Honors text: Ch 13.1 and 14 (all)
Unit 07
NOTES: Behavior of Gases
Properties of Gases
• Gases have weight
• Gases take up space
• Gases exert pressure
• Gases fill their containers
• Gases are mostly empty space
• The molecules in a gas are separate, very small and very far apart
Kinetic Theory of Matter:
 Gas molecules are in constant, chaotic motion
 Collisions between gas molecules are elastic (there is no energy gain or loss)
 The average kinetic energy of gas molecules is directly proportional to the absolute temperature
 Gas pressure is caused by collisions of molecules with the walls of the container
Measurement of Gases
To describe a gas, its volume, amount, temperature, and pressure are measured.
• Volume:
• Amount:
• Temperature:
• Pressure:
Units of Pressure:
1 atmosphere =
=
=
=
=
Intro to Gas Laws:
Boyle’s Law: relation of volume to pressure
Example: A sample of gas occupies 12 L under a pressure of 1.2 atm. What would its volume be if the pressure
were increased to 3.6 atm? (assume temp is constant)
Honors text: Ch 13.1 and 14 (all)
Unit 07
Charles’ Law: relation of volume to temperature
**temp must be expressed in Kelvin!
Example: A sample of nitrogen gas occupies 117 mL at 100°C. At what temperature would it occupy 234 mL if the
pressure does not change? (express answer in K and °C)
Standard Temperature & Pressure (STP): 0°C (273 K) and 1 atm (760 torr, 760 mm Hg)
The Combined Gas Law Equation
Examples:
1. A sample of neon gas occupies 105 L at 27°C under a pressure of 985 torr. What volume would it occupy at
standard conditions?
2. A sample of gas occupies 10.0 L at 240°C under a pressure 80.0 kPa. At what temperature would the gas occupy
20.0 L if we increased the pressure to 107 kPa?
3. A sample of oxygen gas occupies 23.5 L at 22.2°C and 1.3 atm. At what pressure (in mm Hg) would the gas
occupy 11.6 L if the temperature were lowered to 12.5°C?
Honors text: Ch 13.1 and 14 (all)
Unit 07
Gases: Standard Molar Volume & The Ideal Gas Law
• Avogadro’s Law: at the same temperature and pressure, equal volumes of all gases contain the same # of molecules
(moles).
• Standard Molar Volume =
(this is true of “ideal” gases; at reasonable temperatures & pressures, the behavior of many “real” gases is nearly ideal)
Example: 1.00 mole of a gas occupies 36.5 L, and its density is 1.36 g/L at a given temperature & pressure.
a) What is its molecular weight? (molar mass)
b) What is the density of the gas at standard conditions?
The Ideal Gas Law: shows the relationship among the pressure, volume, temp., and the # of moles in a sample of gas.
Where,
P
=
V
=
n
=
T
=
R
=
=
(the units of R depend on the units used for P, V, and T)
Examples:
1) What volume would 50.0 g of ethane, C2H6, occupy at 140°C under a pressure of 1820 torr?
2) Calculate: a) the # of moles in, and (b) the mass of an 8.96 L sample of methane, CH4,
measured at standard conditions.
3) Calculate the pressure exerted by 50.0 g of ethane, C2H6, in a 25.0 L container at 25°C.
Honors text: Ch 13.1 and 14 (all)
Unit 07
CALCULATION using MM and D: Use PM = dRT (a derivation of PV = nRT)
** You can still use and rearrange PV = nRT, but PM = dRT is easier
#46 in honors textbook:
How many grams of gas are present in a sample that has a molar mass of 70,0 g/mol and occupies a 2.00 L container at
117 kPa and 35.1 °C.
Extra practice #49 pg. 438 in honors textbook.
Determining Molecular Weights & Molecular Formulas of Gases: if the mass of a volume of gas is known, we can use
this info. to determine the molecular formula for a compound.
Examples:
1) A 0.109 g sample of a pure gaseous compound occupies 112 mL at 100°C and 750 torr. What is the molecular
weight of the compound?
