Ideal gases (A-level only) — AQA A-Level Physics

This topic introduces the ideal gas model, a fundamental concept in thermal physics that links the macroscopic variables of pressure, volume, and temperature to the microscopic behaviour of gas molecules. You will learn the equation of state pV = nRT and the assumptions that define an ideal gas, including negligible molecular volume and no intermolecular forces. These ideas are essential for understanding real gas behaviour and for later topics such as thermodynamics and kinetic theory.

The ideal gas equation is a cornerstone of A-level physics because it combines experimental gas laws (Boyle's, Charles's, and the pressure law) into a single relationship. It also provides a bridge between macroscopic measurements and the microscopic kinetic theory model, which explains pressure in terms of molecular collisions. Mastery of this topic is crucial for exam questions that require both calculation and explanation, and it underpins many engineering and environmental applications.

• →The ideal gas equation pV = nRT relates pressure (Pa), volume (m^3), amount in moles (mol), and absolute temperature (K).
• →The molar gas constant R has a value of 8.31 J mol^-1 K^-1 and is the same for all ideal gases.
• →Absolute temperature must be used in kelvin: T(K) = T(degrees C) + 273.
• →Kinetic theory assumptions: gas molecules are in random motion, collisions are elastic, volume of molecules is negligible compared to container, and no intermolecular forces except during collisions.
• →Real gases deviate from ideal behaviour at high pressure (molecular volume significant) and low temperature (intermolecular forces significant).

• States Boyle's law: for a fixed mass of gas at constant temperature, pV is constant, so p₁V₁ = p₂V₂.
• States Charles's law: at constant pressure, V is directly proportional to thermodynamic temperature, so V₁ ÷ T₁ = V₂ ÷ T₂.
• States the pressure law: at constant volume, p is directly proportional to thermodynamic temperature, so p₁ ÷ T₁ = p₂ ÷ T₂.
• Explains that each law is an experimental relationship valid only for a fixed mass of gas, with the named variable held constant.
• Converts Celsius temperatures to kelvin by adding 273 before substituting into any gas-law calculation.
• Combines the relationships into pV ÷ T = constant and links this to the ideal gas equation pV = nRT.
• Absolute zero is the temperature at which the pressure of an ideal gas would be zero at constant volume, or the volume would be zero at constant pressure.
• Absolute zero is defined as 0 K, which is equivalent to −273.15 °C.
• The Kelvin scale is an absolute thermodynamic temperature scale, and temperatures in kelvin are used in the ideal gas equation because T is directly proportional to the average kinetic energy of particles.
• In the classical ideal gas model, at absolute zero, particles have zero kinetic energy and the gas has zero internal energy.
• Converting between Celsius and kelvin: T(K) = θ(°C) + 273.15, often approximated as +273.
• The ideal gas equation can be written as pV = nRT, where n is the number of moles and R is the molar gas constant.
• The alternative form is pV = NkT, where N is the number of molecules and k is the Boltzmann constant.
• The constants are related by R = N_A k, where N_A is the Avogadro constant.
• In calculations, pressure must be in pascals, volume in cubic metres, and temperature in kelvin.
• The equation assumes an ideal gas: negligible intermolecular forces and negligible molecular volume.
• Boyle's law: for a fixed mass of gas at constant temperature, pV = constant, so p is inversely proportional to V and a graph of p against 1/V is a straight line through the origin.
• Charles's law: for a fixed mass of gas at constant pressure, V/T = constant, so V is directly proportional to absolute temperature T, and a graph of V against T in kelvin is a straight line through the origin.
• Apparatus and method for Boyle's law: trap a fixed mass of gas, vary volume slowly, measure pressure with a pressure gauge or sensor and volume from a syringe or column length, allowing time for thermal equilibrium.
• Apparatus and method for Charles's law: heat a fixed mass of gas in a water bath, keep pressure atmospheric by allowing expansion, measure volume and temperature, and convert temperatures to kelvin by adding 273.
• Graph analysis: plot p against 1/V for Boyle's law and V against T for Charles's law; a straight line through the origin supports the proportionality, and gradients relate to the constant pV or V/T.
• Control of variables: keep temperature constant in the Boyle's law experiment and pressure constant in the Charles's law experiment; use a fixed mass of gas and avoid leaks.
• Uncertainties and improvements: repeat readings, use a wide range of values, allow thermal equilibrium, avoid parallax when reading volume, and consider the dead volume in tubing or syringe.

