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Gases Unit 10

Gases are perhaps the most mysterious of all of the phases of matter. For the most part gases are

invisible to us, and it was once believed that in the air there is no matter at all.

Consider, however, how finely tuned our own bodies are to gases in general, and oxygen in particular.

We would die in a few minutes if deprived of oxygen, and our respiration system is in constant motion

to take advantage of this energy-providing gas.

The goal of this unit is to discover how gases behave physically. Or to state it more specifically, how

do gases behave as temperature, volume, or pressure change? The first lab is designed to give you

enough equipment to discover these things on your own. We will then compare these observations to

the known Gas Laws.

Tentative Schedule:

Day 1: Introduction to gases activity: Lab 10.1

Homework: Complete lab report.

Day 2: Comparison of the Class Gas Laws to the known Gas Laws (Slides 1-8)

Homework: Complete WS10.1 (Boyle’s Law), 10.2 (Charles Law), and 10.3 (Gay-Lussac’s Law).

Day 3: Avogadro’s Principle; Ideal Gas Law (Slides 9-11)

Homework: Complete WS10.4 (Avogadro’s Principle) and 10.5 (Ideal Gas Law).

Day 4 Gases Review

Homework: Complete “How to ace the Gases Unit”

Day 5: Gases Test

How do gases behave?

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Name_______________________________ Date: ______ Period:_____ Lab10.1

Introduction to Gases Activity

Note: Pay particular attention to your graphs. Although time is limited, try to get enough data

points to see if the relationship is linear, or if your lines are curved.

Station 1: Syringe.

This station contains a syringe and some books. Your goal is to discover how gas pressure and

volume are related.

Describe briefly the experiment you performed. (Remember, the best experiments give

quantitative results)

What did you discover about gas pressure and volume? Answer this

question, and complete a brief graph, labeling both axes.

Introduction: The goal of this activity is to see how three physical properties of gases- volume,

pressure, and temperature - relate to one another. These processes are interacting constantly,

but you may have never looked at them very deeply.

At each station, design your own experiment, and take whatever measurements you think will be

helpful. Not all of the equipment at each station is necessary to perform the experiment. At each

station you are asked to determine the relationship between two specific gas properties. For

example, at the first station you will measure how gas pressure affects gas volume. At the last

station you can create any safe experiment you choose to see how gases behave physically.

As for all experiments, safety is critical. You must wear goggles at all times to perform these

experiments. If there is any question in your mind as to the safety of your experiment, do not

perform it.

Note that there will be up to four people at each station. Work together and share ideas. This

report must be filled out and submitted for each group of two.

This report will be graded on the validity of your experiment and the interpretation of your

results. Although each experiment is brief, remember to include a control whenever possible, and

to only include one independent variable. The best experiments will give data that can be graphed

using numbers- these are quantitative experiments.

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Please restack your books and clean your station before you leave.

Station 2: Popcorn

You have available a popcorn popper and some popcorn kernels, and a thermometer. Your goal is to

discover how gas pressure and temperature are related.

Describe what you did, and what you observed:

What did you discover?

For your experiment, hypothesize as to what gas may be involved in your experiment:

Complete a brief graph that shows the relationship between temperature

and pressure, labeling both axes:

Please throw out any popped popcorn and clean your station before you

leave.

Station 3: Vacuum Pump.

This station includes a mechanical vacuum pump, a balloon, a marshmallow, a glass of water, and a

thermometer. Your goal is to discover how reduced pressure and volume are related.

Safety warning: Use care when working with the large glass bell jar.

Describe what you did, and what you observed:

What did you discover? Consider the relationship between any pressure

and reduced volume.

Complete a brief graph summarizing this relationship:

Please clean up this station and turn off the pump before you leave.

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Station 4: Balloon. This station contains balloons, string, a thermometer, and a hair drier. Caution: The hair drier must

be kept from moisture, and will get hot. Your goal is to determine the relationship between volume

and temperature.

For this experiment you should obtain quantitative, graphable results.

Describe what you did, and what you observed. Include a brief graph

using real data.

