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DP IB Chemistry: SL

Revision Notes

Home / IB / Chemistry: SL / DP / Revision Notes / 1. Stoichiometric Relationships / 1.2 Reacting Masses & Volumes / 1.2.5 Gas Law Relationships


1.2.5 Gas Law Relationships


Gas Law Relationships

  • Gases in a container exert a pressure as the gas molecules are constantly colliding with the walls of the container

States of Matter Pressure, downloadable IB Chemistry revision notes

Gas particles exert a pressure by constantly colliding with the walls of the container

Changing gas volume

  • Decreasing the volume (at constant temperature) of the container causes the molecules to be squashed together which results in more frequent collisions with the container wall
  • The pressure of the gas increases

States of Matter Volume and Pressure, downloadable IB Chemistry revision notes

Decreasing the volume of a gas causes an increased collision frequency of the gas particles with the container wall

  • The pressure is therefore inversely proportional to the volume (at constant temperature)
  • This is known as Boyle's Law
  • Mathematically, we say P ∝ 1/V or PV = a constant
  • We can show a graphical representation of Boyle's Law in three different ways:
    • A graph of pressure of gas plotted against 1/ volume gives a straight line
    • A graph of pressure against volume gives a curve
    • A graph of PV versus P gives a straight line

Graphs of Boyle’s Law, downloadable IB Chemistry revision notes

Three graphs that show Boyle’s Law

Changing gas temperature

  • When a gas is heated (at constant pressure) the particles gain more kinetic energy and undergo more frequent collisions with the container walls
  • 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 in Kelvin (at constant pressure)
  • This is known as Charles' Law
  • Mathematically, V ∝ T or V/T = a constant
  • A graph of volume against temperature in Kelvin gives a straight line

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

Increasing the temperature of a gas causes an increased collision frequency of the gas particles with the container wall (a); volume is directly proportional to the temperature in Kelvin (b)

Changing gas pressure

  • Increasing the temperature (at constant volume) of the gas causes the molecules to gain more kinetic energy
  • This means that the particles will move faster and collide with the container walls more frequently
  • The pressure of the gas increases
  • The temperature is therefore directly proportional to the pressure (at constant volume)
  • Mathematically, we say that P ∝ T or P/T = a constant 
  • A graph of temperature in Kelvin of a gas plotted against pressure gives a straight line

States of Matter Temperature and Pressure, downloadable IB Chemistry revision notes

Increasing the temperature of a gas causes an increased collision frequency of the gas particles with the container wall (a); temperature is directly proportional to the pressure (b)

Pressure, volume and temperature

  • Combining these three relationships together:
    • P/V = a constant
    • V/T = a constant
    • P/T = a constant
  • We can see how the ideal gas equation is constructed
    • PV/T = a constant
    • PV = a constant x T
  • This constant is made from two components, the number of moles, n, and the gas constant, R, resulting in the overall equation:
    • PV = nRT

Changing the conditions of a fixed amount of gas

  • For a fixed amount of gas, n and R will be constant, so if you change the conditions of a gas we can ignore n and R in the ideal gas equation
  • This leads to a very useful expression for problem solving
  • Where P1, V1 and T1 are the initial conditions of the gas and P2, V2 and T2 are the final conditions

Worked Example

At 25 oC and 100 kPa a gas occupies a volume of 20 dm3. Calculate the new temperature, in oC, of the gas if the volume is decreased to 10 dm3 at constant pressure.

Answer:

Step 1: Rearrange the formula to change the conditions of a fixed amount of gas. Pressure is constant so it is left out of the formula

Step 2: Convert the temperature to Kelvin. There is no need to convert the volume to m3  because the formula is using a ratio of the two volumes

 V1 = 20 dm3 

V2 = 10 dm3 

T1 = 25 + 273 = 298 K

Step 3: Calculate the new temperature

Worked Example

A 2.00 dm3 container of oxygen at a pressure of 80 kPa was heated from 20 oC to 70 oC The volume expanded to 2.25 dm3 . What was the final pressure of the gas?

