H o n o r r s s C h e m i i s s t t r r y
U n i i t t 1 4
( ( 2 0 1 3 2 0 1 4 )
G a s s L L a w s s







1

The kinetic-molecular theory is an explanation of the macroscopic properties of gases, using the idea of particle interactions and motions. This theory postulates, gas consists of very small particles that have mass; the distances separating gas particles are large; the particles are in constant, rapid, random motion; collisions of gas particles with each other, or the wall of the container are elastic; the average kinetic energy of the gas particles depends only on the temperature of the gas; gas particles exert no force on one another – the attractive forces between gas particles are very weak.
Standard Temperature and Pressure (STP) is the condition under which various properties of gases are normally measured and reported in order to make the discussion of the comparable behavior of gas convenient.
When the temperature remains constant the pressure and volume of a sample of gas are inversely proportional to each other. If the pressure remains constant, the volume of a fixed amount of gas is directly proportional to its absolute temperature. Absolute temperature is based on a scale that has its minimum temperature at absolute zero – theoretically, the lowest possible temperature that can be reached. In combination with the idea that equal volumes of gases at the same temperature and pressure contain an equal number of particles
(Avogadro’s Law), the physical behavior of an ideal gas is represented by an equation (PV=nRT) where R is the ideal gas constant (represented in multiple formats, 8.31 Joules/ (mole x K) is one example).
We are learning to:
Know the relationships between pressure, temperature volume and moles of gases
We are looking for:
Combined Gas Law P
1
V
1
/T
1
= P
1
V
1
/T
1
(moles must remain constant)
Avogadro’s Law V
1
/ n
1
= V
2
/ n
2
(pressure and temperature must remain constant)
Ideal Gas Law PV = nRT
Dalton’s Law of Partial Pressures P total = P1 + P2 + ….
Gas Stoichiometry (including volume and Molar Mass)
Standard Temperature and Pressure (STP) is 273K and 1atm
2

3

Kinetic-Molecular Theory of gases:
Used to explain the behavior and physical property of all gases.
Assumptions:

Gases consist of large number of tiny particles that are far apart relative to their size.

Collisions between gas particle and container are perfectly elastic.

Gas particles are in continuous, rapid, random motion.

There are no forces of attraction or repulsion between gas particles.

The average kinetic energy of gas particles depends on the temperature of the gas.
Ideal Gas = A gas that perfectly fits all of the assumptions of the kinetic-molecular theory
Pressure: force per unit area

Measured with a barometer

Units o Atmosphere (atm) = average atmospheric pressure at sea level at 0ºC o 1 atm = 760 mm of mercury (mm Hg) o 1 atm = 760 torr o 1 atm = 101.325 kiloPascals (kPa) o 1 atm = 14.7 pounds per square inch (psi)
Temperature: measure of the average kinetic energy of the particles

Measured with a thermometer

Units o Celsius (ºC) o Kelvin (K)
K = ⁰C + 273
Standard Temperature and Pressure (STP):
 used to compare volumes of gases
 pressure = 1atm
 temperature =273 K
1.00 atm = 101.3 kPa = 760 mm Hg = 29.92 in Hg = 14.7 psi
4

(1746 – 1823)

French Scientist

One of 1 st balloonists

Charles’s Law relates temperature and volume
V
1

V
2
T T
1 2
(1778 – 1850)

French Scientist

Another balloonist

Gay-Lussac’s Law relates temperature and pressure
P
1

P
2
T T
1 2
(1627 – 1691)


English Chemist

Considered “Father of Chemistry”

Lots of experiments; used quantitative methods
Boyle’s Law relates pressure and volume
1
P V
1

