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Name: ___________________________________________

Block: ____________

Unit 9 Packet: Gas Laws

Introduction to Gas Laws Notes:

• Gas Variables:

o Pressure (P) -

o Temperature (T) -

o Volume (V) –

o Moles (n)

Relationship of Variables

V T n

P

V

T

Equations Representing Relationships:

Standard Temperature and Pressure (STP):

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Pressure and Kinetic Molecular Theory Notes

What is pressure?

�������� =����

���

What is force? You can think of it like weight or like a push. How much does your body push on the

floor? How much do you have to push to move something across the floor?

Liquids and solids exert pressure.

Ex: Diving, your body is under more pressure when under water than when above it.

If you are trapped under a piece of furniture you feel the pressure of the furniture on

you.

What does area have to do with it?

Could you sleep on a bed of nails? How about just one nail?

Carpenters…why are screws pointy at the end instead of flat?

The same force over a smaller area results in a higher pressure.

Gas pressure is similar but hard to visualize.

KINETIC MOLECULAR THEORY

1. Gases have a very small ______________

2. Gases are constantly in ______________at high speeds in random but ____________ line

paths

3. Gases experience no _____________ attractions between ___________

a. All collisions between particles in a gas are

perfectly __________________.

i. No attractive or repulsive forces

ii. No transfer of Kinetic Energy

iii. The average Kinetic Energy is

dependent only on _____________

4. The speed of a gas molecule is directly ______________to its mass and speed.

a. As the temperature increases, the speed of the gas molecule ___________.

These assumptions are good for IDEAL gases and are used quite often with little error. However,

when one needs to be exact that you must account for the fact that REAL gases

• Have volume

• Experience electrostatic attractions

For Introductory Chemistry, though, we will just deal with Ideal gases.

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Pressure is the sum of all the forces of all the gas molecules colliding with a surface.

Gas particles are in __________ _,________ __, ____ ______; exerting pressure as they

collide with the walls of the container. Therefore, the ______ ____collisions, the ______

_____the pressure.

Gases have certain properties that can be explained by the KMT.

1. Low Density they _____________ because the molecules are moving at a high rate of speed and

are not held back by electrostatic attractions as well as being spread out, they have low density.

2. Compressibility, they can be _____________ to compress because the molecules have space

between them, unlike liquids and solids where there is little space between the molecules

3. Expansion, they will __________ given the opportunity because the molecules are moving at a

high rate of speed.

4. Diffusion they will spread out, again because the

molecules are moving at a high rate of speed,

a. Example: perfume diffusing through air

b. Example: Liquids also diffuse: food coloring in water

5. Effusion, molecules moving at a high rate of speed will

eventually “collide” with a hole and escape.

a. Effusion is gas escaping through a hole,

b. Example: air escaping through a hole in your tire

Units of pressure

• Kilopascals = SI units of pressure, named after scientist Pascal

• Torr = named after scientist Torricelli

• mmHg = millimeters of mercury, comes from old way of measuring pressure by the height of a

column of mercury open to atmosphere

• atm = atmosphere, unit most often used in chemistry. One atmosphere is what we feel

experience every day. It is the standard pressure on earth.

• psi = pounds per square inch. Most often used in real life (tire pressure)

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Gas Laws Notes

Steps to Solve any Gas Law Problem: o Step 1: Write everything you are given in the problem.

o Step 2: Which law do you want to use? (What remains constant?)

o Step 3: Do your units match? If not, convert. (Temperature must always be in Kelvin)

o Step 4: Plug in your values and solve.

• Boyle's Law

o As the pressure decreases, the volume increases.

o Indirectly proportional

o Temperature remains constant

Example Problem: A balloon contains 30.0 L of helium gas at 1 atmosphere, and it rises to an altitude

where the pressure is only 0.25 atm, assuming the temperature remains constant, what is the volume

of the balloon at its new pressure?

• Charles' Law

o Lower temperature leads to a lower volume

o Higher temperature leads to a higher volume

o Directly proportional

o Temperature must be converted to Kelvin

o Pressure remains constant

Example Problem: A balloon inflated in a room at 24OC has a volume of 4.00 L. The balloon is then

heated to a temperature of 58OC what is the new volume if the pressure remains constant?

