1. Chapter 13: Gas Laws
Gases

2. Phases of matter Gases Liquids
~are the most random. Molecules fly around randomly with large spaces in between them.
Solids
~are more random
than solids.
The molecules
flow around one another, and are scattered about more.
~tend to
be the most compact
and orderly. The
atoms only vibrate!
Volume- amount of
space something takes up.

3. Density of phases Density is mass per volume.
For the diagrams, all phases had the same number of molecules, therefore the same mass (mass is the amount of matter present).
Gases tend to have the most volume, liquids less and solids have the least.
Therefore solids tend to be most dense, liquids less and gases the least.

4. Gases float on everything
Gases are less dense than other phases so buoyant forces make them float.
Gases do have mass (and weight) though.
Gases are not weightless!
Helium is lighter than air (nitrogen/oxygen mix), but it still has a weight!
Think of a full propane tank (gas grill) compared to an empty tank.
The same applies to a helium tank. A full tank is heavier than an empty tank.

5. Exception to the rule
Water actually is most dense at 4o C (water), ice is less dense than water.
Hydrogen bonding pulls everything in tighter when it is a liquid.
Buoyant forces make things less dense float on things that are more dense.
Ice floats on water.

6. Gases exert a pressure Pressure is the force per unit of area.
Since gas molecules fly around randomly, they run into things.
Each time they hit something they apply a force.
More times they hit the more force (therefore the more pressure) they apply.

7. Kinetic Energy Kinetic energy is ½ mass (velocity)2
The average kinetic energy is temperature.
The sum of KE is the heat energy.
The more heat energy present the faster these are moving.
The faster they are moving the harder they will hit.

8. Pressure

9. Atmospheric Pressure ~pressure caused by the atmosphere.
Atmospheric pressure squeezes on everything from every direction and attempts to fill in empty spaces.
If you have less pressure inside something and more pressure outside, the outside pressure will squeeze it.
It could implode depending on the strength of the wall. The reverse is also true.

10. Gases can be compressed
Neither solids nor liquids can be compressed (squeezed to a smaller size) but gases can be easily compressed.
It can be done with an air pump (into a bike tire or basketball or anything that is inflatable.
If the compression force is larger than the force (pressure) of the gas, it can be made smaller.
The reverse is also true.

11. H is high pressure L is low pressure
If the walls are weak enough… H L L H H H L L H L

12. H is high pressure L is low pressure
It could implode
Or explode H L L H H H L L H L

13. Volume and Pressure
If you seal a container and decrease the volume (squeeze it) the pressure inside will
increase.
If you increase the volume the pressure will decrease.
This is Boyle’s Law
The volume of a gas is inversely proportional to the pressure of the gas.
Standard pressure is 101 kPa or 29.9 inches of mercury (Hg)

14. Other units of Pressure
Name
Abbreviation
Standard
Pressure
Where it is used.
Torr
mm Hg or torr
760
weather
Kilopascal
kPa
101
metric standard
Atmospheres
Atm
1.00
deep sea diving
Pounds per square inch
psi
14.7
anything inflatable

15. Boyle’s law
Volume of a gas is inversely proportional to the pressure on a gas.
V  1/P
Therefore VP = k (some constant for each gas)
ViPi = VfPf
i is initial f is final

16. Boyle’s Law
If you have 145 mL of a gas at 67 kPa. What volume will it occupy at 127 kPa?
VP = VP

17. You can see Boyle’s Law
If you fill a cup with water under the water level, turn it upside down and pick it up.
This will (attempt to) increase the volume inside the cup.
Which will decrease the pressure.
The outside pressure will push in allowing you to pick up the water against gravity.
as long as you don’t raise the cup over the water line

18. Water in a cup Gravity wants to pull the water in the cup down.
However if it fell it would leave a big space of nothing (vacuum)
Air pressure pushes to stop the vacuum from forming by pushing
on the surface of the liquid.
Not allowing the water level
to rise.
Cup (with a
little bit of air
in it)
Which would
make the
water level
rise.
Water
The water will fall once the air pressure equals the pressure (weight divided by area) of the water being lifted.

