IB Physics

1. 3.2.3 Ideal Gases
IB Physics SL
Mrs. Hwang

2. Real Gases and Ideal Gases
Real gases
An ideal gas is one that would obey the gas laws and the ideal gas equation under all conditions – so ideal gases
cannot be liquefied. In 1863, the Irish physician and chemist Thomas Andrews succeeded in plotting a series of
p–V curves for carbon dioxide; these curves deviated from the Boyle’s law curves at high pressures and low
temperatures. Until this time it had been believed that certain gases could never be liquefied. Andrews showed that
there was a critical temperature above which the gas could not be liquefied by simply increasing the pressure. He
demonstrated that for carbon dioxide the critical temperature is approximately 31 °C.
• ideal gases
o Obey the gas laws under all conditions
o Cannot be liquefied
o Each molecule has negligible volume when compared with the volume of the gas as a whole.
o The molecules undergo perfectly elastic collisions between themselves and also with the walls
of their containing vessel; during collisions each momentum of each molecule is reversed.
o There are no intermolecular forces between the molecules between collisions (energy is
entirely kinetic).

3. Real Gases and Ideal Gases
The best approximation of a
real gas to an ideal gas is at
• high temperature and
• low pressures

4. The Gas Laws
Boyle’s Law
Charles's Law
Avogadro’s Law
Gay Lussac's Law
While it is important to understand the relationships covered by each law, knowing the originator is not as important and will be rendered
redundant once the combined gas law is introduced. So concentrate on understanding the relationships rather than memorizing the names.

5. Boyle's Law
Boyle's Law states that the volume of a given amount of gas held at constant temperature varies inversely
with the applied pressure when the temperature and mass are constant.
The reduction in the volume of the gas means that the molecules are striking the walls more often
increasing the pressure, and conversely if the volume increases the distance the molecules must
travel to strike the walls increases and they hit the walls less often thus decreasing the pressure.

6. Boyle's Law
When Temperature and number of moles remain the same:
𝑷𝑽 = 𝒄𝒐𝒏𝒔𝒕𝒂𝒏𝒕 P = constant/V=
P = constant (1/V)

7. • A gas is confined in a cylinder with a movable piston. The pressure-volume
relations is investigated under various temperatures. The result is shown in the
following graph. Rank the temperatures. _____________________
PV =nRT
T3 >T2 >T1

8. Linearize PV graph

9. Charles's Law
Charles' Law gives the relationship between volume and temperature if
pressure and amount of gas are held constant.

10. Charles's Law
When the pressure and number of mole remain constant:
𝑽 𝟏
𝑻 𝟏
=
𝑽 𝟐
𝑻 𝟐
,
𝑽
𝑻
= 𝒄𝒐𝒏𝒔𝒕𝒂𝒏𝒕

11. Charles's Law
• A gas is confined in a cylinder with a movable piston. The Volume-Temperature relations is
investigated under various pressure while the volume is changing slowly. The result is shown in the
following graph. Rank the pressure. _____________________
𝑽
𝑻
= 𝒄𝒐𝒏𝒔𝒕𝒂𝒏𝒕
PV = nRT
P1 < P2 <P3 <P4

12. Avogadro’s Law
Avagadro's Law- Gives the relationship between volume and amount of gas in moles when pressure
and temperature are held constant.
If the amount of gas in a container is increased, the volume increases. If the amount of gas in a
container is decreased, the volume decreases. This is assuming of course that the container has
expandible walls.

13. Avogadro’s Law
When pressure and temperature remain constant.
𝑽 𝟏
𝒏 𝟏
=
𝑽 𝟐
𝒏 𝟐
𝑽
𝒏
= 𝒄𝒐𝒏𝒔𝒕𝒂𝒏𝒕

14. Gay Lussac's Law
Gay Lussac's Law states that the pressure of a given amount of gas held at constant volume is
directly proportional to the Kelvin temperature.

15. Gay Lussac's Law
When the volume stays constant:
𝒑 𝟏
𝑻 𝟏
=
𝒑 𝟐
𝑻 𝟐
𝒑
𝑻
= 𝒄𝒐𝒏𝒔𝒕𝒂𝒏𝒕

16. Gay Lussac's Law
• A gas is confined in a cylinder with a piston. The Pressure-Temperature relations is investigated under various
volumes. The result is shown in the following graph. Rank the Volumes. _____________________
PV = nRT
V1 < V2 < V3 < V4

17. Ideal Gas Law
PV=nRT
• Boyle’s Law, 𝑉 ∝
1
𝑝
• Charles’s Law, 𝑉 ∝ 𝑇
• Avogadro’s Law, 𝑉 ∝ 𝑛
𝑽 ∝
𝒏𝑻
𝒑
𝑽 = 𝑹
𝒏𝑻
𝒑

18. Ideal Gas Law
PV=nRT
https://www.youtube.com/watch?v=CYdvFRaCS7k

19. 1. A 25 L (= 0.025 m3)container that holds
40 moles of gas at a temperature of
203o C. What is the pressure inside of
the container?
2. A sample of argon at STP occupies 50.2
L(=0.052 m3). Determine the number of
moles of argon and the mass in the sample.
STP is defined as a temperature of 273.15 K (0 °C, 32 °F) and
an absolute pressure of exactly 105 Pa (100 kPa, 1 bar).
Molar mass of Argon is 40.0 g.
2. PV=nRT, n =PV/RT
n= (105)(0.052)/(8.31)(273) =2.3 mol
Mass = (amolar mass)(mole)=(40 g)(2.3)=92 g
Given V = 0.025 m3 , n= 40 mol,
T = 203o C = 476K
PV = nRT
P = 6.3x106 Pa