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• Gay-Lussac's Law

o Temperature always in Kelvin Scale

o Volume remains constant

Example Problem: Aeresol cans carry labels warning not to store them above a certain temperature.

The gas in a used aerosol can is at a pressure of 1atm at 25oC. If the can is thrown into a fire, what will

the pressure be when the temperature reaches 1201oC?

• The Combined Gas Law

o No variable remains constant

o Temperature always in Kelvin Scale

Example Problem: The volume of a gas filled balloon is 30.0L at 313 K and has a pressure of 153 kPa.

What would the volume be at standard temperature and pressure (STP)?

• Remember Avogadro’s Law

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Gas Laws Practice:

1) A chemist collects 59.0 mL of sulfur dioxide gas on a day when the atmospheric pressure is

0.989 atm. On the next day, the pressure has changed to 0.967 atm. What will the volume of

the SO2 gas on the second day?

2) A can contains a gas with a volume of 56 mL and 20.0 °C. What is the volume in the can if it is

heated to 50.0 °C?

3) A gas with a volume of 4.0L at a pressure of 90.0 kPa is allowed to expand until the pressure

drops to 20.0 kPa. What is the new volume?

4) At a winter carnival, a balloon is filled with 5.00 L of helium at a temperature of 273 K. What

will be the volume of the balloon when it is brought into a warm house at 295 K?

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5) The initial temperature of a 1.00 liter sample of argon is 20.0° C. The pressure is decreased

from 720 mm Hg to 360 mm Hg and the volume increases to 2.14 liters. What was the change

in temperature of the argon?

6) 2.2 L of hydrogen at 6.5 atm pressure is used to fill a balloon at a final pressure of 1.15 atm.

What is its final volume?

7) The pressure in an automobile tire is 200. kPa at a temperature of 25°C. At the end of a

journey on a hot sunny day the pressure has risen to 223 kPa. What is the temperature of the

air in the tire?

8) A sample of argon has a volume of 5.00 L and the pressure is 0.920 atm. If the final

temperature is 30.0° C, the final volume is 5.7 L, and the final pressure is 800. mm Hg, what

was the initial temperature of the argon?

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Ideal Gas Law and Dalton’s Law Notes

• Ideal Gas Law

R = 0.0821 � �∗�

���∗� = 8.315

���∗�

���∗� = 62.4

����∗�

���∗�

o To determine which R value to use, look at your unit of ____________________

o If gases follow the Kinetic Molecular Theory, they are said to be ideal gases.

o Although there is no such thing as an ideal gas, the theory still provides a good model to

explain gas properties (P,V, T)

• At 34oC, the pressure inside a nitrogen filled tennis ball with a volume of 0.148 L is 212 kPa.

How many moles of nitrogen gas are in the tennis ball?

• A deep underground cavern contains 2.24 x106 L of methane gas (CH4) at a pressure of

1.50x103 kPa and a temperature of 315 K. How many kilograms of methane does the cavern

contain?

Ideal Gasses vs. Real Gasses

Ideal Gas assumptions:

- No volume

- No attractive forces between particles of gas

There is no gas which exhibits these qualities, but there are many conditions which real gasses

behave the same as an ideal gas.

Real gasses differ most from an ideal gas at low temperatures and high pressures.

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• Dalton’s Law of Partial Pressures

o The total pressure exerted by a mixture of gases is the sum of the individual of each gas

o Each individual gas behaves as if it were independent of the others.

Ptotal=P1+P2+P3+…

o For example, if two gases such as oxygen and nitrogen are present in a flask and Pnitrogen

= 250 mmHg and Poxygen = 3.0x102 mmHg, then the total pressure is 550 mmHg.

• If CO2 gas is collected over water at 25 oC at atmospheric pressure (1.00 atm), and the partial

pressure of water vapor at 25 oC is 0.54 atm. What is the partial pressure of the dry gas?

o Mole Fraction (X) – the ratio of the number of moles of a given component in a mixture

to the total number of moles in the mixture.

o At constant volume and temperature, mole ratios and pressure ratios mean the same

thing.