19. Barometer Pressure can be measured with a barometer.
Which works just like the cup but with mercury.
And you simply measure
how high the mercury can
be held.
Complete vacuum
(no air or anything)
There is not an infinite amount of mercury that can be suspended.
Only until its pressure equals the outside air pressure. Once it falls a little you can measure it.
This is inches of Hg or
mm Hg (torr). This is how
pressure is reported on the news
Mercury
mm of Hg are also called torr after the inventor of the barometer
Evangelista Torricelli

20. If it is so dangerous why use mercury?
Mercury is very dense, so you don’t need that tall of a tube to make it so it will start to fall.
A little smaller than a meter will pretty much always fall a little under normal conditions.
If you used water it would have to be over 10 m high to get it to fall a little.
Standard pressure is 760 torr or 29.9 in Hg

21. Modern Barometers
Digital Barometers and barometers with a dial use a sensor on a sealed drum.
The top of the drum is flexible.
Sealed inside the drum is air at a known (calibrated) pressure.
Higher outside pressure caves the drum in.
Lower outside pressure bows the drum out.

22. High pressure
drum
low pressure

23. High pressure
drum
low pressure

24. High pressure
drum
low pressure

25. Heating things make them expand…
and cooling makes them contract.
This is noticeably true with gases.
This is the Charles’ Law
~The volume of a gas is directly proportional to the temperature of that gas.
V  T; V/T = k
Vi/Ti = Vf/Tf

26. Charles’ Law
If you have 6.7 L of a gas at 298 K, what volume will it occupy at 0o C?
V/T = V/T
6.7 L / (298 K) = V / (273 K)
*Temp must be in Kelvin because zero would make it undefined!
V = 6.1 L

27. Charles’ Law
If you have .731 L of a gas at 318 K, what temperature will it be if it occupies 1.34 L?
V/T = V/T

28. Gay-Lussac’s Law
The pressure of a gas is directly proportional to its temperature.
T/P = T/P
This is why an aerosol can or a tire feels cooler when air is released.
It is also how a diesel engine ignites the fuel. It compresses it until it ignites.

29. Refrigeration/Air Conditioning
Refrigeration and air conditioning work using these principals.
WE CANNOT MAKE COLD AIR!!
We can only separate cold air from hot air.
AC works by compressing air at one point (causing it to heat up) and decompressing at another, causing it to cool down.

30. AC refrigerator

31. Combined Gas Law This is made by combining Charles’ and Boyle’s Law.
Vi Pi / Ti = Vf Pf / Tf
Temperature has to be in Kelvin (so it can never be 0)
volume and pressure can be in any unit as long as it is the same on both sides.

32. A problem
If a gas occupies 34 L at 1.2 atm and 290 K, what volume will it occupy at 1.1 atm and 280 K?
Vi Pi / Ti = Vf Pf / Tf

33. A problem
If a gas occupies 24 mL at 115 kPa and 13o C, what volume will it occupy at 101 kPa and 0o C?

34. Standard Temperature and Pressure
Normally volumes are reported at standard conditions.
It is normally abbreviated STP (standard temperature and pressure)
Standard temperature is 273 K or 0o C
Standard pressure is 101 kPa, or 760 torr, or 1.00 atm.

35. Avogadro’s Law
Avogadro discovered that the size or type of molecule or atom of a gas had no effect on the volume of that gas.
His law states…
~equal volumes of different gases at the same temperature and pressure contain the same number of molecules.
1.00 mol of any gas at STP will occupy 22.4 L

36. To convert… What volume will .67 mol of a gas occupy at STP?
What volume will .67 mol of a gas occupy at 740 torr and 295 K?

37. More
What volume will .83 mol of a gas occupy at .82 atm and 264 K?

38. A problem
126 mL of nitrogen at 113 kPa and 39o C will occupy what volume at STP?
VP/T = VP/T

39. Ideal Gas Law

40. Ideal Gas Law
For every problem we have done, we also could have used the ideal gas law.
On the test, you will have to do a couple of problems with the combined gas law, some with the ideal gas law and then you will be able to choose which you want to use.