Describe what you observed:

What did you discover? Consider the relationship between gas temperature and volume.

Station 5: ( Varies)

This station contains various equipment. Use it to create your own experiment that investigates a

P,V,T relationship.

Describe what you did, and what you observed:

What did you discover? Consider the relationship between any of the following: temperature,

pressure, and volume.

Our Gas Laws

Please be sure to complete this part: these are your own gas laws that you discovered :)

2. What did you learn about the interaction of pressure, temperature, and volume of gases?

Summarize your results by using an up arrow ( ) for increasing, a down arrow ( ) for decreasing,

and write constant if this property is unchanged. Support each case with examples.

Temperature Volume Pressure Example

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Name: _____________________________________ Date: _____ Period: _____ WS10.1

Boyles’ Law Practice Problems

When you press on a closed syringe with only air in it, the volume goes down, and the pressure goes

up. This shows the fundamental relationship between the pressure and volume of a gas at constant

temperature. Boyle wrote it mathematically:

P1V1=P2V2

where

P1 is the original pressure

P2 is the final pressure

V1 is the original volume

V2 is the final volume

For this formula any units can be used as long as they cancel. The preferred (SI) units are liters and

atmospheres.

1. A balloon filled with helium gas has a volume of 500 mL at a pressure of 1 atm. After the balloon

in released, it reaches an altitude of 6.5 km, where the pressure is 0.5 atm. What volume does the

gas occupy at this height?

2. A sample of oxygen occupies a volume of 5 L at a pressure of 200 mm Hg. After undergoing an

increase of pressure, the new volume is 2.5 L. What must the new pressure be?

3. If the pressure exerted on a 240 mL sample of hydrogen gas is increased from 325 mm Hg to 550

mm Hg, what will the final volume of the sample be?

Example: A 10 liter oxygen cylinder is under 800 atmospheres of pressure. When the oxygen is

released to the air (1 atmosphere), what will the volume of the oxygen be?

Solution: L 8000 atm) (1

L) atm)(10 (800 V );atm)(V (1 L) atm)(10 (800 ;VPVP 222211

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Name: ______________________________ Date: ______ Period: _____ WS10.2

Charles’ Law Practice Problems

A balloon will expand as it is heated: as the temperature of a gas increases (at constant pressure),

volume increases. Charles wrote this mathematically: 2

2

1

1

V

T

V

T

For this formula any volume units may be used as long as they cancel, and Kelvin must be used for

temperature. Remember K = OC + 273

1. A sample of hydrogen gas has a volume of 275 mL at 25C. If the temperature is increased to

130C, what is its new volume?

2. A 35 L oxygen sample originally has a temperature of 20C. If the sample is cooled to 10C, what

is its new volume?

3. A nitrogen sample at 50C occupies a volume of 800 cm3. After heating, the sample occupies a

volume of 1000 cm3. What is the new temperature of the gas?

Example: A sample of air has a volume of 140.0 mL at 67C. To what temperature must the gas be

lowered to reduce its volume to 50.0 mL?

Solution: Be sure to use Kelvin, not Celsius. T1/V1 =T2/V2 T2 = T1V2/V1

= 340 K x 50 mL/140 mL = 121.4 K (that’s -151.6 oC; very cold) Reality check : Both the temp and the volume decreased nearly by a factor of 3

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WS10.3

Name: _____________________________________ Date: _____ Period: _____

Gay-Lussac’s Law Practice Problems

Heating a sealed empty bottle is dangerous- it could explode. As the temperature of a gas increases

in a closed non-expandable container, the pressure increases. Gay-Lussac wrote it mathematically:

2

2

1

1

P

T

P

T

For this formula any units of pressure may be used as long as they cancel, and the temperature must

be in Kelvin (remember K = OC + 273)

1. Before a trip from New York to Boston, the pressure in a car tire is 1.8 atm at 20C. 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?

2. A sample of hydrogen at 47C exerts a pressure of 250 mm Hg. If the gas is heated to 77C at a

constant volume, what will its new pressure be?

3. To what temperature must a sample of nitrogen at 300K and 0.625 atm be heated to so that its

pressure becomes 1.125 atm?

