1. The Ideal Gas Law and Kinetic Theory
Chapter 14
The Ideal Gas Law and Kinetic Theory

2. Avogadro’s number
Mole – amount of substance containing a number of atoms (molecules) equal to the number of atoms in a 12 g sample of 12C
This number is known as Avogadro’s number (NA):
NA = 6.02 x 1023 mol -1
The number of moles in a sample
N – total number of atoms (molecules)
m – total mass of a sample, m0 – mass of a single atom (molecule); M – molar mass
Amedeo Avogadro
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3. Chapter 14
Problem 10
A cylindrical glass of water (H2O) has a radius of 4.50 cm and a height of 12.0 cm. The density of water is 1.00 g/cm3. How many moles of water are contained in the glass?

4. Ideal gases Ideal gas – a gas obeying the ideal gas law:
R – gas constant
R = 8.31 J/mol ∙ K
kB – Boltzmann constant
kB = 1.38 x 1023 J/K
Ludwig Eduard
Boltzmann
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5. Chapter 14
Problem 29
One assumption of the ideal gas law is that the atoms or molecules themselves occupy a negligible volume. Verify that this assumption is reasonable by considering gaseous xenon (Xe). Xenon has an atomic radius of 2.0 x m. For the standard temperature and pressure (STP) conditions, calculate the percentage of the total volume occupied by the atoms. Express your answer as a percentage with no units.

6. Ideal gases The gas under consideration is a pure substance
All molecules are identical
Macroscopic properties of a gas: P, V, T
The number of molecules in the gas is large, and the average separation between the molecules is large compared with their dimensions – the molecules occupy a negligible volume within the container
The molecules obey Newton’s laws of motion, but as a whole they move randomly (any molecule can move in any direction with any speed)

7. Ideal gases
The molecules interact only by short-range forces during elastic collisions
The molecules make elastic collisions with the walls and these collisions lead to the macroscopic pressure on the walls of the container
At low pressures the behavior of molecular gases approximate that of ideal gases quite well

8. Ideal gases

9. Ideal gases
Root-mean-square (RMS) speed:

10. Translational kinetic energy
Average translational kinetic energy:
At a given temperature, ideal gas molecules have the same average translational kinetic energy
Temperature is proportional to the average translational kinetic energy of a gas

11. Internal energy For the sample of n moles, the internal energy:
Internal energy of an ideal gas is a function of gas temperature only

12. Chapter 14
Problem 42
Compressed air can be pumped underground into huge caverns as a form of energy storage. The volume of a cavern is 5.6 × 105 m3, and the pressure of the air in it is 7.7 × 106 Pa. Assume that air is a diatomic ideal gas whose internal energy U is given by U = (5/2)nRT. If one home uses 30.0 kW h of energy per day, how many homes could this internal energy serve for one day?

13. Distribution of molecular speeds
Not all the molecules have the same speed
Maxwell’s speed distribution law:
NvΔv – fraction of molecules with speeds in the range from v to v + Δv
James Clerk Maxwell
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14. Distribution of molecular speeds
Average speed:
RMS speed:
Most probable speed:

15. Questions?