RI 2022 The Gaseous State v2.0

Content Raffles Institution Year 5 H2 Chemistry 2022 Lecture Notes 4 - The Gaseous State • Ideal gas behaviour and deviations from it • pV = nRT and its use in determining a value for Mr • Dalton's Law and its use in determining the partial pressures of gases in a mixture Learning Outcomes Candidates should be able to: (a) state the basic assumptions of the kinetic theory as applied to an ideal gas (b) explain qualitatively in terms of intermolecular forces and molecular size: (i) the conditions necessary for a gas to approach ideal behaviour (ii) the limitations of ideality at very high pressures and very low temperatures (c) state and use the general gas equation pV = nRT in calculations, including the determination of Mr (d) use Dalton's Law to determine the partial pressures of gases in a mixture Lecture Outline 1. Introduction 2. Gas Laws 3. The Ideal Gas Equation 4. Sketching of Graphs Using Ideal Gas Equation 5. The Kinetic Theory of Gases 6. Real Gases and Ideal Gases 7. Mixture of Gases 8. Vapour Pressures 1. INTRODUCTION Resources 1. Chemistry The Molecular Nature of Matter and Change, Silberberg 2. Chemistry, Cann and Hughes 3. Chemistry Principles and Practice, Reger, Goode and Ball 4. https://phet.colorado.edu/en/simulation /gas-properties Gases are made up of particles that are separated by large distances (due to weak intermolecular forces between the particles) and these particles are constantly moving around. These constant movements in a container result in constant collisions with ' • • • / • ' 1 j the walls of the container, giving rise to the phenomenon known as the • • - • \ e "pressure" of the gas. __ @ ., _ • The gas particles are constantly moving as they possess kinetic energy (K.E.). The amount of K.E. depends on the temperature of the gas. In summary, the gaseous state is characterised by the following physical properties: • Gases do not have a fixed shape and volume, i.e. gases assume the volumes and shapes of their containers. • Gases are highly compressible and gas volume changes greatly with pressure. • Gases exert pressure equally in all directions. • Gases mix evenly and completely when confined to the same container. • Gases have much lower densities than solids or liquids. • Gases are poor heat conductors, i.e. good insulators. 1

2. GAS LAWS Over the past few centuries, scientists performed multiple experiments to understand the common behaviors of gases. They have observed that a gas's physical condition depends on four measurable macroscopic properties: p = pressure exerted by the gas V = volume occupied by the gas T = temperature of the gas n = amount of the gas SI units Pa m3 K mol Through a series of experimental studies, the relationships between these four variables are expressed in the following gas laws. 2.1 Avogadro's Law Avogadro's hypothesis states that at constant T and p, gases of the same volume contain the same number of particles. This means that one mole of any gas occupies the same volume as another gas at the same T and p. The volume occupied by 1 mol of any gas, Vm, is called the molar gas volume. At s.t.p. At r.t.p. Vm = 22.7 dm3 mo1-1 Vm = 24 dm3 mo1-1 at 105 Pa [1 bar] and 273 K [0 °C] at 101325 Pa [1 atm] and 293 K [20 °C] *Information can be found in the data booklet. This means that 1 mol of neon gas occupies the same volume as 1 mol of ammonia gas under the same temperature and pressure. Under r.t.p., 1 mol of either gas will occupy 24 dm3. Stemming from Avogadro's hypothesis, Avogadro's Law states that "for a gas at constant temperature and pressure, the volume of the gas is directly proportional to the number of moles of the gas." Ne NH3 At constant T and p, El (same number of moles) This means that Y... = constant. The effect of changing number of moles on the volume for a gas at n constant T and p can be deduced using: I V, = v, I n1 n2 Example 1 4.00 g of methane, CH4, occupies a volume of 6.25 dm3 at a particular temperature and pressure. Find the volume of the same mass of hydrogen under the same conditions. Note: Constant T & p. n1 = 4· 00 = 0.25 mol 16.0 n2 = 4.00 = 2.00 mol 2.0 V1 = 6.25 dm3 2 Applying Avogadro's Law, VI ,I " .... (\,.. 'I-I ' _.- - vi" V} .,., , v I Y\ I . ...., -;:;v r" I . 3 :. volume of H2 = SO .0 lM.

