1. Ideal Gases

2. Describing Gases
Experiments with a wide variety of gases revealed that four variables were sufficient to fully describe the state of a gas
Pressure (P)
Volume (V)
Temperature (T)
The amount of the gas in moles (n)

3. The Definition of Pressure
The pressure of a gas is best defined as the forces exerted by gas on the walls of the container
Define P = force/area
The SI unit of pressure is the Pascal
1 Pa = N/m2 = (kg m/s2)/m2

4. The Measurement of Pressure
How do we measure gas pressure?
We use an instrument called the barometer - invented by Torricelli
Gas pressure conversion factors
1 atm = 760 mm Hg = 760 torr
1 atm = kPa = bar
1 bar = 1 x 105 Pa (exactly)

5. The Temperatures Scales
T (K) = [ tc ]
Freezing point of water: tc = 0 °C; T = K
Boiling point of water: tc = 100 °C; T = K
Room temperature: tc = 25 °C; T = 298 K
NOTE tc = °C; T (K) = K
NO DEGREE SIGN

6. The amount of gas
One mole of a substance is the amount of that substance which contains the same number of particles (atoms, molecules, etc.) as there are in 12 g of carbon-12.
Symbol: n
1 mole of gas contains 6.02 x 1023 molecules.
Avogadro’s number
nA = nB
The same conditions
Their properties are the same

7. Boyle's Law The gas volume/pressure relationship
The volume occupied by the gas is inversely proportional to the pressure
V 1/P
note temperature and the amount of the gas are fixed or constant

8. Boyle's Law V
1/P V P

9. Charles and Gay-Lussac's Law
Defines the gas volume/temperature relationship.
V  T (constant pressure and amount of gas)
Note T represents the temperature on the absolute (Kelvin) temperature scale

10. Charles and Gay-Lussac's LawV
t / C
Absolute Zero
(-273C = 0 K)

11. Amonton’s Law and the Combined Gas Law
The pressure/temperature relationship
For a given quantity of gas at a fixed volume, P  T, i.e., if we heat a gas cylinder, P increases!
Combined Gas Law
(P1 x V1) / T1 = (P2  x V2 ) / T2

12. Questions
A 2.0 Liter sample of gas initially at 25°C is heated to 100°C at fixed pressure. What is its final volume?
A sample of a gas having a volume of 1 L at 25°C and 1 atm pressure is subjected to an increase in pressure and a decrease in temperature. The volume of the gas:
A. decreases B. increases C. remains the same D. either increases or decreases, depending on the sizes of the pressure and temperature changes

13. Questions
A sample of a gas having a volume of 1 L at 25°C and 1 atm pressure is subjected to an increase in pressure and an increase in temperature. The volume of the gas:
A. decreases B. increases C. remains the same D. either increases or decreases, depending on the sizes of the pressure and temperature changes   

14. Avogadro’s Law
The volume of a gas at constant T and P is directly proportional to the number of moles of gas
V  n => n = number of moles of gas

15. The Ideal Gas Equation of State
We have four relationships
V  1/P; Boyle’s law
V  T; Charles’ and Gay-Lussac's law
V  n; Avogadro’s law
P  T; Amonton’s law

16. The Ideal Gas Law
Combine these relationships into a single fundamental equation of state - the ideal gas equation of state

17. The Definition of an Ideal Gas
An ideal gas is a gas that obeys totally the ideal gas law over its entire P-V-T range
Ideal gases – molecules have negligible intermolecular attractive forces and they occupy a negligible volume compared with the container volume

18. Standard Temperature and Pressure
Define: STP (Standard Temperature and Pressure)
Temperature °C = K
Pressure atm
The volume occupied by mole of an ideal gas at STP is L!

19. Remembering Brownian Motion

20. Kinetic Theory of Ideal Gases
Point masses
The gas consists of very small particles with non-zero mass
The average distance separating the gas particles is large compared to their size.
No intermolecular forces
They exert no forces on one another except during collisions.
Random motion
The rapidly moving particles constantly collide with the walls of the container.

21. Kinetic Theory of Ideal Gases
Elastic collisions
There is no change in potential energy since intermolecular forces are negligible (recall gravitation)
The average kinetic energy of the gas particles depends only on the temperature of the system.

22. Pressure exerted by a gas
p = 1/3 (Nm/V) v2
where N = number of molecules
m = mass of gas in kg
V = volume in m3
v = average translational speed of gas molecules

23. Boltzmann Constant PV = NkbT Kavg = (3/2) kbT
kb is known as Boltzmann constant
Boltzmann constant = × m2 kg s-2 K-1
Kavg = (3/2) kbT

24. Example