41. Ideal gas law can be derived from the combined gas law
n (22.4) = Volume of any gas at STP (n is the number of moles)
plug this into combined gas law for initial state.
PV/T = PV/T (using kPa for pressure)
PV/T = (101.2 kPa) (n • L) / 273 K
PV = n (8.31 kPa•L/K mol) T
8.31 kPa•L/K mol is the ideal gas constant for these units. It is abbreviated “R”

42. The equation PV = nRT *R can also be .0821 atm •L/K mol
The units of R must match the other units in the problem.
If you are using 8.31 kPa•L/K mol, your units are:
kPa(L) = mol (8.31 kPa•L/K mol) K

43. Converting pressures Use the standard pressures as a conversion factor
1.00 atm = 101 kPa = 760. torr
convert 135 kPa to atm
convert 768 torr to kPa

44. Using the ideal gas law
What volume will .76 mol of a gas occupy at .82 atm and 264 K?

45. Ideal Gas Law Problem
If a gas occupies 14 L at 135 kPa and 285 K, what volume will it occupy at STP?

46. Another Problem
What volume will .34 mol of a gas occupy at 634 torr and 15o C?

47. Kinetic Molecular Theory

48. The model of Gases
Most of our knowledge of gases comes from a model of how gases work.
The model of a real gas would look something like a large open room filled with several bouncing balls flying around at very high speeds (2x the speed of sound)
If the room was about the size of this classroom, the “balls” could be kept in the mole box.

49. Dalton’s Law of Partial Pressure
John Dalton found that in a mixture of gases, the pressure each gas exerts is the same as if it were alone in the container.
The total pressure of all gases is the sum of each partial pressure of the gases present
P = P1 + P2 + P3…

50. If you have two containers
.5 mol of N2
2.4 atm
1.5 mol of H2
7.2 atm
And I force both of these gases into one
.5 mol of N2 2.4 atm
1.5 mol of H2 7.2 atm
9.6 atm
The total pressure would be

51. Therefore PV = nRT P = nRT/V
Using Dalton’s law of partial pressure for a mixture of two gases
Ptotal = n1 (RT/V) +n2 (RT/V)…
Ptotal = (n1 + n2…) (RT/V)
Ptotal = ntotal (RT/V)

52. Implications
When calculating pressure, the total number of gas particles in the only thing that is important.
The type of gas particle is irrelevant.
The mass of the atom/molecule or volume atom/molecule is irrelevant.

53. Kinetic Molecular Theory
Laws explain “what”
Theories try to explain “why”
Theories can NEVER become laws.
The kinetic molecular theory explains why gases act the way they do.
Gases that act like the kinetic molecular theory predicts are called ideal gases.

54. Ideal Gases
Gases consist of tiny particles that have negligible volume compared with the overall volume of the gas.
Atoms/molecules are in constant random motion, that constantly collide with one another and the wall of the container.
There is no attraction, repulsion or “desire” of the gas particles to go anywhere.
The result of these collisions is the pressure exerted by the gas.

55. More on ideal gases
All collisions are elastic, which means no kinetic energy is lost (to sound, light or heat energy).
The temperature of a gas relates to the average speed of each individual atom/molecule (kinetic energy) depending upon the mass as well.
KE = ½ mv2

56. Real Gases
Most real gases will act like ideal gases under normal conditions.
Under extremely high pressure or extremely low temperatures a gas no longer acts like an ideal gas.

57. Diffusion Effusion

58. Diffusion
~Movement of particles from an area of high concentration to an area of low concentration.
This is why you can smell perfume all throughout a room when it is sprayed.
Using the ideal gas model- you wouldn’t expect a certain type of atoms to stay together.

59. Diffusion
High
Low
All particles move randomly. There is no desire to travel anywhere. However, there are more particles at high pressure than low pressure. So the probability of particles going from high to low is higher than from low to high.

60. Diffusion
On the last slide say there were 5 particles at low pressure and 100 at high pressure.
Each particle has a 1/5 chance of moving from 1 circle to the other. What happens?
1 moves from low to high
20 move from high to low
That means we have a net flow of 19 particles from high to low.
To make it a reasonable amount we really need much more than 100 particles to start so put a x1020 at the end of all numbers.

61. Effusion
~a movement of particles from high to low concentration through an opening.
Like a tire with a leak in it.
Really this only depends on the likelihood of a particle reaching the “hole”.
Which is dependant upon the number of particles present and the speed of the particles.

62. Tire with a leak
The particle inside have a higher
pressure than the particles outside.
That means there is more gas particles on the inside than on the outside
Tire
The material will
be weak on either
side and open like
flaps
Therefore they should hit the hole and escape more often than outside particles.