• The partial pressure of oxygen was observed to be 156 torr in the air with an atmospheric

pressure of 743 torr. Calculate the mole fraction of oxygen present.

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Ideal Gas Law and Dalton’s Law Practice:

1. How many moles of air molecules are contained in a 2.00 L flask at 98.9 atm and 245 K?

2. How many moles of gas are contained in 51.41 liters at 101.325 kPa and 0°C?

3. How many moles of gases are contained in a can with a volume of 800.0 mL and a pressure of

600.0 atm at 20 °C?

4. Find the total pressure for a mixture that contains four gases with partial pressures of 0.39 kPa,

0.53 kPa,0.73 kPa,0.72 kPa.

5. Hydrogen gas is collected over water at 25ºC at atmospheric pressure and the partial pressure

of water vapor at 25 ºC is 3.17 kPa. What is the partial pressure of the hydrogen? Hint: if a

reaction is conducted at atmospheric pressure, than that is the total pressure.

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• Atmospheric pressure is

measured using a

_________________________.

• The pressure of a gas is measured using a __________________________.

o A Manometer is a device to measure the pressure of an enclosed gas

sample. A common simple manometer consists of a U shaped tube of glass

filled with some liquid. Typically the liquid is mercury because of its high

density.

o The height difference determines the pressure.

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Calculate the pressure inside each flask, given an atmospheric pressure of 760 mmHg.

The gas in the flask has a higher pressure than

760 mmHg. The pressure is .

The gas in the flask has a lower pressure than

760 mmHg. The pressure is .

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Kinetic Molecular Theory Worksheet

1. The word kinetic comes from a Greek word that means “to move.” The kinetic molecular theory

is based upon the assumption that particles of matter (atoms or molecules) are in constant

2. Of the three states of matter, which one has

the most kinetic energy?

3. Which state of matter has particles that are

separated by the largest distance?

4. A scientific theory is an explanation of some type of natural phenomena. Theories are normally

developed from careful study of the way the world behaves. Let’s look at how gases behave

and see if the kinetic molecular theory makes sense.

5. Compared to liquids and solids, gases tend to have ________ ______ densities. This can

be explained because the particles of gas are ________.

6. If you apply pressure to a sample of gas, it is fairly easy to ________ its

volume (think about what would happen to a balloon if you squeeze it gently). This can be

explained because there is a lot of _______ between gas

particles.

7. If someone sprays perfume in one corner of the room, eventually a person on the other side of

the room can smell it. This can be explained because gas particles move and

. In general, we would expect lighter gas particles to travel

than heavier gas particles.

8. When two gases mix together or move through each other, this process is known as

. When gas particles escape out of a tiny hole in a

container, this process is known as ________. You should know the

difference between these two words so you can avoid any confusion!

9. Kinetic molecular theory can be summarized as follows:

a. Gas particles are in constant .

b. Gas particles are separated by relatively ______ distances.

c. When gas particles collide, they

kinetic energy.

d. Gas particles have attractive or repulsive forces between them.

e. The kinetic energy of a gas is dependent on the

of the gas.

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Gas Law Worksheet:

1. A sample of gas occupies 25.0 L under a pressure of 1.0 atm. What will its volume be if the

pressure is increased to 2.0 atm? Assume the temperature of the gas sample does not change.

2. A sample of oxygen occupies 10.0 L under a pressure of 105 kPa. At what pressure will it

occupy 13.4 L if the temperature does not change?

3. Helium gas in a balloon occupies 2.5 L at 300.0 K. The balloon is dipped into liquid nitrogen that

is at a temperature of 80.0 K. What will the volume of the helium in the balloon at the lower

temperature be?

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4. A sample of neon gas has a volume of 752 mL at 25.0 °C. What will the volume at 50.0 °C be if

pressure is constant?

5. The pressure in an automobile tire is 200. kPa at a temperature of 25°C. At the end of a

journey on a hot sunny day the pressure has risen to 223 kPa. What is the temperature of the

air in the tire?

6. A certain amount of gas will occupy a volume of 8.50L at a temperature of 35.0°C. What

temperature will change the volume to 15.5L?

