1. Chapter 10 Key Terms
Diffusion Permeability Compressibility Pressure Barometer Ideal Gas Law Molar Volume STP Vapor Pressure Avogadro’s Law Boyle’s Law Charles’s Law Pascal PSI

2. Chapter 10
Gases

3. Gases Comes from the Greek word khaos which means “formless matter”
Meaning the move about freely
Kinetic Theory:
Particles move at random, with high velocities, in all directions, and at many different speeds
Particles are tiny compared to the great distances between them
Particles do not interact except during momentary collisions

4. Gases Collisions between gas particles are elastic
They conserve energy
Sum of the particles energies before = sum of the energy after
Ex. Newton’s cradle
Ex. If particle A, with an energy of 560 J, bumps into particle B, which has an energy of 240 J. Both particles leave the collision with an energy of 400 J.
If particle A leaves the collision with an energy of 500 J, what energy does particle B have?
The average kinetic energy of the gas particles is directly proportional to the temperature of the gas in Kelvin

5. Physical Properties of Gases
Low Density
Amount of matter within a certain volume
Density = mass/volume
Diffusibility
Expands to fill its container with an even concentration
Diffusion: when a substance goes from an area of high concentration to an area of low concentration

6. Physical Properties of Gases
Permeability
Ability of a gas to mingle with another porous substance
Gas particles move into the spaces between other molecules
Compressibility
A gas can be “compressed” into a smaller container
Expansibility
Gases can expand without limit
This happens because molecules are constantly in motion

7. Gases cause pressure
Pressure: the average force exerted per unit area when molecules collide with a boundary
Measured in force per unit area
Pounds per square inch (PSI)
Millimeters of mercury (mm Hg)
Torr
Atmosphere (atm)
Pascal (Pa, kPa)

8. Pressure Measured with a barometer
Mercury barometers measure pressure in millimeters mercury (mm Hg)
Another name for mm Hg is a torr
Pascal is the SI unit for pressure
Standard pressure is the normal atmospheric pressure at sea level at 45o latitude
1 atmosphere = 760 mm Hg = 760 torr = 14.7 psi = 101,325 Pa = kPa

9. Pressure Conversions
1atm = 760 mm Hg = 760 torr = 14.7 psi = 101,325 Pa = kPa 12 atm = ________ kPa 526 mm Hg = ________ Pa torr = ________ atm 0.91 kPa = ________ psi 892 mm Hg = ________ torr

10. Pressure, Temperature, & Volume
Case
Pressure (P)
Temperature (T)
Volume (V) 1
Increase/Decrease
Constant
Decrease/Increase 2 3
Case 1: Inverse Relationship
Case 2: Direct Relationship
Case 3: Direct Relationship

12. Standard Conditions Standard Temperature and Pressure (STP)
Standard temp: 0oC or 273 K
Standard Pressure: 760 torr, 1 atm…

13. Boyle’s Law Named for Robert Boyle (1627-1691)
Found that increased pressure decreased the volume of gas
Boyle’s Law: The volume of a dry gas is inversely related to the pressure if the temperature is held constant
P1V1 = P2V2
Twice the pressure = half the volume
Units:
Volume: mL, L, ft3, cm3, m3
Pressure: torr, atm, mm Hg…

14. Boyle’s Law
A gas at 35oC occupies 85 mL at standard pressure. What will the volume be if the pressure increases to 2.67 atm?
At standard pressure, the Helium in a balloon occupies mL. What is the new volume of Helium when the pressure increases to 120,014 Pa?

15. Charles’ Law Named for Jacques Charles (1747-1823)
Charles’s Law: When the pressure on a sample of a dry gas is held constant, the Kelvin temperature and the volume are directly related
Temperature doubles: volume doubles
V 1 T 1 = V 2 T 2

16. Gay-Lussac’s Law
Pressure is directly proportional to Kelvin temperature for a fixed mass of gas held in a constant volume
Ex. Car tire pressure increasing during trip, basketball loses bounce when cold
P 1 T 1 = P 2 T 2
At the beginning of her trip, Glenda measured the pressure in her tires to be 38 psi at a temperature of 14oC. When she stopped for gas 3 hours later, she measured the pressure to now be 41 psi. What was the new temp of the air in her tires?