63. Tire with a leak
Any individual particle inside or outside of the tire should have the same chance of hitting the “hole”.
The particles inside have a higher pressure than the particles outside. Which means there are more particles in a given area inside the tire than outside.
Tire
Therefore more inside particles should hit the hole than outside particles,
The material will
be weak on either
side and open like
flaps
and there should be net flow of
air particles outward.

64. Comparing the rates of effusion of gas molecules
All gases will not effuse at the same rate.
It depends on the speed of each gas molecule.
At the same temperature, all particles will have the same kinetic energy, but they all have different masses (their molar mass).

65. What that means
A bowling ball with the same amount of kinetic energy as a golf ball must be moving significantly slower, right?
Imagine that at an atomic level.
Heavier particles move more slowly than lighter particles if they both are at the same average kinetic energy (temperature)

66. Oxygen and hydrogen at the same temperature
If they have the same temperature, the kinetic energy will be equal.
½ mv2 oxygen = ½ mv2 hydrogen
½ 32 v2 oxygen = ½ 2 v2 hydrogen
16 v2 oxygen = v2 hydrogen
4 v oxygen = v hydrogen
So hydrogen has to move 4x as fast as oxygen to have the same kinetic energy

67. 4x the speed means… It should effuse 4x as fast.
And experiments show it does.
If you have a container holding both H2 and O2 the hydrogen should leave 4x more quickly than oxygen.
Graham’s Law of effusion
va/vb = Mb/Ma (under the same conditions)
M is the molar mass

68. Quick example
va/vb = Mb/Ma
So carbon dioxide and water vapor

69. Gas Identification

70. Reactivity Flame tests Hydrogen- POPS in the presence of a flame
Helium- puts flame out
Carbon Dioxide- puts flame out
Nitrogen- Puts flame out
Oxygen- reignites flame if it is smoldering
Methane- produces a larger flame (burns)

71. What makes gases float
Gases float in air if their density is less than that of air, and sink if it is more.
Air is composed of 78% Nitrogen (N2), 21 % Oxygen (O2) and 1 % Argon (Ar); with other gases in trace amounts.
Density = mass/volume
One mole of ANY gas is 22.4 L
The mass of one mole is the molar mass.

72. Gases that float
Very few gases are actually lighter than air and do float.
Air has a density of 1.28 g/L (28.672g/22.4L)
Hydrogen (H2) is the least dense gas at .09 g/L (2.016 g/22.4 L)
Helium (He) is .179 g/L (4.008 g /22.4 L)
Methane (CH4) is .716 g/L ( g/22.4 L)
Ammonia (NH3) is .760 g/L ( g/22.4 L)

73. Gases that sink
Most gases are actually more dense than air and will sink
Carbon Dioxide, Oxygen, Ozone, krypton, xenon, radon, and butane.
Propane heated houses can possibly blow up if a propane leak fills up the basement of the house, that eventually ignites.
If propane was less dense it would float to the attic which almost always has a vent in it.
Radon is a radioactive gas that also collects in the basement of houses if there is a source.

74. Colored Gas If you see one… Run they are all poisonous!!
Fluorine- A VERY pale yellow color which is difficult to see.  It is the most reactive nonmetal on the planet and is incredibly toxic.
Chlorine- A green gas which will react nearly everything and is good at killing people.
Bromine- A vapor that is very intense red-orange color. It is pretty, but will kill you.
Nitrogen Dioxide- A brown gas which is VERY good at killing people.
Iodine- A pale violet color, inhaling the vapor can cause lung damage and could kill you.

75. Gases and Vapors Vapors are gases!
A vapor is a substance that is normally a solid or a liquid at the current conditions (temperature and pressure), however, it is kind of dissolved in the air.
Water that has evaporated is a vapor, rubbing alcohol readily evaporates into a vapor, so do bromine and iodine

76. Water Vapor Water Vapor is invisible to the human eye.
You can see steam because some tiny droplets of the water are condensing (turning back into liquid water) and forming a mini-cloud.
You can see your breath when it is cold for the same reason

77. Distinct Odor Hydrogen Sulfide- smells like rotten eggs Ammonia Ozone
Mercaptan- odor in natural gas. Natural gas by itself is odorless, this is added so you know if there is a leak.