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Ideal Gas Law and Dalton’s Law Worksheet

1) The air in a person’s lungs consists of 0.177 mol of gas particles at 310 K and 101.3 kPa

pressure. What is the volume of the air?

2) How many moles of gas are contained in 22.41 liters at 101.325 kPa and 0°C?

3) How many moles of gases are contained in a can with a volume of 555 mL and a pressure of

600.0 atm at 20 °C?

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4) Calculate the pressure exerted by 43 mol of nitrogen in a 65 L cylinder at 5 °C.

5) What is the volume of 45 grams of Argon gas at a pressure of 85.6 kPa and 26.0 °C?

6) A mixture of oxygen, carbon dioxide and nitrogen has a total pressure of 4.59 atm. What is the

partial pressure of oxygen if the partial pressure of CO2 is 0.44 atm and the partial pressure of

N2 is 0.02 atm.

7) What is the partial pressure of hydrogen gas in a mixture of hydrogen and helium if the total

pressure is 4.58 mmHg and the partial pressure of helium is 0.23 mmHg?

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Unit 9 Review: Gas Laws

1. If temperature is constant, the relationship between pressure and volume is

a. direct

b. inverse

2. If pressure is constant, the relationship between temperature and volume is

a. direct

b. Inverse

3. One way to increase pressure on a gas is to

a. decrease temperature

b. increase volume

c. increase the number of gas particles

d. lower the kinetic energy of the gas molecules

4. How do gas particles respond to an increase in volume?

a. increase in kinetic energy and decrease in temperature

b. decrease in kinetic energy and decrease in pressure

c. increase in temperature and increase in pressure

d. increase in kinetic energy and increase in temperature

5. If pressure of a gas is increased and its volume remains constant, what will happen to its temperature?

a. increase

b. decrease

c. stay the same

6. If a gases volume is decreased and pressure is constant, its temperature will

a. increase

b. decrease

c. remain the same

7. If the temperature of a gas remains constant but pressure is decreased, the volume will

a. increase

b. decrease

c. remain the same

8. Convert 2.3 atm into mmHg.

a. 2300 mmHg

b. 1750 mmHg

c. 2.3 mmHg

d. 0.0030 mmHg

9. Convert 6.7 liters into milliliters.

a. 0.0067 mL

b. 0.0088 mL

c. 5092 mL

d. 6700 mL

10. The pressure of a gas is 750.0 torr when its volume is 400.0 mL. Calculate the pressure (in atm) if the gas

is allowed to expand to 600.0 mL at constant temperature.

a. 0.660 atm

b. 1.48 atm

c. 500.0 atm

d. 1125 atm

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11. The volume of a gas is increased from 150.0 mL to 350.0 mL by heating it. If the original temperature of

the gas was 25.0 °C, what will its final temperature be (in °C)?

a. 146°C

b. 10.7°C

c. 58.3°C

d. 422°C

e. 695°C

12. A gas exerts a pressure of one atm at standard temperature (273.0 K). What must the temperature be

adjusted to for the gas to exert a pressure of 4.00 atm? (Give your answer in °C)

a. -205°C

b. 68.3°C

c. 819°C

d. 1092°C

13. A quantity of gas has a volume of 250.0 liters at 17.0°C and 3.00 atm of pressure. To what volume must

the gas be increased for the gas to be under STP conditions?

a. 78.4 L

b. 88.5 L

c. 706 L

d. 771 L

e. 797 L

14. What are standard temperature and pressure conditions for gases?

a. 0°C and 0 torr

b. 0 K and 760 torr

c. -273°C and 1 atm

d. 0°C and 760 torr

e. 0°C and 1 torr

15. If the volume of a confined gas is doubled while the temperature remains constant, what change (if any)

would be observed in the pressure?

a. It would be half as large.

b. It would double.

c. It would be four times as large.

d. It would be 1/4 as large.

e. It would remain the same.

16. A given mass of gas in a rigid container is heated from 100°C to 500°C. Which of the following responses

best describes what will happen to the pressure of the gas?

a. The pressure will decrease by a factor of five.

b. The pressure will increase by a factor of five.

c. The pressure will increase by a factor of about two.

d. The pressure will increase by a factor of about eight.

e. The pressure will increase by a factor of about twenty-five.