Answer:

Step 1: Rearrange the formula to change the conditions of a fixed amount of gas

Step 2: Substitute in the values and calculate the final pressure

P1 = 80 kPa

V1 = 2.00 dm3 

V2 = 2.25 dm3 

T1 = 20 + 273 = 293 K

T2 = 70 + 273 = 343 K



  • 1. Stoichiometric Relationships
    • 1.1 Matter, Chemical Change & the Mole Concept
      • 1.1.1 Elements, Compounds & Mixtures
        • 1.1.2 Equations
          • 1.1.3 State Changes
            • 1.1.4 The Mole Concept
              • 1.1.5 Moles-Mass Problems
                • 1.1.6 Empirical Formulae
                • 1.2 Reacting Masses & Volumes
                  • 1.2.1 Reacting Masses
                    • 1.2.2 Reaction Yields
                      • 1.2.3 Avogadro's Law & Molar Gas Volume
                        • 1.2.4 The Ideal Gas Equation
                          • 1.2.5 Gas Law Relationships
                            • 1.2.6 Real Gases
                              • 1.2.7 Standard Solutions
                                • 1.2.8 Concentration Calculations
                                  • 1.2.9 Titrations
                                • 2. Atomic Structure
                                  • 2.1 Atomic & Electronic Structure
                                    • 2.1.1 The Nuclear Atom
                                      • 2.1.2 Deducing Subatomic Particles
                                        • 2.1.3 Relative Atomic Mass Calculations
                                          • 2.1.4 The Electromagnetic Spectrum
                                            • 2.1.5 Emission Spectra
                                              • 2.1.6 Energy Levels & Sublevels
                                                • 2.1.7 Sublevels & Orbitals
                                                  • 2.1.8 Writing Electron Configurations
                                                • 3. Periodicity
                                                  • 3.1 The Periodic Table & Periodic Trends
                                                    • 3.1.1 The Periodic Table
                                                      • 3.1.2 Periodic Trends: Physical - Atomic & Ionic Radius
                                                        • 3.1.3 Periodic Trends: Physical - Ionisation Energy
                                                          • 3.1.4 Periodic Trends: Physical - Electron Affinity
                                                            • 3.1.5 Periodic Trends: Physical - Electronegativity
                                                              • 3.1.6 Periodic Trends: Chemical
                                                              • 3.2 Oxides, Group 1 & Group 17
                                                                • 3.2.1 Periodic Trends: Oxides Across a Period
                                                                  • 3.2.2 Periodic Trends: Group 1 - The Alkali Metals
                                                                    • 3.2.3 Periodic Trends: Group 17 - The Halogens
                                                                  • 4. Chemical Bonding & Structure
                                                                    • 4.1 Ionic & Covalent Bonding
                                                                      • 4.1.1 Forming Ions
                                                                        • 4.1.2 Ionic Compounds
                                                                          • 4.1.3 Formulae & Names of Ionic Compounds
                                                                            • 4.1.4 Covalent Bonds
                                                                              • 4.1.5 Bond Polarity
                                                                                • 4.1.6 Lewis Structures
                                                                                • 4.2 Resonance, Shapes & Giant Structures
                                                                                  • 4.2.1 Resonance Structures
                                                                                    • 4.2.2 Shapes of Molecules
                                                                                      • 4.2.3 Predicting Molecular Shapes
                                                                                        • 4.2.4 Molecular Polarity
                                                                                          • 4.2.5 Giant Covalent Structures
                                                                                          • 4.3 Intermolecular Forces & Metallic Bonding
                                                                                            • 4.3.1 Types of Intermolecular Forces
                                                                                              • 4.3.2 Deducing Intermolecular Forces
                                                                                                • 4.3.3 Properties of Covalent Compounds
                                                                                                  • 4.3.4 Metallic Bonding
                                                                                                    • 4.3.5 Trends in Melting Points of Metals
                                                                                                      • 4.3.6 Alloys & their Properties
                                                                                                    • 5. Energetics / Thermochemistry
                                                                                                      • 5.1 Energetics
                                                                                                        • 5.1.1 Energy Changes in Reactions
                                                                                                          • 5.1.2 Standard Enthalpy Change
                                                                                                            • 5.1.3 Calorimetry
                                                                                                              • 5.1.4 Calorimetry Experiments
                                                                                                              • 5.2 Hess's Law
                                                                                                                • 5.2.1 Hess's Law
                                                                                                                  • 5.2.2 Using Hess's Law - Cycles
                                                                                                                    • 5.2.3 Using Hess's Law - Equations
                                                                                                                      • 5.2.4 Using ∆Hf° to Find Enthalpy Changes
                                                                                                                      • 5.3 Bond Enthalpy
                                                                                                                        • 5.3.1 Bond Enthalpy
                                                                                                                          • 5.3.2 Bond Enthalpy Calculations
                                                                                                                            • 5.3.3 Energy Profiles
                                                                                                                              • 5.3.4 Case Study: Ozone
                                                                                                                            • 6. Chemical Kinetics
                                                                                                                              • 6.1 Chemical Kinetics
                                                                                                                                • 6.1.1 Collision Theory
                                                                                                                                  • 6.1.2 Rate of Reaction
                                                                                                                                    • 6.1.3 Measuring Rates
                                                                                                                                      • 6.1.4 Activation Energy
                                                                                                                                        • 6.1.5 Rate Experiments
                                                                                                                                          • 6.1.6 Explaining Rates
                                                                                                                                            • 6.1.7 Maxwell-Boltzmann Curves
                                                                                                                                              • 6.1.8 Energy Profiles & Catalysis
                                                                                                                                            • 7. Equilibrium
                                                                                                                                              • 7.1 Equilibrium
                                                                                                                                                • 7.1.1 The State of Equilibrium
