1. Chapter 17 (2) Kinetic Theory of Gases

2. Ideal Gas Law The law R = 0.08206 L.atm/(mol.K)
is approximately true for real gases at low
pressure and density.
An ideal gas is a gas that obeys this law.

3. PV Diagram - Isotherms

4. Example 17 - 3 What is the volume of 1 mol of an ideal gas
at T = 0oC and P = 1 atm?

5. Example 17 – 4 (1) Initial Volume of gas V1 = 2 L
Initial Temperature T1 = 30o C
Initial Pressure P1 = 1 atm
Final Volume of gas V2 = 1.5 L
Final Temperature T2 = 60o C
Final Pressure P2 = ?

6. Example 17 – 4 (2)
Remember: must use absolute temperature
in gas law

7. Molar Mass The mass per mole of a substance is
called its molar mass (units g/mol)
Example – Molar mass of CO2
= molar mass(C) + molar mass(O2)
= 12 g/mol + (16 g/mol + 16 g/mol)
= 44 g/mol

8. Example 17 - 6 100 g of CO2 occupies a volume of 55 L
at P = 1 atm. What is its temperature?
Number of moles:
n = m / M
= 100 g / 44g/mol
= 2.27 mol
But T = PV / n R, so T = 295 K

9. 17-5 The Kinetic Theory of Gases

10. Kinetic Theory of Gases (1)
The kinetic theory of gases is a theory that tries to derive the properties of an ideal gas from first principles, in particular, from Newton’s laws.

11. Kinetic Theory of Gases (2)
In a time Dt, on average, ½ the molecules
in volume (vx Dt)A
are moving right.
Therefore, the
number of
molecules that
hit the wall is A

12. Kinetic Theory of Gases (3)
The total change in the x component
of the momentum
of these molecules is A

13. Kinetic Theory of Gases (4)
The force exerted on the wall is
F = Dt / Dt and the
pressure P = F/A A

14. Kinetic Theory of Gases (5)
From the kinetic theory
one gets A

15. Kinetic Theory of Gases (6)
But since the molecules do not all have the
same speed we must replace
By the its average value

16. Kinetic Theory of Gases (7)
We now compare the law found
experimentally
with the formula from the kinetic theory
and deduce that

17. Kinetic Theory of Gases (8)
But, given that the average squared speed is
we find that

18. What is Temperature ? From the kinetic theory of gases we have
discovered that temperature is a measure
of the average kinetic energy of a molecule:

19. Root Mean Square Speed From
we can calculate the rms speed of a molecule

20. Example 17 – 7 (1) The molar mass of O2 is about 32 g/mol
The molar mass of H2 is about 2 g /mol
What is the rms speed of O2 and H2
at T = 300 K?

21. Example 17 – 7 (2)
rms speed for O2 is

22. Example 17 – 7 (3)
Since
then the rms speed for H2 is given by

23. Example 17 – 7 (4)
So the rms speed for H2 is