P V
2
=
5

(If a variable is not mentioned in the problem, assume that it is remaining constant)
Work the following out on a separate sheet of paper. Show your work with units!!
Don’t forget, temperature must be in Kelvin when working out the problems!
1.
I have an unknown volume of gas held at a temperature of 115 K in a container with a pressure of 60.0 atm. If by increasing the temperature to 225 K and decreasing the pressure to 30.0 atm causes the volume of the gas to be 29 liters, how many liters of gas did I start with?
2.
A balloon filled with helium gas has a volume of 500.0 mL at a pressure of 1.050 atm. The balloon is released and reaches an altitude of 6.50 km, and has expanded to a volume of 750.0 mL. If the temperature remains constant, what is the pressure, in kPa, of the gas inside the balloon at this height?
3.
A gas takes up a volume of 17 liters, has a pressure of 1748 mmHg, and a temperature of 299 K. If I raise the temperature to 350 K and lower the pressure to 1.5 atm, what is the new volume of the gas?
4.
A child receives a helium balloon filled with 2.30 L of helium from a vendor at an amusement park. The temperature outside that day is 31.0 ⁰C (87.8 ⁰F). What will the volume of the balloon be when the child brings it home to an air conditioned house at 21.5 ⁰C (70.7 ⁰C)?
5.
Divers get “the bends” if they come up too fast because gas in their blood expands, forming bubbles in their blood. If a diver has 0.050 L of gas in his blood under a pressure of 250 atm, then rises instantaneously to a depth where his blood has a pressure of 50.0 atm, what will the volume of gas in his blood be? Do you think this will harm the diver?
6.
A helium-filled balloon has a volume of 2.75 L at 20.0 o C. The volume of the balloon decreases to 2.46 L after it is placed outside on a cold day. What is the outside temperature in Kelvin? In o C?
7.
A gas has a temperature of 14 0 C, and a volume of 4.5 liters. If the temperature is raised to 29 0 C and the pressure is not changed, what is the new volume of the gas?
8.
On hot days, you may have noticed that potato chip bags seem to “inflate”, even though they have not been opened. If I have a 250. mL bag at a temperature of 35.0 0 C. I leave the bag in my closed car and the bag expands to 398 mL. What is the new temperature, in ⁰C, of the gas in the bag in my car?
9.
A gas that has a volume of 28 liters, a temperature of 45 0 C, and an unknown pressure has its volume increased to 34 liters and its temperature decreased to 35 0 C. If I measure the pressure after the change to be 2.0 atm, what was the original pressure of the gas?
10.
A soda bottle is flexible enough that the volume of the bottle can change even without opening it. If you have an empty soda bottle (volume of 2.0 L) at room temperature (25 0 C), what will the new volume be if you put it in your freezer (-4.0 0 C)?
11.
At standard temperature a gas is 90.2 kPa of pressure. If the pressure on the gas is raised to standard in kPa, what is the new temperature in o C?
6

12.
I have an unknown volume of gas at a pressure of 0.50 atm and a temperature of 325 K. If I raise the pressure to 1.2 atm, decrease the temperature to 320 K, and measure the final volume to be 48 liters, what was the initial volume of the gas?
13.
If I initially have a gas at a pressure of 12 atm, a volume of 23 liters, and a temperature of 200.0 K, and then I raise the pressure to 14 atm and increase the temperature to 300.0 K, what is the new volume of the gas?
14.
If I have 17 liters of gas at a temperature of 67 0 C and a pressure of 88.89 atm, what will be the pressure of the gas (in kPa) if I raise the temperature to 94 0 C and decrease the volume to 12 liters?
15.
A gas occupies a volume of 907 mL at 19.0 o C. What will be the new volume of the gas when the temperature is changed to standard temperature?
16.
The gas in an aerosol can is at a pressure of 3.00 atm at 25.0 o C. Directions on the can warn the user not to keep the can in a place where the temperature exceeds 52.0 o C. What would the gas pressure in the can be at this temperature?
17.
If I have 21 liters of gas held at a pressure of 78 atm and a temperature of 900.0 K, what will be the volume of the gas if I decrease the pressure to 45 atm and decrease the temperature to 750 K?
18.
If a sample of chlorine gas occupies a volume of 259 mL at 112 kPa, what will the new volume be when the pressure becomes the standard pressure value?
19.
Before a trip from New York to Boston, the pressure in an automobile tire is 1.8 atm at a temperature of
20.0 ⁰C. At the end of the trip, the pressure gauge reads 1.9 atm. What is the new Celsius temperature of the air inside the tire?
20.
If I have 2.9 L of gas at a pressure of 5.0 atm and a temperature of 50.0
0 C, what will be the temperature of the gas if I decrease the volume of the gas to 2.4 L and decrease the pressure to 3.0 atm?
7

(1776 – 1856)

Italian scientists

Equal volumes of gases under the same temperature and pressure will contain the same number of molecules.