                                                                                                                                                  • 7.1.2 The Equilibrium Law
                                                                                                                                                    • 7.1.3 Equilibrium Constant Relationships
                                                                                                                                                      • 7.1.4 The Reaction Quotient
                                                                                                                                                        • 7.1.5 Le Chatelier's Principle
                                                                                                                                                          • 7.1.6 Catalysts & Equilibrium
                                                                                                                                                        • 8. Acids & Bases
                                                                                                                                                          • 8.1 Theories & Reactions of Acids & Bases
                                                                                                                                                            • 8.1.1 Brønsted–Lowry Acids & Bases
                                                                                                                                                              • 8.1.2 Conjugate Acid-Base Pairs
                                                                                                                                                                • 8.1.3 Characteristic Reactions of Acids
                                                                                                                                                                  • 8.1.4 Neutralization
                                                                                                                                                                  • 8.2 More About Acids
                                                                                                                                                                    • 8.2.1 Acid-base Titrations
                                                                                                                                                                      • 8.2.2 pH & [H⁺]
                                                                                                                                                                        • 8.2.3 Interpreting pH
                                                                                                                                                                          • 8.2.4 The Ionic Product of Water
                                                                                                                                                                            • 8.2.5 Acid-Base Calculations
                                                                                                                                                                              • 8.2.6 pH Meters & Universal Indicator
                                                                                                                                                                                • 8.2.7 Strong & Weak Acids & Bases
                                                                                                                                                                                  • 8.2.8 Comparing Strong & Weak Acids
                                                                                                                                                                                  • 8.3 Acid Deposition
                                                                                                                                                                                    • 8.3.1 Acid Deposition
                                                                                                                                                                                      • 8.3.2 Effects of Acid Deposition
                                                                                                                                                                                        • 8.3.3 Reducing Sulfur Oxide Emissions
                                                                                                                                                                                      • 9. Redox Processes
                                                                                                                                                                                        • 9.1 Redox Processes
                                                                                                                                                                                          • 9.1.1 Oxidation & reduction
                                                                                                                                                                                            • 9.1.2 Deducing Oxidation Numbers
                                                                                                                                                                                              • 9.1.3 Oxidizing & Reducing agents
                                                                                                                                                                                                • 9.1.4 Naming Transition Metal Compounds
                                                                                                                                                                                                  • 9.1.5 Half Equations
                                                                                                                                                                                                    • 9.1.6 The Activity Series
                                                                                                                                                                                                      • 9.1.7 Redox Titrations
                                                                                                                                                                                                        • 9.1.8 The Winkler Method
                                                                                                                                                                                                          • 9.1.9 Voltaic Cells
                                                                                                                                                                                                            • 9.1.10 Electrolytic Cells
                                                                                                                                                                                                          • 10. Organic Chemistry
                                                                                                                                                                                                            • 10.1 Fundamentals of Organic Chemistry
                                                                                                                                                                                                              • 10.1.1 Homologous Series
                                                                                                                                                                                                                • 10.1.2 Understanding Organic Molecules
                                                                                                                                                                                                                  • 10.1.3 Nomenclature
                                                                                                                                                                                                                    • 10.1.4 Organic Families - Hydrocarbons
                                                                                                                                                                                                                      • 10.1.5 Organic Families - Halogenoalkanes
                                                                                                                                                                                                                        • 10.1.6 Organic Families - Alcohols & Ethers
                                                                                                                                                                                                                          • 10.1.7 Organic Families - Carbonyls
                                                                                                                                                                                                                            • 10.1.8 Organic Families - Carboxylic Acids & Esters
