1. 4.3.4 Ideal Gases

2. 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

3. 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

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

5. Charles’ Law
V/m3
θ /°C
T/K
This graph shows the result of cooling a fixed mass of gas at a constant pressure

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

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

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

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

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

11. 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

12. 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

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

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

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

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

17. 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)

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

19. 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

20. 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

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

22. 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

23. 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’

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

25. 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

26. 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 JK-1)
T = temperature (K)
Gas has no other types of energy eg electrical

27. Questions Now do SAQ’s 15 to 19 on page 100 and
End of Chapter Questions on pages