Example: You have a closed aluminum can that can handle a pressure of 4 atmospheres before it

bursts. If this closed 2 liter can at a pressure of 1.2 atmospheres is heated from 25 degrees

Celsius to 100 degrees Celsius, will it burst?

Solution: atm. 1.64 K 227.5

K 373 atm x ;

atm x

K 373 227.5 ;

atm x

K 373

atm 1.2

K 273 ;

P

T

P

T

2

2

1

1

The can will handle up to 4 atmospheres, so it will not burst.

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WS10.4

Name: _______________________________ Date: _____ Period: ______

Avogadro’s Principle: Problems

A mole of an ideal gas occupies 22.4 L at STP (standard temperature and pressure: 273K, 1 atm):

All of these problems are solved using this relationship:

22.4L/mol, or 1 mol/22.4 L

1. Calculate the number of moles present for an ideal gas with a volume of 40 liters at STP.

2. What is the density of CO2 gas in g/L at STP? Molar mass of CO2 = 44 g/mol.

3. A gas is found to have a density of 2.595 g/L at STP. What is the molar mass of this gas in g/mol?

4. Calculate the volume that 2.0 kg of methane gas (CH4) will occupy at STP

Example: How much did the hydrogen in the Hindenburg weigh, assuming STP and a volume of 200

million liters?

Solution: Hydrogen g million 17.9 H mole

H g 2 x

H liters 22.4

H mole x H liters million 200

2

2

2

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22.4 L of an ideal gas = 1 mole.

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WS10.5

Name: _______________________________ Date: _____ Period: ______

Ideal Gas Law Problems

Combining the laws or principles of Boyle, Charles, Gay-Lussac, and Avogadro provides:

Where

P = pressure in atmospheres

V = volume in Liters

n = the number of moles

R = 0.0821 atmL/molK (note that R is always this number)

T = temperature in Kelvin

Note that all of these units must be used- this is the most common error (see below).

Here are some helpful conversions:

1 atm = 760 mm Hg = 14.7 psi

1 L = 1000 mL

Tc + 273 = Tk

***Here are the most common errors:***

1. Don’t know where to start

Solution: Find out what you are given- in all cases you get 3 of the four P V n T

variables- it must be an ideal gas problem. Rearrange the equation to solve for the

missing one, and plug in your correct units (see #2)

2. Didn’t use Liters (L), atmospheres (atm), mole (mol), and Kelvin (K) units.

Solution: use the helpful conversions above and convert to L atm mol K.

3. What do I do with grams in these problems?

Solution: Convert to moles (n). If you have 16 grams of methane, then n = 1 since the

molar mass of methane is 1 g/mol (12 +1+1+1+1). Similarly, if the question asks for

grams, solve for n then convert moles to grams…for example if you have 9 grams of

water, that is half a mole (9/18).

For all of these questions please circle your answer and be sure you have included your units.

1. What is the volume (in L) occupied by 0.25 mol of oxygen at 20C and 740 mm Hg?

Example: What is the temperature of 2 moles of an ideal gas at 300 mm Hg and 12 liters of

volume?

Solution: convert to SI units and plug into the ideal gas equation.

PV = nRT; T = PV/nR = (0.395 atm)(12 L)/ (2 mol)(0.0821 atmL/molK) = 45.5 K

PV = nRT

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2. How many moles of chlorine are contained in a 10 mL tank at 27C and 3.5 atm of pressure?

3. What is the pressure on a 6-L system containing 32 g Oxygen gas at 45C?

4. How many grams of Neon gas are contained in a 200-mL tank at 421C, with a pressure of 420 mm

Hg?

5. How many molecule of H2O are present in a 230-mL container, held with a temperature 485K, with

a pressure 12.8 psi?

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Gas Law Worksheet

Challenge Problems: 6,8,16,17

These problems include one new law:

The combined gas law: P1V1/T1 = P2V2/T2

(see #8, for example)

1. In a certain experiment a sample of helium in a vacuum system was compressed at 25 °C from

a volume of 200.0 mL to a volume of 0.240 mL where its pressure was found to be 30.0 mm

Hg. What was the original pressure of the helium?