2) A compound that contains only C and H is 80.0% C and 20.0% H by mass. At STP 546 mL of the gas has a mass of
0.732 g. What is the molecular (true) formula for the compound?
Notes: Partial Pressures and mole Fraction (Dalton’s Law)
In a mixture of gases each gas exerts the pressure it would exert if it occupied the volume alone.
The total pressure exerted by a mixture of gasses is the sum of the partial pressures of the individual gases:
Example: If 100.0 mL of hydrogen gas, measured at 25ºC and 3.00 atm, and 100.0 mL of oxygen, measured at 25ºC and
2.00 atm, what would be the pressure of the mixture of gases?
Honors text: Ch 13.1 and 14 (all)
Unit 07
Vapor Pressure of a Liquid: (values can be found at http://www.watervaporpressure.com/)
Temp (ºC)
18
19
20
21
22
v.p. of water
(mm Hg)
15.48
16.48
17.54
18.65
19.83
Temp. (ºC)
23
24
25
26
27
v.p. of water
(mm Hg)
21.07
22.31
23.76
25.14
26.74
Example: A sample of hydrogen gas was collected by displacement of water at 25C. The atmospheric pressure was
748 mm Hg. What pressure would the dry hydrogen exert in the same container?
Example: A sample of oxygen was collected by displacement of water. The oxygen occupied 742 mL at 27C. The
barometric pressure was 753 mm Hg. What volume would the dry oxygen occupy at STP?
Example: A student prepares a sample of hydrogen gas by electrolyzing water at 25C. She collects 152 mL of H2 at a
total pressure of 758 mm Hg. Calculate (a) the partial pressure of hydrogen, and (b) the number of moles of
hydrogen collected.
Graham’s Law of Diffusion & Effusion
Where,
Rate = rate of diffusion or effusion
MM=molar mass
Stoichiometry of Gaseous Reactions
A balanced equation can be used to relate moles or grams of substances taking part in a reaction. (AND VOLUME!)
Example: Hydrogen peroxide is the active ingredient in commercial preparations for bleaching hair. What mass of
hydrogen peroxide must be used to produce 1.00 L of oxygen gas at 25 C and 1.00 atm?
Honors text: Ch 13.1 and 14 (all)
Unit 07
Wkst 1: COMBINED GAS LAW
In practical terms, it is often difficult to hold any of the variables constant. When there is a change in pressure,
volume and temperature, the combined gas law is used.
P1 x V1 P2 x V2

or P1V1T2  P2 V2 T1
T1
T2
Complete the following chart.
1
2
3
P1
V1
T1
P2
1.5 atm
3.0 L
20. C
2.5 atm
720 torr
256 mL
25 C
600. mmHg
2.5 L
22 C
760 mmHg
750 mL
0.0 C
2.0 atm
500. mL
25 C
101 kPa
6.0 L
198 C
900. torr
225 mL
150.  C
2.5 L
30.  C
100. mL
75 C
4
5
6
7
8
95 kPa
4.0 L
650. torr
100.  C
850 mmHg
1.5 L
125 mL
125 mL
100. kPa
T2
30.  C
250 mL
15 C
Show your work here for at least the first example:
V2
50.  C
1.8 L
Honors text: Ch 13.1 and 14 (all)
Unit 07
Wkst 2: IDEAL GAS LAW
P = pressure in atmospheres
V = volume in liters
n = number of moles
R = Universal Gas Constant = 0.0821 L  atm
mol  K
T = Kelvin temperature
1.
At what temperature will 5.00 g of Cl2 exert a pressure of 900. torr at a volume of 750. mL?
2. What is the density of NH3 at 800. torr and 25 C?
3. If the density of a gas is 1.2 g/L at 745. torr and 20. C, what is the molar mass?
4. Find the number of grams of CO2 that exert a pressure of 785 torr at the volume of 32.5 L and a temperature
of 32 C.