2.2 Gay-Lussac's Law Gay-Lussac's Law states that "for a fixed mass of gas at constant volume, the pressure of the gas is directly proportional to its absolute temperature", i.e. temperature in Kelvin. At constant V and n, EJ This means that = constant. The effect of changing temperature on the pressure for this fixed mass of gas at constant V can be deduced using: 2.3 Charles' Law L_}__lJ Charles' Law states that "for a fixed mass of gas at constant pressure, the volume of the gas is directly proportional to its absolute temperature", i.e. temperature in Kelvin. At constant p and n, B This means that V = constant. The effect of changing temperature on the volume for this fixed mass T of gas at constant p can be deduced using: Example 2 ll1J A sample of gaseous argon, maintained at constant pressure, is found to have a volume of 10.5 m3 at 25 °C. If the system is heated to 250 °C, what is the resulting volume? Note: Constant p for the same sample of gas. V1 = 10.5 m3 TK=Toc+273 Applying Charles' Law, ~( Ir v, T, ;, "i :. '1, 11' T 1 = 25 + 273 = 298 K \)" •1,j T2 = 250 + 273 = 523 K :.resulting volume= ___ .. , 3

2.4 Boyle's Law Boyle's Law states that "for a fixed mass of gas at constant temperature, the volume of the gas is inversely proportional to the pressure." At constant T and n, I V « ¾ I This means that pV = constant The effect of changing pressure on the volume for this fixed mass of gas at constant T can be deduced using: Example3 At constant T and n, • High volume, low pressure Low volume, high pressure A sample of a gas has a pressure of 2.00 atm and a volume of 45.0 dm3• Find its pressure if it is compressed to 10.0 dm3 at constant temperature. Note: Constant T for the same sample of gas. Applying Boyle's Law, P1 = 2.00 atm V1 = 45.0 dm3 P2 =? V2 = 10.0 dm3 ~IV f ::. VY Vt 9 "L :.pressure when volume is 10.0 dm3 = q. iJl~,A-~ 4

3. THE IDEAL GAS EQUATION Candidates should be able to @ state and use the general gas equation pV = nRTin calculations, including the determination of Mr. 3.1 Ideal Gas Equation The four gas laws are all inter-related. Putting all the gas laws together: Boyle's Law Charles' Law Gay-Lussac's Law Avoaadro's Law at constant T and n at constant p and n at constant V and n at constant p and T 1 Voc:.- Voc:.T poc:.T Voc:.n p Combining these individual effects into one relationship, we get p V oc n T By introducing a constant of proportionality known as R, the molar gas constant, into the relationship above, the ideal gas equation is obtained: Ideal gas equation: I pV = nRT In the Data Booklet, the value of the molar gas constant R is stated as 8.31 J K-1 moI-1. Note the useful conversions: Example4 To use R = 8.31 J K-1 moI-1 (SI units) pV = nRT Pao( t t 'K Nm· 2 m 3 mol 1 dm3 = 1000 cm3 1 dm3 = 10-3 m3 1 cm3 = 10-6 m3 1 atm = 101325 Pa 1 bar = 1 x 1 05 Pa TK=Toc+273 Calculate the amount of nitrogen gas with a volume of 200 cm3, at a temperature of 100 °C and pressure of 10 atm. V= T= p= 111-· 5

Example 5 A 1.00 dm3 balloon filled with helium gas is released at sea-level where the temperature is 29 °C and the pressure is 1.00 atm. What will be its volume when it reaches a height where the temperature is 27 °C and the pressure is 0.98 atm? Note: Constant amount of He gas (i.e. constant n) p, = 1.00 atm V, = 1.00 dm3 P2 = 0.98 atm Since n is a constant, T, = 29 + 273 = 302 K T2 = 27 + 273 = 300 K :. the new volume of the balloon= \ · ...:.,___.__ 3.2 Determining the molar mass of a gas Through a rearrangement of the ideal gas equati