2. A hydrogen gas volume thermometer has a volume of 100.0 cm3 when immersed in an ice-water

bath at 0 °C. When immersed in boiling liquid chlorine, the volume of the hydrogen at the same

pressure is 87.2 cm3. Find the temperature of the boiling point of chlorine in °C.

3. 2.50 grams of XeF4 is introduced into an evacuated 3.00 liter container at 80.0 °C. Find the

pressure in atmospheres in the container.

4. A lighter-than-air balloon is designed to rise to a height of 6 miles at which point it will be

fully inflated. At that altitude the atmospheric pressure is 210 mm Hg and the temperature is

-40 °C. If the full volume of the balloon is 100,000.0 L, how many kilograms of helium will be

needed to inflate the balloon?

5. How many liters of pure oxygen, measured at 740 mm Hg and 24 °C, would be required to burn

1.00 g of benzene, C6H6 (l), to carbon dioxide and water? (Hint: find the moles of oxygen

needed from the balanced equation, then use gas laws.)

6. Air from the prairies of North Dakota in winter contains essentially only nitrogen, oxygen, and

argon. A sample of air collected at Bismarck at -22 °C and 98.90 kPa had 78.0 % N2, 21.0% O2,

and 1.0% Ar. Find the partial pressures of each of these gases.

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7. For a mole of ideal gas, sketch graphs of

a. P vs. V at constant T.

b. P vs. T at constant V.

c. V vs. T at constant P.

8. What would be the partial pressure of N2 in a container at 50 °C in which there is 0.20 mole

N2 and 0.10 mole CO2 at a total pressure of 101.3 kPa?

9. What volume of Ne at one atm and 25.0 °C would have to be added to a sign having a volume of

250 mL to create a pressure of one mm Hg at that temperature?

10. Find the volume of a gas at 800.0 mm Hg and 40.0 °C if its volume at 720.0 mm Hg and 15.0 °C

is 6.84 L.

11. 12.8 L of a certain gas are prepared at 100.0 kPa and -108 °C. The gas is then forced into an

855 mL cylinder in which it warms to room temperature, 22.0 °C. Find the pressure of this gas

in kilopascals.

12. In a laboratory experiment, 85.3 mL of a gas are collected at 24 °C and 733 mm Hg pressure.

Find the volume at STP.

13. What is the mass of 18.9 L of NH3 at 31.0 °C and 97.97 kPa?

14. 0.279 moles of O2 in a 1.85 L cylinder exert a pressure of 3.68 atm. What is the temperature

in the cylinder (in °C)?

15. A quantity of potassium chlorate is selected to yield, through heating, 75.0 mL of O2 when

measured at STP. If the actual temperature is 28 °C and the actual pressure is 0.894 atm,

what volume of oxygen will result?

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16. A mixture of hydrocarbons contains three moles of methane, four moles of ethane, and five

moles of propane. The container has a volume of 124 liters and the temperature is 22 °C. Find

the partial pressures of the three gases, in kPa.

17. How many liters of H2 at 23 °C and 733 mm Hg are released by the reaction between 1.98

grams of Na and unlimited water by the following equation?

2 Na + 2 H2O -- > H2 + 2 NaOH

Answers: 1) 0.0360 mm Hg 2) -35 °C 3) 0.117 atm 4) 5.8 kg 5) 2.4 L 6) 77.1 kPa N2, 20.8 kPa O2,

9.89 kPa Ar 7) a - hyperbola, b&c - straight lines 8) 67 kPa N2, 34 kPa CO2 9) 0.329 mL 10) 6.69

L 11) 2680 kPa 12) 75.6 mL 13) 12.5 g 14) 24 °C 15) 92.5 mL 16) 59.3 kPa methane, 79.0 kPa

ethane, 98.8 kPa propane 17) 1.08 L

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How to ace the Gases Test

We have been observing the behavior of gases for several days. Our goal has been to determine how

the physical properties of gases interrelate.