5. An elemental gas has a mass of 10.3 g. If the volume is 58.4 L and the pressure is 758 torr at a temperature of
2.5 C, what is the gas?
Honors text: Ch 13.1 and 14 (all)
Unit 07
Wkst 3: DALTON’S LAW OF PARTIAL PRESSURES
Dalton’s Law says that the sum of the individual pressures of all gases that make up a mixture is equal to the
total pressure or: PT = P1 + P2 + P3 + … The particle pressure of each gas is equal to the mole fraction of each
gas  total pressure.
PT  P1  P2  P3  ... or
moles gas x
x PT  Px
total moles
Solve the following problems.
1. A 250 mL sample of oxygen is collected over water at 25 C and 760.0 torr
pressure. What is the pressure of the dry gas alone? (Vapor pressure of water at
25 C = 23.8 torr)
2. A 32.0 mL sample of hydrogen is collected over water at 20.  C and 750.0 torr
pressure. What is the volume of the dry gas at STP? (Vapor pressure of water at
20.  C = 17.5 torr)
3. A 54.0 mL sample of oxygen is collected over water at 23 C and 770.0 torr
pressure. What is the volume of the dry gas at STP? (Vapor pressure of water at
23 C = 21.1 torr)
4. A mixture of 2.00 moles of H2, 3.00 moles of NH3, 4.00 moles of CO2 and 5.00
moles of N2 exerts a total pressure of 800. torr. What is the partial pressure of
each gas?
5. The partial pressure of F2 in a mixture of gases where the total pressure is 1.00
atm is 300. torr. What is the mole fraction of F2?
Honors text: Ch 13.1 and 14 (all)
Unit 07
Wkst 4: Graham’s Law of Diffusion/Effusion
Graham’s Law says that gas will effuse at a rate that is inversely proportional to the square root of its molecular
mass, MM. Express mathematically:
rate1
MM 2

rate 2
MM1
Solve the following problems.
1. Under the same conditions of temperature and pressure, how many times faster
will hydrogen effuse compared to carbon dioxide?
2. If the carbon dioxide in Problem 1 takes 32 sec to effuse, how long will the
hydrogen take?
3. What is the relative rate of diffusion of NH3 compared to He? Does NH3 effuse
faster or slower than He?
4. If the He in Problem 3 takes 20 sec to effuse, how long will the NH3 take?
5. An unknown gas diffuses 0.25 times as fast as He. What is the molecular mass of
the unknown gas?
Honors text: Ch 13.1 and 14 (all)
Unit 07
Wkst 5: Gas Laws Problem Set
1 atm = 760 mm Hg = 760 torr = 101.3 kPa = 1.013 bar
PV = nRT
R = 0.0821 L•atm / mol•K
1. A sample of carbon dioxide has a volume of 2.5 L at a temperature of –10°C. What volume will this sample have when the
temperature is increased to 110°C? (assume pressure is constant)
2. What is the volume occupied by 10.0 L of gas at 1.2 atm after it has been compressed (at a constant temperature) to 3.5 atm?
3. A sample of nitrogen gas having a volume of 2.55 L is collected at a pressure of 0.67 atm. What volume will the gas occupy when
its pressure is changed to 1.45 atm if the temperature is held constant?
4. A gas has a pressure of 5.7 atm at 100.0°C. What is its pressure at 20.0°C? (assume volume is unchanged)
5. If a scuba diver is to remain submerged for 1 hour, what pressure must be applied to force sufficient air into the tank to be used?
Assume 0.500 L of air per breath at STP, a respiration rate of 38 breaths per minute, and a tank capacity of 30.0 L.
Honors text: Ch 13.1 and 14 (all)
Unit 07
6. Freon-12, dichlorodifluoromethane (CCl2F2), was a widely-used refrigerant. Consider a 2.23 L sample of gaseous Freon at a
pressure of 0.05 atm and a temperature of –1.36°C. Calculate the volume of the gas at a pressure of 0.01 atm and a temperature of
5.5°C.
7. If a sample of gas occupies 4.4 L at 19°C and 0.9 atm, what volume will the same gas occupy at STP?
8. What volume will 64.0 g of oxygen gas (O2) occupy at STP?
9. A 28.02 g sample of nitrogen (N2) is sealed in a 6.00 L container and heated to a temperature of 327°C. What is the pressure of
the gas?