17. Which of the following has the most molecules?

a. 1.00 L of CH4 at 0°C and 1.00 atm

b. 1.00 L of N2 at 0°C and 1.00 atm

c. 1.00 L of O2 at 20°C and 1.00 atm

d. 1.00 L of CO2 at 50°C and 1.25 atm

e. 1.00 L of CO at 0°C and 1.25 atm

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18. Avogadro stated that equal volumes of gases under the same conditions of temperature and pressure

have equal

a. numbers of molecules.

b. numbers of grams.

c. molar masses.

d. atoms.

e. speeds.

19. What volume of CH4 at 0°C and 1.00 atm contains the same number of molecules as 0.50 L of N2

measured at 27°C and 1.50 atm?

a. 0.37 L

b. 0.46 L

c. 0.68 L

d. 0.50 L

e. 0.82 L

20. If 3.0 L of helium at 20.0°C is allowed to expand to 4.4 L, with the pressure remaining the same, what is

the new temperature?

a. 702°C

b. 430°C

c. 157°C

d. -30.0°C

e. -55°C

21. At what temperature will 41.6 grams N2 exerts a pressure of 815 torr in a 20.0 L cylinder?

a. 134 K

b. 176 K

c. 238 K

d. 337 K

e. 400 K

22. A mixture of the gases neon and krypton is in a 2.00 liter container. The partial pressure of the neon is

0.40 atm and the partial pressure of the krypton is 1.20 atm. What is the mole fraction of neon?

a. 0.20

b. 0.25

c. 0.33

d. 0.60

e. 0.80

23. Which of the following gases has the greatest density at 0°C and 1 atm?

a. N2

b. 02

c. F2

d. Ne

e. CO

24. What volume of O2, collected at 22.0°C and 728 mmHg would be produced by the decomposition of 8.15

g KClO3?

2KClO3(s) � 2KCl(s) + 3 O2(g)

a. 1.12 L

b. 1.48 L

c. 1.68 L

d. 2.23 L

e. 2.52 L

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25. Ammonia gas is synthesized according to the balanced equation

N2(g) + 3H2(g) � 2NH3(g)

If 15.0 liters of nitrogen are reacted with an excess of hydrogen, how many liters of ammonia could be

produced? Assume all gas volumes are measured at the same temperature and pressure.

a. 5.00 L

b. 10.0 L

c. 15.0 L

d. 20.0 L

e. 30.0 L

26. A gas has a volume of 3.4 L at 25 °C, what is the final temperature if the volume increases to 4.7

L?

27. The initial pressure of a gas is 457 mm Hg, the final volume is 750 mL with a final pressure of

650 mm Hg. What is the initial volume of the gas?

28. A gas of 3.4 moles occupies a volume of 40.6 mL at 298 K, what is the pressure of the gas?

29. A gas of 1 mole has a temperature and volume at STP, the temperature of the gas is increased

to 311 K.

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30. At 18 °C , 34.7 grams of carbon dioxide gas creates a pressure of 613 mm Hg, what is the

volume of the gas? Hint: get into the correct units before you start.

31. A 3.00 L pocket of air at sea level has a pressure of 100 atm. Suppose the air pockets rise 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?

32. The gas in a balloon occupies 3.50 L at 300. K. At which temperature will the balloon expand to

8.50 L?

33. A gas is collected by water; it contains 78.5 atm of nitrogen, 998.7 atm of oxygen and 324.1 atm

of hydrogen. Determine the total pressure of this gas.

34. How many moles of argon are there in 20.0 L, at 25 °C and 96.8 kPa?

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35. What volume will 2.00 mol of oxygen gas occupy at STP?

36. A weather balloon has a volume of 1750 L at 103 kPa. The balloon is released to the

atmosphere. At the highest point above the ground, the pressure on the balloon is 35.0 kPa.

What is the new volume of the balloon at this height?

37. Find the total pressure for a mixture that contains four gases with partial pressures of 0.39 kPa,

0.53 kPa,0.73 kPa,0.72 kPa.