1. Gases

2.    GASES manometers pressure Kinetic theory of gases
Units of pressure 
Behavior of gases
Partial pressure
of a gas
Pressure vs.
volume
Pressure vs.
temperature
Temperature vs.
volume
Diffusion/effusion
Combined gas law
Ideal gas law

3. Properties of Gases Very low density Low freezing points
Low boiling points
Can diffuse (rapidly and spontaneously spread out and mix)
Flow
Expand to fill container
Compressible

4. Kinetic Molecular Theory of Gases
Particles move non-stop, in straight lines.
Particles have negligible volume (treat as points)
Particles have no attractions to each other (no repulsions, either).
Collisions between particles are “elastic” (no gain or loss of energy)
Particles exert pressure on the container by colliding with the container walls.

7. Temperature Temperature is a measure of average kinetic energy.
Temperature measures how quickly the particles are moving. (Heat IS NOT the same as temperature!)
If temperature increases, kinetic energy increases.
Which has greater kinetic energy: a 25 g sample of water at 25oC or a 25 g sample of water at -15oC?

8. Why use the Kelvin scale?
In the Kelvin scale, there is an absolute correlation between temperature and kinetic energy.
As temperature in Kelvin increases, kinetic energy increases.
Absolute zero: All molecular motion ceases. There is no kinetic energy.
0 K

9. Kelvin-Celsius Conversions
K = oC
oC = K –

10. Pressure Pressure = force/area Atmospheric pressure
Because air molecules collide with objects
More collisions  greater pressure

11. Pressure is a measure of the number of collisions between atoms or molecules with the walls of the container

12. Atmospheric Pressure

13. Pressure Units Atmosphere Pounds per square inch (psi) mm Hg Torr
Pascal (Pa) or kilopascal (kPa)
1 atm = 14.7 psi = 760 mm Hg = 760 torr = kPa

14. Energy flows from warmer objects to cooler objects. Plasma
At the same temperature, smaller molecules (i.e., molecules with lower gfm) have faster average velocity.
Energy flows from warmer objects to cooler objects.
Plasma
High energy state consisting of cations and electrons
Found in sun, fluorescent lights

15. Boyle’s Law Pressure-volume relationships
For a sample of a gas at constant temperature, pressure and volume are inversely related.
Equation form:
P1V1 = P2V2

16. Charles’ Law Volume-temperature relationships
For a sample of a gas at constant pressure, volume and temperature are directly related.
Equation form:

17. Guy-Lussac’s Law Pressure temperature relationships
For a sample of a confined gas at constant volume, temperature and pressure are directly related.

18. Combined Gas Law Sometimes, all three variables change simultaneously
This single equation takes care of the other three gas laws!

20. Summary of the Named Gas-Laws:
RELAT-IONSHIP
CON-STANTS
Boyle’s
P V
P1V1 = P2V2
T, n
Charles’
V T
V1/T1 = V2/T2
P, n
Gay-Lussac’s
P T
P1/T1 = P2/T2
V, n

21. Barometer Torricelli-1643
Air molecules collide with liquid mercury in open dish
This holds the column up!
Column height is an indirect measure of atmospheric pressure

22. Manometer Two types: open and closed
Use to measure the pressure exerted by a confined gas

23. Dalton’s Law of Partial Pressures
For a mixture of (nonreacting) gases, the total pressure exerted by the mixture is equal to the sum of the pressures exerted by the individual gases.

24. Collecting a sample of gas “over water”
Gas samples are sometimes collected by bubbling the gas through water

25. If a question asks about something relating to a “dry gas”, Dalton’s Law must be used to correct for the vapor pressure of water!
Table: Vapor Pressure of Water

26. Ideal Gas Law
The number of moles of gas affects pressure and volume, also!
n, number of moles
n  V
n  P
P  1/V
P  T
V  T
Where R is the universal gas constant
R = L●atm/mol●K

27. Ideal vs. Real Gases
Ideal gas: completely obeys all statements of kinetic molecular theory
Real gas: when one or more statements of KMT don’t apply
Real molecules do have volume, and there are attractions between molecules