10. A helium-filled weather balloon has a volume of 7,775 L. How many grams of helium would be required to inflate this balloon to
a pressure of 745 mm Hg at 21.0°C
11. Analysis of a gas shows that it contains 85.7% carbon and 14.3% hydrogen by mass. At standard conditions, 100.0 mL of the
compound has a mass of 0.188 gram. What is its molecular weight (molar mass)? What is its molecular formula?
Honors text: Ch 13.1 and 14 (all)
Unit 07
Wkst 6: Study Guide - Gases
Objectives:
1. Use Boyle’s Law, Charles’ Law, Avogadro’s Law, and the combined gas law, as appropriate, to calculate changes in pressure, volume, temperature, and
amount of gas.
2. Use the ideal gas law equation to do calculations about a sample of gas.
3. Do calculations involving gas densities and the standard molar volume.
4. Determine molecular weights and formulas of gaseous substances from measured properties of gases.
5. Carry out calculations with gaseous compounds involved in chemical reactions (volume, mass, # of moles, etc.)
6. Use the law of partial pressure to calculate the pressure exerted by gases in a mixture (including gases collected over a liquid; factor in vapor pressure of
the liquid)
7. Describe the kinetic-molecular theory of gases, and how this theory is consistent with the observed gas laws.
Equations:
Combined gas law:
P1V1 / T1 = P2V2 / T2
Ideal gas law:
PV = nRT, where R = 0.0821 Latm / molK
Partial pressure:
Graham’s Law of Effusion:
Ptotal
=
P1 + P2 + P3 + …
Pgas
=
Patm – PH2O
rate1
=
rate 2
MM 2
MM 1
Problems:
1. A 250.0 mL volume of gas is collected at 30.0C. What volume would the sample of gas occupy at 20.0C,
assuming constant pressure?
2. A 3.00 L pocket of air at sea level has a pressure of 1.00 atm. Suppose the air pocket rises in the atmosphere to
a certain height and expands to a volume of 10.0 L. What is the pressure of the air at the new volume? (assume
constant temperature)
3. A weather balloon has a volume of 1750. L at 1.10 atm. The balloon is released into the atmosphere. At the
highest point above the ground, the pressure on the balloon is 0.350 atm. What is the new volume of the
balloon at this height? (assume constant temp.)
4. A gas with a pressure of 875 mm Hg at 305C occupies 2.50 L. What volume will the gas occupy at STP?
5. What volume will 5.70 mol of nitrogen gas, N2, occupy at 54.0C and 675 mm Hg?
Honors text: Ch 13.1 and 14 (all)
Unit 07
6. A 54.76 g sample of carbon dioxide gas is sealed in a 7.55 L container and heated to a temperature of 354C.
What is the pressure of the gas?
7. Calculate the mass of oxygen gas, O2, measured at 1765 mm Hg and 35.5C in 4.35 L.
8. How many grams of helium, He, will be required to fill 12 balloons at STP, assuming that each balloon has a
volume of 455 mL?
9. What is the molecular weight of a gas that occupies a volume of 278 mL, at a pressure of 680.0 mm Hg, a
temperature of 21.7C, and a mass of 35.9 g?
10.
What is the molecular weight of an ideal gas if 0.520 g of the gas occupies 610.0 mL at 385 mm Hg and 45.0C?
11.
Analysis of a gaseous compound shows that it contains 85.7% carbon and 14.3% hydrogen by mass. At standard
conditions, 100.0 mL of the compound has a mass of 0.188 gram. What is its molecular formula?
12.
Calculate the density of NO2 gas, in g/L, at 1.24 atm and 50.0C?
13.
A 300.0 mL sample of hydrogen was collected over water 21.0C on a day when the atmospheric pressure was
748 mm Hg.
a)
What is the partial pressure of the hydrogen gas?
b)
How many moles of H2 were present?
c)
What would be the mass of the hydrogen sample if it were dry?