, so their own volume becomes significant.
  • This reduces the space available for movement.
Low temperature
  • Low temperature attractions between molecules become significant.
  • This reduces the frequency and force of wall collisions, giving a lower pressure than predicted.

Part 9 of 9More from the specification

More from the specification
Ideal gas equation (PV
Ideal gas equation (PV nRT)
  • Relates pressure, volume, temperature, and amount of gas;
    • requires converting variables to correct SI units (P in Pa, V in m3, T in K).
Temperature conversion
  • Temperature in Celsius must be converted to Kelvin by adding 273.15 before applying gas law formulas.
Kinetic molecular theory
  • Increasing temperature increases average kinetic energy and velocity of gas particles, causing increased collision frequency and higher wall pressure.
Combined gas equation manipulation
  • Rearranging (P1 V1)/T1 = (P2 V2)/T2 to calculate changing pressure, volume, or temperature in a closed gas system.
Formula
  • Symbols and numbers showing the atoms in a compound.

Key terms

TermMeaning
Ideal gasA gas that follows all the assumptions of the kinetic theory.
Boyle's lawAt constant temperature, PV is constant.
Charles' lawAt constant pressure, V/T is constant.
Gas constantR = 8.31 J K−1 mol−1.
Elastic collisionA collision in which kinetic energy is conserved.
Real gasA gas that deviates from ideal behaviour, especially at high pressure and low temperature.

Avoid these mistakes

1
Using volume in dm3 or cm3 with R = 8.31 — convert to m3 first.
2
Using temperature in °C in gas law calculations — use kelvin.
3
Saying real gases are ideal at high pressure and low temperature — they are most ideal at low pressure and high temperature.
4
Forgetting that pressure must be in pascals when using PV = nRT.

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