Lesson 12 Ideal Gases

Refresh What volume of sulfur trioxide, in cm3, can be prepared using 40 cm3 sulfur dioxide and 20 cm3 oxygen gas by the following reaction? Assume all volumes are measured at the same temperature and pressure. 2SO2(g) + O2(g) → 2SO3(g) 20 40 60 80

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Lesson 12: Ideal Gas Equation Objectives: Understand the ideal gas equation Complete a circus of short experiments to explore the ideal gas equation Perform calculations using the ideal gas equation

Molar Volume of a Perfect Gas We learnt about the molar volume of gases last lesson….how can they be the same? The distance between particles is much bigger than the size of the particles….so particle size makes very little difference: The blue particle is twice the size of the red particle, but the blue particles are not taking up twice the amount of space. In reality, the relative distance between the molecules is much much greater than this. 10 units

The Ideal Gas Equation The volume a gas takes up is determined by: Pressure Temperature Moles of gas This combines to form the ideal gas equation PV = nRT Where: P = pressure in Pa V = volume in m3 n = moles of gas R = gas constant, 8.31 J K-1 mol-1, this appears in many places in chem T = temperature in K

Ideal Gas Assumptions Particles occupy no volume Particles have zero intermolecular forces These are not always valid, particularly at: Low temperature – when intermolecular forces become significant High pressure – when particle volume becomes significant

Study the equation and predict the lines you would expect on these graphs (assuming the third factor is fixed): PV = nRT Temperature Volume Temperature Pressure Volume Pressure

Example 1: 1.048 g of unknown gas A, occupies 846 cm3 at 500K and standard pressure. What is it’s molecular mass? State ideal gas equation Rearrange for chosen subject Sub in numbers with unit conversion and evaluate 𝑀 𝑚 𝐴 = 𝑚𝑎𝑠𝑠 𝑚𝑜𝑙𝑎𝑟 𝑚𝑎𝑠𝑠 = 1.048 0.02056 =60.0 Complete further calculations

Example 2 (your turn): A fire extinguisher containing 45 Example 2 (your turn): A fire extinguisher containing 45.4 mol CO2 has a volume of 3000 cm3. What is the pressure inside at 50OC? State ideal gas equation Rearrange for chosen subject Sub in numbers with unit conversion and evaluate

Where doe this come from? One last example: The volume of an ideal gas at 54.0 °C is increased from 3.00 dm3 to 6.00 dm3. At what temperature, in °C, will the gas have the original pressure? Use a modified version of the ideal gas equation: Since original and final pressure should be the same, we can remove this from the equation as they cancel out: 3.00 / 327.0 = 6.00 / T2 T2 = (6.00 x 327.0 / 3.00) = 653 K Where doe this come from? 54.0 converted to Kelvin by adding 273

Key Points The Ideal Gas equation: PV = nRT Also: Provided that: Molecules have zero volume Molecules experience no attraction to each other