17. Review Boyle’s Law Charles’ Law Gay-Lussac’s Law P1V1 = P2V2
𝑽 𝟏 𝑻 𝟏 = 𝑽 𝟐 𝑻 𝟐
Gay-Lussac’s Law
𝑷 𝟏 𝑻 𝟏 = 𝑷 𝟐 𝑻 𝟐

18. Combined Gas Law 𝑷 𝟏 𝑽 𝟏 𝑻 𝟏 = 𝑷 𝟐 𝑽 𝟐 𝑻 𝟐
𝑷 𝟏 𝑽 𝟏 𝑻 𝟏 = 𝑷 𝟐 𝑽 𝟐 𝑻 𝟐
When all 3 values change, we can use the combined gas law
When 1 value is constant, we use one of the laws
A gas has a volume of 3.6 L when it is at STP. What will its new volume be at a pressure of atm and -15oC?

19. Dalton’s Law Dalton’s Law of Partial Pressures
The total pressure of a mixture of gases equals the sum of the partial pressures
1 L of oxygen at STP is added to 1 L of nitrogen at the same pressure. The pressure inside the container of nitrogen and oxygen is now 1520 torr. What are the partial pressures of nitrogen and oxygen?
1520 torr x 50%
Partial pressure of O = 760 torr
Partial pressure of N = 760 torr

20. Dalton’s Law
A sample of dry air contains 78% N, 21% O, and 1% Ar. At 760 torr, what are the partial pressures of those gases?
N = torr
O = torr
Ar = 7.6 torr

21. Vapor Pressure
When gases are collected “over water” some of the water evaporates and mixes with the gas
The water molecules exert a pressure called “vapor pressure”
If no pressure is given, we can assume the pressure is the same as the atmospheric pressure at STP
To find the pressure of the gas being measured, we subtract the vapor pressure from the total pressure

22. Vapor Pressure
A sample of He is collected over water at a temperature of 95oC with a total pressure of 801 torr. What is the actual pressure of Helium?
801 torr – torr = torr
A sample of gas collected over water has a pressure of torr at 15.0oC. The gas is a mixture of 38.21% oxygen and % nitrogen (without factoring in the water vapor). What are the partial pressures of oxygen and nitrogen?

23. Sample Problem 𝐏 𝟏 𝐕 𝟏 𝐓 𝟏 = 𝐏 𝟐 𝐕 𝟐 𝐓 𝟐
46 mL of O2 gas is collected over water at 25oC when the atmospheric pressure is 102 kPa. What volume of pure oxygen would this be at STP?
102kPa – 3.167kPa = kPa = 99 kPa
Now we can use the Combined Gas Law
𝐏 𝟏 𝐕 𝟏 𝐓 𝟏 = 𝐏 𝟐 𝐕 𝟐 𝐓 𝟐
mL or with sig figs, 41 mL

24. Law of Combining Volumes
Formulated by Joseph-Louis Gay-Lussac in 1808
Under equivalent conditions, the volumes of reacting gases and their gaseous products are expressed in ratios of small whole numbers (mole ratios)
H2 + Cl2  2 HCl
2 H2 + O2  2 H2O
N2 + 3 H2  2 NH3

25. Avogadro’s Law
The volume of a gas, maintained at a constant temperature and pressure, is directly proportional to the number of moles of the gas
H2 + Cl2  2 HCl
2 H2 + O2  2 H2O
At STP, a volume of 22.4 L contains 1 mole of a gas
22.4 L is considered the molar volume of a gas
Does not matter what type of gas is being considered

26. Avogadro’s Law What volume would 4.00 mol of ammonia occupy at STP?
How many moles of a gas is contained in 420 L at STP?
What volume will 2.50 mol of hydrogen gas occupy at 300. K and at a pressure of 400. torr?
A sample of oxygen gas occupies 1.00 L when its temperature is K and its pressure is 129 kPa. How many moles of oxygen are present?