Avogadro’s Law relates volume and number of moles of a gas (n).
V
1

V
2 n n
1 2
1.
A 5.60 L balloon contains 1.20 moles of Helium. How large will the balloon be with 3.40 moles of Helium?
Assume constant Pressure and Temperature.
2.
A 4.00 L balloon contains 0.21 moles of Helium. How much Helium must be added in order for the balloon to be 7.12L? Assume constant Pressure and Temperature.
3.
3O
2
 2O
3
(Ozone)
We have a sample of oxygen gas that has a volume of 15.0 liters and contains 0.750 moles of gas. If all of the oxygen is converted to ozone, at constant temperature and pressure, what will the volume of the ozone be?
8

=

L atm mole K
R

PV nT
PV
 nRT
Using the ideal gas law, what is the volume of mole of gas at the conditions of STP?
What volume would 100.0 grams of oxygen (O
2
) have at STP?
9

"Ideal Gas Law"
Directions: Complete the following problems on a separate sheet of paper. Show ALL work. Use the factor label method for ALL conversions.
1) If I have 4.0 moles of a gas at a pressure of 5.6 atm and a volume of 12 liters, what is the temperature?
2) If I have an unknown quantity of gas at a pressure of 1.2 atm, a volume of 31 liters, and a temperature of 87 0 C, how many moles of gas do I have?
3) If I contain 3.0 moles of gas in a container with a volume of 60.0 Liters and at a temperature of 400.0 K, what is the pressure inside the container?
4) If I have 7.7 moles of gas at a pressure of 0.090 atm and at a temperature of 56 0 C, what is the volume of the container that the gas is in?
5) If I have 17 moles of gas at a temperature of 67 0 C, and a volume of 88.89 liters, what is the pressure of the gas?
6) If I have an unknown quantity of gas at a pressure of 0.50 atm, a volume of 25 liters, and a temperature of 300.0 K, how many moles of gas do I have?
7) If I have 21 moles of gas held at a pressure of 78 atm and a temperature of 900.0 K, what is the volume of the gas?
8) If I have 1.9 moles of gas held at a pressure of 5.0 atm and in a container with a volume of 50.0 Liters, what is the temperature of the gas?
9) If I have 2.4 moles of gas held at a temperature of 97 0 C and in a container with a volume of 45 Liters, what is the pressure of the gas?
10) If I have an unknown quantity of gas held at a temperature of 1195 K in a container with a volume of 25 liters and a pressure of 560 atm, how many moles of gas do I have?
11) If I have 0.275 moles of gas at a temperature of 75 K and a pressure of 1.75 atmospheres, what is the volume of the gas?
12) If I have 72 liters of gas held at a pressure of 3.4 atm and a temperature of 225 K, how many moles of gas do I have?
13) A sample of nitrogen gas has a pressure of 2.50 atm at a temperature of 25

C. What temperature is required to increase the pressure to 4.00 atm, assuming that the volume is fixed and the amount of gas does not change?
14) A sample of oxygen gas has a volume of 7.84 cm 3 at a pressure of 71.8 kPa and a temperature of 25 the volume of the gas if the pressure is changed to 101 kPa and the temperature is changed to 0.00


C. What will be
C?
15) A sample of hydrogen gas, H
2
, has a volume of 4003 mL at a temperature of -27

C and a pressure of 820 mmHg.
Calculate the number of grams of H
2
present in this gas sample.
16) At what temperature does 3.20 g of oxygen gas occupy a volume of 65.0 L at a pressure of 100,345 Pa?
17) You have 5.00 moles of gas in a 4.50 L container. The pressure in the container is initially 700.0 torr at a temperature of 26.0

