4.3.4 Ideal Gases

Boyle’s Law Gas has four properties: Pressure (Pa) Temperature (°C or K) Volume (m3) Mass (kg, but more usually in moles) The Gas Laws relate different properties Boyle’s Law relates pressure p and volume v

Boyle’s Law If a gas is compressed, its pressure increases and its volume decreases Pressure and volume are inversely related The pressure exerted by a fixed mass of gas is inversely proportional to its volume, provided the temperature of the gas remains constant pV = constant p  1 V

Boyle’s Law More usefully, the formula can be written: p1V1 = p2V2 Attempt SAQ 4 on page 93

Charles’ Law V/m3 θ /°C -273 0 +100 T/K 0 300 This graph shows the result of cooling a fixed mass of gas at a constant pressure

Charles’ Law The relationship between volume V and thermodynamic temperature T is: V T or V = constant T

Charles’ Law “The volume of a fixed mass of gas is directly proportional to its absolute temperature, provided its pressure remains constant”

Combine the Gas Laws pV = constant T or p1V1 = p2V2 T1 T2

Questions Now do SAQ’s 5 to 8 on page 94

(c) state the basic assumptions of the kinetic theory of gases Objective (c) state the basic assumptions of the kinetic theory of gases

Kinetic Theory of Gases A gas contains a very large number of spherical particles The forces between particles are negligible, except during collisions The volume of the particles is negligible compared to the volume occupied by the gas

Kinetic Theory of Gases Most of the time, a particle moves in a straight line at a constant velocity. The time of collision with each other or with the container walls is negligible compared with the time between collisions The collisions of particles with each other and with the container are perfectly elastic, so that no kinetic energy is lost

Measuring Gases One mole of any substance contains 6.02 x 1023 particles 6.02 x 1023 mol-1 is the Avogadro constant NA

Questions Now do SAQ’s 1 and 2 on pages 91 and 92

Ideal Gas Equation Calculating the number n of moles number of moles (n) = mass (g) molar mass (g mol-1)

Ideal Gas Equation For a gas consisting of N particles: pV = NkT where k = 1.38 x 10-23 JK-1 N = number of particles

Ideal Gas Equation For n moles of an ideal gas: pV = nRT where R = 8.31 J mol-1 K-1 p = pressure (Pa) V = volume (m3) n = number of moles of gas T = temperature (K)

Questions Now do SAQ’s 9 to 14 on page 98

Objective (f) explain that the mean translational kinetic energy of an atom of an ideal gas is directly proportional to the temperature of the gas in kelvin

Mean Translational Kinetic Energy Either: add up all the KE’s of each individual molecules, then calculate the average or watch one molecule over a period of time and calculate the average KE over that time

Mean Translational Kinetic Energy energy due to the molecule moving along, as opposed to energy due to the molecule spinning around (‘rotational’)

Mean Translational Kinetic Energy gas molecules rush around, colliding place a thermometer in the gas, and the molecules will collide with it energy from the molecules will be shared with the thermometer eventually, gas and bulb are at the same temperature (thermal equilibrium) more energy, higher temperature height of the liquid in the thermometer is related to the energy of the molecules

Mean Translational Kinetic Energy therefore: ‘The Mean Translational Kinetic Energy of a molecule of an ideal gas is proportional to the temperature of the gas in kelvin’

Objective (g) select and apply the equation E = 3/2 kT for the mean translational kinetic energy of atoms

Mean Translational Kinetic Energy total kinetic energy of gas  T total internal energy of gas  T therefore: Gas has no other types of energy eg electrical

Mean Translational Kinetic Energy E = 3/2 kT where: E = mean translational KE of an atom in a gas k = Boltzmann constant (1.38 x 10-23 JK-1) T = temperature (K) Gas has no other types of energy eg electrical

Questions Now do SAQ’s 15 to 19 on page 100 and End of Chapter Questions on pages 101 - 102