28. When to expect ideal behavior?
Gases are most likely to exhibit ideal behavior at…
High temperatures
Low pressures
Gases are most likely to exhibit real (i.e., non-ideal) behavior at…
Low temperatures
High pressures

29. Diffusion and Effusion
The gradual mixing of 2 gases due to random spontaneous motion
Effusion
When molecules of a confined gas escape through a tiny opening in a container

30. Graham’s Law Thomas Graham (1805-1869)
Do all gases diffuse at the same rate?
Graham’s law discusses this quantitatively.
Technically, this law only applies to gases effusing into a vacuum or into each other.

31. Graham’s Law Conceptual: Consider H2 vs. Cl2
At the same temperature, molecules with a smaller gfm travel at a faster speed than molecules with a larger gfm.
As gfm , v 
Consider H2 vs. Cl2
Which would diffuse at the greater velocity?

32. Graham’s Law
The relative rates of diffusion of two gases vary inversely with the square roots of the gram formula masses.
Mathematically:

33. Graham’s Law Problem
A helium atom travels an average m/s at 250oC. How fast would an atom of radon travel at the same temperature?
Solution:
Let rate1 = x rate2 = m/s
Gfm1 = radon 222 g/mol
Gfm2 = helium = 4.00 g/mol

34. Solution (cont.)
Rearrange:
Substitute and evaluate:

35. Applications of Graham’s Law
Separation of uranium isotopes
235U
Simple, inexpensive technique
Used in Iraq in early 1990’s as part of nuclear weapons development program
Identifying unknowns
Use relative rates to find gfm

36. Problem 2
An unknown gas effuses through an opening at a rate 3.16 times slower than that of helium gas. What is the gfm of this unknown gas?

37. Solution Let gfm2 = x rate2 = 1 gfm1 = 4.00 rate1 = 3.16
From Graham’s Law,
Rearrange:

38. Solution, cont.
Substitute and evaluate:

39. Gases and Density density = mass / volume
The volume of 1 mole of any gas at STP will be 22.4 L
The ideal gas equation PV = nRT

40. Gases and Density
What is the molar mass of a gas whose density at STP is 0.179g/L
Step 1 extract all the information from the question
Density = g/L
STP therefore 1 mole = 22.4 L

41. Gases and Density Step 2 Calculate the mass of 1 mole
Since the volume of 1 mole = 22.4 L
Density = mass of 1 mole/ 22.4L
0.179g/L = mass of 1 mole/22.4
0.179 x 22.4 = mass of 1 mole
4g = mass of 1 mole
MM =4g/mol

42. Gases and Density
A sample of gas weighs g and occupies a volume of 112 ml at STP. The molecular weight of this gas is:
A) impossible to calculate from the data given
B) 50.0 g/mol
C) 2.23 g/mol
D) 8.0 g/mol

43. Gases and Density Step 1 Mass = 0.250g Volume = 112ml
STP 1mole =22.4 L
Density = mass/ volume
Density = 2.232g/L

44. Gases and Density Density = mass of 1 mole/22.4
Density = mass of 1 mole/22.4
Mass of 1 mole = 22.4 x 2.232
MM = 50g/Mol

45. Gases and Density
We Do: What is the Molar mass of a gas whose density = 1.878g/L at STP
STEP 1
Density =1.878g/L
@ STP 1 mole = 22.4L

46. Gases and Density STEP 2 Density = mass / volume
Density = mass of 1 mole/ 22.4L
Mass of 1 mole = 22.4 x density
Molar mass = 42g/mol

47. Gases and Density
What is the molar mass of a gas whose density is 1.43g/L
Step 1
Step 2

48. Gases and Density
What is the density of Br2 at STP

49. Taking this further More complex problems can be solved since V = nRT
V = nRT P 
1 mole at STP 22.4L
So 22.4 is derived from RT P

50. Taking this further So RT can be substituted for 22.4 L P
MM = RT x density P
This means we can handle more complex problems