C. What will the new pressure of the gas be if the volume expands to 8.65 L, the temperature increases to 35.0

C, and the number of moles of the gases is decreased to 3.00 moles?
10

(1766 – 1844)

English chemist

The total pressure exerted by the mixture of non-reactive gases is equal to the
sum of the partial pressures of individual gases.
P
T

P
1

P
2

P
3
Example:
1) Calculate the pressure in a container that contains O
2
gas at a pressure of 3.22 atm and N
2
gas at a pressure of
1.29 atm.
2) The pressure in a room is caused by the pressure exerted by the air in the room and this pressure is referred to as atmospheric pressure. The air is a mixture of gasses consisting of approximately 78% N
2
, 21% O
2
& 1% other gases.
If the atmospheric pressure in the room is 760 mmHg, what pressure is the pressure exerted by the N
2
?
What is the pressure exerted by the O
2
?
3) If I place 3.00 moles of N
2
and 4.00 moles of O
2
in a 35.0 L container at a temperature of 25.0 0 C, what will the pressure of the resulting mixture of gases be?
4) Two flasks are connected with a stopcock. The first flask has a volume of 5.00 liters and contains nitrogen gas at a pressure of 0.750 atm. The second flask has a volume of 8.00 L and contains oxygen gas at a pressure of 1.25 atm. When the stopcock between the flasks is opened and the gases are free to mix, what will the pressure be in the resulting mixture?
\
11

More Dalton’s Law of Partial Pressures Worksheet
1.
A mixture of neon and argon gases exerts a total pressure of 2.39 atm. The partial pressure of the neon alone is 1.84 atm, what is the partial pressure of the argon?
2.
Oxygen and chlorine gas are mixed in a container with partial pressures of 401 mmHg and 0.639 atm, respectively.
What is the total pressure, in atm, inside the container?
3.
The stopcock between a 3.00 L bulb containing oxygen at 295.0 torr and a 1.00 L bulb containing nitrogen at 530.0 torr is opened. What is the total pressure of the mixture (assume constant T = 25.0 o C)?
4.
Oxygen is pumped into a tank to supply breathing air for scuba diving, until the gas pressure reaches 4.05 atm. Helium is then pumped in until the total pressure is 20.00 atm. The gases mix completely. What is the partial pressure of each gas in the tank?
5.
A metal tank contains three gases: oxygen, helium, and nitrogen. If the partial pressures of the three gases in the tank are 35 atm of O
2
, 3800 torr of N
2
, and 367.5 psi of He, what is the total pressure inside of the tank?
12

Gases, since they mix with other gases readily, must be collected in an environment where mixing can not occur. The easiest way to do this is under water because the gas displaces the water. So when a gas is collected “over water”, that means the container is completely filled with water and the gas is bubbled through the water into the container. Water is always evaporating at the surface creating gaseous water (water vapor). Thus, the pressure of the gases collected over the water inside the container is from the gas AND the water vapor. This is where Dalton’s Law of Partial
Pressures becomes useful. The pressure exerted by the water vapor is related to the temperature of the liquid water in the container. The higher the water temperature, the more the water will evaporate and hence exert more pressure. You will be provided with a table that gives the vapor pressure values for various water temperatures (reference table below).
Vapor Pressure of Water
Temperature o C
0
3
5
Pressure
kPa
0.60
0.80
0.90
Temperature o C
20
21
22
Pressure
kPa
2.30
2.50
2.60
Temperature o C
30
32
35
Pressure
kPa
4.20
4.80
5.60
8
10
12
14
16
18
1.10
1.20
1.40
1.60
1.80
2.10
23
24
25
26
27
28
2.80
3.00
3.20
3.40
3.60
3.80
40
50
60
70
80
90
7.40
12.30
19.90
31.20
47.30
70.10
19 2.20 29 4.00 100 101.30
Practice Problems:
1) A student collects hydrogen gas over water. The temperature of the water is 20.0 ⁰C and the pressure of the gas sample collected over the water is 768 mm Hg. What is the pressure exerted by hydrogen gas?
2) 888 cm 3 of oxygen are collected over water with a temperature of 27.0 o C. The total pressure of the gases is 55.8 kPa.
What is the partial pressure of the dry gas, in kPa?
13