• 💡List the fixed variables before substituting; this shows the examiner which gas law applies.
• 💡Convert temperatures to kelvin as the first step of any calculation and keep the value visible in your working.
• 💡Check the reasonableness of the answer: at constant temperature, a smaller volume must give a larger pressure.
• 💡Always convert temperatures to kelvin before using the ideal gas equation; show the conversion explicitly.
• 💡When explaining absolute zero, refer to the extrapolation of a pressure–temperature graph to zero pressure at constant volume.
• 💡Write down the equation, rearrange algebraically before substituting numbers, and include units in your final answer.
• 💡Check that the temperature is in kelvin and that the gas constant used matches the form of the equation (R for moles, k for molecules).
• 💡For questions involving changes in state, use the combined gas law p₁V₁/T₁ = p₂V₂/T₂ when n is constant.
• 💡State the controlled variable explicitly: constant temperature for Boyle's law and constant pressure for Charles's law.
• 💡When describing graphs, name the axes and the expected shape, and explain how the shape supports the proportionality.
• 💡Include one practical improvement, such as allowing thermal equilibrium or repeating readings and taking a mean, and explain how it reduces uncertainty.
• 💡Always show your working clearly, including the rearrangement of the equation and substitution of values with units. This ensures you get method marks even if the final answer is wrong.
• 💡When explaining pressure changes using kinetic theory, use the chain of reasoning: increased temperature -> increased average kinetic energy -> increased speed -> more frequent and more forceful collisions -> increased pressure.
• 💡For questions about real gas deviation, explicitly state the condition (high pressure or low temperature) and link it to the failure of a specific assumption (negligible volume or no intermolecular forces).

• Substituting Celsius temperatures into a gas-law equation; correct this by converting to kelvin first, since the laws use thermodynamic temperature.
• Allowing gas to escape or be added during an experiment; correct this by sealing the container and checking that the mass of gas is unchanged.
• Inverting a ratio, for example writing p₁ ÷ p₂ = V₁ ÷ V₂ for Boyle's law; correct this by remembering that pressure and volume are inversely proportional, so p₁V₁ = p₂V₂.
• Using degrees Celsius in the ideal gas equation instead of kelvin. Correction: always convert to kelvin by adding 273.15 (or 273 for approximate calculations).
• Stating that real gases have zero volume at absolute zero. Correction: real gases liquefy and solidify before reaching absolute zero; zero volume only applies to the theoretical ideal gas model.
• Believing that absolute zero can be reached. Correction: it is a theoretical limit; it cannot be reached in practice, though temperatures very close to it have been achieved.
• Using temperature in degrees Celsius instead of kelvin. Correction: always convert to kelvin by adding 273.15.
• Mixing units, such as using volume in cm³ or pressure in kPa without converting to m³ and Pa. Correction: convert all quantities to SI base units before substitution.
• Confusing n (number of moles) with N (number of molecules). Correction: use n with R and N with k; remember N = n N_A.
• Using Celsius temperature in Charles's law calculations or graphs; the correction is to convert to kelvin by adding 273 before plotting or calculating.
• Plotting p against V for Boyle's law and expecting a straight line; the correction is to plot p against 1/V, which should be a straight line through the origin.
• Changing the mass of gas during the experiment, for example by leaking gas when adjusting a syringe; the correction is to seal the apparatus and use a fixed mass throughout.
• Students often think that the ideal gas equation requires pressure in atmospheres or volume in litres. Correction: Always use SI units: p in pascals (Pa), V in cubic metres (m^3), n in moles (mol), and T in kelvin (K).
• Many believe that at absolute zero, gas molecules stop moving and pressure is zero. Correction: Absolute zero is the temperature at which an ideal gas would have zero volume and pressure, but real gases liquefy before reaching 0 K; molecular motion does not completely stop at 0 K due to quantum effects.
• Students sometimes assume that the ideal gas equation applies to real gases under all conditions. Correction: It is an approximation that works well at low pressure and high temperature, but fails when intermolecular forces and molecular volume become significant.

1. 1Day 1: Review the assumptions of the ideal gas model and the derivation of pV = nRT from the combined gas laws. Make flashcards for each assumption and its implications.
2. 2Day 2: Practice calculations using pV = nRT, focusing on unit conversions (degrees C to K, cm^3 to m^3, kPa to Pa). Complete at least 5 problems from your textbook.
3. 3Day 3: Study the kinetic theory explanation of pressure and how it relates to the ideal gas equation. Write a model answer for a 4-mark explanation question.
4. 4Day 4: Learn about deviations of real gases from ideal behaviour. Create a table linking each assumption to the conditions where it fails.
5. 5Day 5: Attempt past paper questions on this topic, including multiple-choice and structured questions. Mark your answers using the mark scheme and note common errors.
6. 6Day 6-7: Review weak areas and use active recall to memorise key equations and definitions. Re-attempt any questions you found difficult.

• 📋Calculation questions: Use pV = nRT to find pressure, volume, number of moles, or temperature. Advice: Always convert to SI units and check significant figures.
• 📋Explanation questions: Describe pressure changes in terms of molecular collisions. Advice: Use precise language: 'average kinetic energy', 'frequency of collisions', 'force per unit area'.
• 📋Real gas deviation questions: Explain why a real gas deviates from ideal behaviour under certain conditions. Advice: Link the condition to the specific assumption that fails.
• 📋Graph interpretation: Sketch or interpret p-V or p-T graphs for an ideal gas. Advice: Remember that pV = nRT implies p is inversely proportional to V at constant T, and p is directly proportional to T at constant V.