To begin we created brief experiments at a series of stations where we explored the interactions of

temperature, pressure, and volume within various gaseous systems. For each experiment we looked

for changes in volume, pressure, ands temperature. We then compared these results to the Gas Laws

of Boyle, Charles, Graham, and Gay-Lussac We also looked at a combination of these known as the

ideal gas law,

To ace the gases test you should be able to:

1. Describe the macroscopic (visible) properties of liquids, solids, and gases.

A solid has/does not have a fixed volume and will/will not assume the shape of a container.

A liquid has/does not have a fixed volume and will/will not assume the shape of a container

A gas has/does not have a fixed volume and will/will not assume the shape and volume of a

container

2. Accurately predict the behaviors of molecules as they undergo changes of pressure, temperature,

volume, or the number of molecules.

As the temperature increases in a non-expandable container like a sealed can, the

_____________ increases and the __________ remains constant.

As the temperature increases in an expandable container like a balloon, the _____________

increases and the __________ remains constant.

As the pressure increases in a collapsible container like a syringe, the __________ decreases

and the ____________ remains constant.

3. Apply the Gas Laws to predict how one physical change will affect another if the third remains

constant.

If the pressure increases from 100 to 200 kilopascals in a 3 liter container and the

temperature remains constant, what will the final volume be? (101.7 kilopascals = 1

atmosphere).

If the temperature increases from 273 to 298 Kelvin in a 25 liter balloon and the pressure

remains constant, what will the final volume be?

4. Be able to convert between degrees Celsius and Kelvin.

If the temperature increases from 25 to 100 degrees Celsius in a non-expandable container at

1.2 atmospheres, what will the final pressure be?

5. Be able to solve gas law problems based on Avogadro’s Principle

• 2. What is the density of CO2 gas in g/L at STP? Molar mass of CO2 = 44 g/mol.

6. Be able to solve gas law problems involving multiple changes (ideal gas law)

Example: How many moles of chlorine are contained in a 10 mL tank at 27C and 3.5 atm of

pressure?

As a final Review, complete the activity on the following page in class. If you are doing this at home,

choose your own numbers for the volume of the syringe.

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Name_________________________ Period___________ L2gasreview1

Gas Laws Review: Use the Gas Laws and Principles to solve each problem.

1. Take a 50 ml syringe, and set it to any big volume.

My volume is ___ mL

Push down on it hard. The new volume is ____ mL

How much pressure did you apply (in atmospheres)?

Show your work in the box. Circle your answer.

This question is based on _________’s Law

2. Set your syringe to any volume.

I have just set my syringe to ____ mL.

Now warm it in your hands for 10 seconds.

The new volume is _____.

You warmed it from 25 OC to 37

OC.

What is the new volume supposed to be?

If your syringe didn’t move this is probably because

__________________________________________.

This question is bases on ___________’s Law

3. This time I have set the syringe to _____ mL.

With one hand hold the syringe so it can’t expand.

Warm the syringe with the other hand.

What is the new pressure in the syringe?

This question is based on ____________’s Law

4. Now I am setting my syringe to ___ mL.

How many moles of gas are in your syringe?

(Hint: one mole of gas = 22.4L.

My syringe has ____ moles of air in it.

This question is based on _______________’s Principle.

5. Set your syringe to 40 mL. Push down on it until the volume is 20 mL. We can figure out the

new pressure in our heads: it must be ___atm. Now warm it in your hands to 37 OC. Use this

final data to figure out how many moles of gas are in the syringe.

Final Volume:_____

Final Pressure:_____

Final Temperature:_____

Number of moles:_____

This question is based on the ___________ Law.

6. (L1 only; extra credit for L2). Assuming an average molecular mass of 30 g/mol, calculate the

density of air in g/L using Avogadro’s Principle.

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Gas Laws Worksheet Answer Key

1.

2.

3.

4. 5. 2 C6H6 (g) + 15 O2 (g) --> 12 CO2 (g) + 6 H2O (g)

6.

7.

8.

9.

10.

11.

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12.

13.

14.

15. 16. This can be done by a couple of methods. One possible way is:

17.