3) Carbon Dioxide gas is collected over water which is at 17.0 ⁰C . The pressure of the gas sample is 97.932 kPa. What is the pressure exerted by the CO
2
gas, in kPa?
4) A 450 cm 3 sample of hydrogen is collect over water at 12 o C. The pressure of the hydrogen and water vapor mixture is
78.5 kPa. What is the partial pressure of the dry hydrogen gas, in kPa?
5) A sample of nitrogen gas is collected over water at 20.0
o C and a pressure of 1.00 atm. The volume of the collected gas is 250.0 L. What is the mass of N
2
collected?
Ptotal = Pnitrogen + Pwater
More Dalton’s Law of Partial Pressures Problems
Solve the following problems on a separate sheet of paper.
1) Blast furnaces give off many unpleasant and unhealthy gases. If the total air pressure is 754 mmHg, the partial pressure of carbon dioxide is 0.050 atm, and the partial pressure of hydrogen sulfide is 0.020 atm, what is the partial pressure, in atm, of the remaining air?
2) If the air from problem 1 contains 22% oxygen, what is the partial pressure of oxygen near a blast furnace?
3) A container with two gases, helium and argon, is 30.0% by volume helium. Calculate the partial pressure of helium and argon if the total pressure inside the container is 4.00 atm.
4) If 60.0 L of nitrogen is collected over water at 40.0 °C when the atmospheric pressure is 760.0 mm Hg, what is the partial pressure of the nitrogen?
5) 80.0 liters of oxygen is collected over water at 50.0 °C. The atmospheric pressure in the room is 96.00 kPa. What is the partial pressure of the oxygen?
6) A tank contains 480.0 grams of oxygen and 80.00 grams of helium at a total pressure of 7.00 atmospheres.
Calculate the partial pressure of O
2 and He.
7) A mixture of 14.0 grams of hydrogen, 84.0 grams of nitrogen, and 2.0 moles of oxygen are placed in a flask at standard temperature. When the partial pressure of the oxygen is 78.00 mm of mercury, what is the total pressure in the flask?
8) Two flasks at the same temperature are joined by a glass tube with a stopcock. Flask A is a 4.0 L flask containing
N
2
(g) at 2.0 atm, while flask B is a 10.0 L flask containing CO(g) at 1.4 atm. What is the final pressure in the flasks after the stopcock is opened?
14

Work out the following problems on a separate sheet of paper. Use the gas laws and your prior knowledge of stoichiometry (grams of “A” to grams of “B”) to solve the following problems:
1.
How many moles of nitrogen gas is needed to react with 44.8 liters of hydrogen gas to produce ammonia gas at STP? N
2 (g)
+ 3 H
2 (g)
 2 NH
3 (g)
2.
How many liters of ammonia are produced when 89.6 liters of hydrogen are used in the above reaction from
#1?
3.
When 11.2 liters of hydrogen gas at STP is made by adding zinc to sulfuric acid, what mass of zinc is needed? Zn
(s)
+ H
2
SO
4 (aq)
 H
2 (g)
+ ZnSO
4 (aq)
4.
How many grams magnesium hydroxide do you need to use in the following reaction to produce 500. L of ammonia gas at STP? Mg(OH)
2
+ (NH
4
)
2
SO a
 MgSO
4
+ 2 H
2
O + 2 NH
3 (g)
5.
If 1.39 g of carbon monoxide is reacted with oxygen, what volume of carbon dioxide is produced at 12.3
o C at 107.4KPa? 2 CO
(g)
+ O
2 (g)
 2 CO
2 (g)
6.
If 14.4 L of ethane is combusted at 102.7
o
2 C
2
H
6 (g)
+ 5 O
2 (g)
C and 744.8 mmHg, how many grams of water will be produced?
 4 CO
2 (g)
+ 6 H
2
O
(g)
7.
Exhaust fumes are sometimes used to fill large airbags to upright flipped tractor trailers. What mass of
C
8
H
18
must be burned in order to fill a 1.40 L airbag with CO
2 (g)
if the wrecker truck burns octane at STP?
For simplification, assume water produced is in liquid form.
2 C
8
H
18
+ 25 O
2 (g)
 16 CO
2 (g)
+ 18 H
2
O
8.
If 34.6g of Zn are reacted with an excess of hydrochloric acid at standard pressure, what is the temperature of the hydrogen gas produced if it occupies a 2.00 L
Zn + 2 HCl  H
2 (g)
+ ZnCl
2 container?
9.
Your car burns motly octane, C
8
H
18
, as a fuel. Assuming complete combustion, how many liters of oxygen gas are needed to burn 1.00 kg of octane if your engine’s temperature is 93.3˚C at standard pressure?
2 C
8
H
18
+ 25 O
2 (g)
 16 CO
2 (g)
+ 18 H
2
O
10.
Oxygen gas and hydrogen gas combine to make water. What volume of oxygen is needed to react with 47.8 liters of hydrogen at 2.30atm and 54.0 ˚C?
2 H
2 (g)
+ O
2 (g)
 2 H
2
O
15