27. Densities of Gases Density is defined as mass per unit of volume
Just because a volume contains the same number of particles/molecules does not mean they have the same density
Density is what causes certain objects to float and to sink
Same idea with gases – Helium balloons
Explained by the molar volume concept
1 mole of gas occupies 22.4 L at STP
1 mole of a compound has a certain mass
Density at STP = 𝐌𝐨𝐥𝐚𝐫 𝐦𝐚𝐬𝐬 𝐌𝐨𝐥𝐚𝐫 𝐕𝐨𝐥𝐮𝐦𝐞 = g L

29. Densities Use 3 significant figures
What is the density of Hydrogen gas?
An unknown gas has a density of g/L at STP. What is its Molar Mass?
What is the density of carbon dioxide?

30. Mass (grams) Mass (grams) Mole Mole Particles Particles
Molar mass (periodic table)
Molar mass (periodic table)
Mass
(grams)
mole ratio
Mole
Mole
Particles
(atoms,
molecules,
formula units)
Particles
(atoms,
molecules,
formula units)
6.02 x 1023
6.02 x 1023

31. Stoichiometry
Using the following equation, what mass of aluminum acetate is made if 125 grams of acetic acid reacts with excess aluminum hydroxide?
3 C2H3O2H + Al(OH)3  Al(C2H3O2)3 + 3 H2O
125 g C2H3O2H x 𝟏 𝐦𝐨𝐥 𝐂 𝟐 𝐇 𝟑 𝐎 𝟐 𝐇 𝟔𝟎.𝟎𝟓𝟐𝟓𝟔 𝐠 𝐂 𝟐 𝐇 𝟑 𝐎 𝟐 𝐇 x 𝟏 𝐦𝐨𝐥 𝐀𝐥( 𝐂 𝟐 𝐇 𝟑 𝐎 𝟐 ) 𝟑 𝟑 𝐦𝐨𝐥 𝐂 𝟐 𝐇 𝟑 𝐎 𝟐 𝐇 x 𝟐𝟎𝟒.𝟏𝟏𝟓𝟑𝟗𝟖 𝐠 𝐀𝐥( 𝐂 𝟐 𝐇 𝟑 𝐎 𝟐 ) 𝟑 𝟏 𝐦𝐨𝐥 𝐀𝐥( 𝐂 𝟐 𝐇 𝟑 𝐎 𝟐 ) 𝟑
= 142 g Al(C2H3O2)3

32. Volume of Gas at nonstandard conditions
Mass
Volume of Gas at nonstandard conditions
Volume of Gas at STP
Number of Particles
Moles
Combined Gas Law
Coefficient from balanced equation
Molar Volume
Molar Mass
Mole Ratio
Avogadro’s Number

33. Stoichiometry
When 2.00 mol of Ca reacts with excess water, what volume of hydrogen gas will be produced at STP?
Ca + 2 H2O  Ca(OH)2 + H2
How many grams of water will be produced if L of oxygen gas at STP is burned with hydrogen?
2 H2 + O2  2 H2O

34. Stoichiometry
If 15.0 L of oxygen were used in the following reaction, determine the mass AND volume of carbon dioxide produced in the following reaction. Assume STP for both gases.
2 C4H O2  8 CO H2O
In the reaction above, if g of C4H10 were used in the reaction, what volume of CO2 will be produced at 755 torr and 20oC?

35. Ideal Gases A gas that behaves just as kinetic theory says it should
Not yet been found on Earth
Kinetic Theory assumes:
Gas molecules are very small
Molecules are far apart from each other
Forces act on the particles only during collisions

36. Ideal Gas Law
PV = nRT
Relates pressure, volume, temperature and number of moles
The value and units depend on the units used for P, V, n and T
R = L•atm mol•k
R = L•torr mol•k
How many moles of H2 is in a 3.1 L sample measured at atm and 20.oC?

37. Ideal Gas Law
How many moles of CO2 is in a 5.6 L sample measured at STP?
Calculate the volume of 4.50 mol of SO2 measured at STP.
What volume would the previous gas occupy at 25oC and 150 atm?
Make sure all units in your equations are the same
Don’t combine atm with torr, or L with mL