                                                                                                                                                                                                                              • 10.1.9 Organic Families - Organic Nitrogen Compounds
                                                                                                                                                                                                                                • 10.1.10 3-D modelling
                                                                                                                                                                                                                                  • 10.1.11 Primary, Secondary & Tertiary atoms
                                                                                                                                                                                                                                    • 10.1.12 Benzene
                                                                                                                                                                                                                                    • 10.2 Functional Group Chemistry
                                                                                                                                                                                                                                      • 10.2.1 Alkanes - Combustion
                                                                                                                                                                                                                                        • 10.2.2 Alkanes - Halogenation
                                                                                                                                                                                                                                          • 10.2.3 Alkenes - Reactivity
                                                                                                                                                                                                                                            • 10.2.4 Alkenes - Hydrogenation
                                                                                                                                                                                                                                              • 10.2.5 Alkenes - Halogenation
                                                                                                                                                                                                                                                • 10.2.6 Alkenes - Hydrohalogenation
                                                                                                                                                                                                                                                  • 10.2.7 Alkenes - Hydration
                                                                                                                                                                                                                                                    • 10.2.8 Addition Polymers
                                                                                                                                                                                                                                                      • 10.2.9 Alcohols - Combustion
                                                                                                                                                                                                                                                        • 10.2.10 Alcohols - Oxidation
                                                                                                                                                                                                                                                          • 10.2.11 Alcohols - Esterification
                                                                                                                                                                                                                                                            • 10.2.12 Halogenoalkanes
                                                                                                                                                                                                                                                              • 10.2.13 Reactions of Benzene
                                                                                                                                                                                                                                                            • 11. Measurements & Data Processes
                                                                                                                                                                                                                                                              • 11.1 Spectroscopic Identification
                                                                                                                                                                                                                                                                • 11.1.1 Index of Hydrogen Deficiency
                                                                                                                                                                                                                                                                  • 11.1.2 Mass Spectrometry
                                                                                                                                                                                                                                                                    • 11.1.3 Nuclear Magnetic Resonance Spectroscopy
                                                                                                                                                                                                                                                                      • 11.1.4 Infrared Spectroscopy
                                                                                                                                                                                                                                                                      • 11.2 Synoptic Data Handling & Graphical Skills
                                                                                                                                                                                                                                                                        • 11.2.1 Recording Data
                                                                                                                                                                                                                                                                          • 11.2.2 Processing Errors
                                                                                                                                                                                                                                                                            • 11.2.3 Reducing the Impact of Errors
                                                                                                                                                                                                                                                                              • 11.2.4 Percentage Error
                                                                                                                                                                                                                                                                                • 11.2.5 Drawing Graphs
                                                                                                                                                                                                                                                                                  • 11.2.6 Analysing Graphs
                                                                                                                                                                                                                                                                                Stewart Hird

                                                                                                                                                                                                                                                                                Author: Stewart

                                                                                                                                                                                                                                                                                Stewart has been an enthusiastic GCSE, A Level and IB Chemistry teacher for more than 30 years in the UK as well as overseas, and has been an examiner for IB and A Level, also. As a long-standing Head of Department, Stewart brings a wealth of experience to creating Topic Questions and revision materials for Save My Exams.


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