"Review of All Gas Laws"
Work the following problems out on a separate sheet of paper.
1) A gas exerts a pressure of 0.892 atm in a 5.00 L container at 15.0 degrees Celsius. The density of the gas is 1.22 g/L. What is the molar mass of the gas? What is the formula of this diatomic gas?
2) A 25.00 mL sample of gas is enclosed in a flask at 22.0 degrees Celsius. If the flask was placed in an ice bath at 0.00 degrees
Celsius, what would the new gas volume, in Liters, be if the pressure is held constant?
3) How many moles of gas are contained in 890.0 mL at 21.0 °C and 750.0 mm Hg pressure?
4) 0.00109 kg of H
2
is contained in a 2.00 L container at 20.0 °C. What is the pressure in this container in kPa
5) What volume, in Liters, will 20.00 g of Argon occupy at STP?
6) The initial pressure and volume of a sample of nitrogen gas is 5.09 torr and 40.00 L respectively. If the volume is cut in half, what is the new pressure, in atm?
7) At what temperature (in o C) will 0.654 moles of neon gas occupy 12.30 liters at 1.95 atmospheres?
8) A 62.0 g gas sample occupies 11.2 L at STP. Find the molar mass of this gas.
9) 96.0 g of a gas occupies 48.0 L at 700.0 mm Hg and 20.0 °C. What is its molar mass?
10) A 50.00 liter tank at - 15.00 °C contains 14.00 grams of helium gas and 10.00 grams of nitrogen gas. a) Determine the moles of helium gas in the tank. b) Determine the moles of nitrogen gas in the tank. c) Determine the partial pressure of helium gas in the tank. d) Determine the partial pressure of nitrogen gas in the tank. e) Determine the total pressure of the mixture in the tank.
16

Name __________________________________
Honors Chemistry Problems
"R Lab Practice"
1) You conduct an experiment to determine the value for R, the universal gas constant. You decide to use a canister of carbon dioxide. The CO
2
canister had an initial mass of 17.099 g. After filling an inverted cylinder in water with 347 mL of the gas, the canister then had a final mass of 16.524g. The temperature of the room was 23.5 ˚C, the temperature of the water was 17.0 ˚C, and the pressure in the room was
97.932 kPa.
Vapor Pressure of Water a.
Why is it important to make sure the water level inside and outside the cylinder match when reading the volume of gases? o C kPa o C kPa o C kPa
0 0.60 20 2.30 30 4.20
3 0.80 21 2.50 32 4.80 b.
Determine the value for R, the universal gas constant, using the experimental data above.
5 0.90 22 2.60 35 5.60
8 1.10 23 2.80 40 7.40
10 1.20 24 3.00 50 12.30
12 1.40 25 3.20 60 19.90
14 1.60 26 3.40 70 31.20
16 1.80 27 3.60 80 47.30
18 2.00 28 3.80 90 70.10
19 2.20 29 4.00 100 101.30 c.
Determine the percent error from the accepted value for R.
17