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GASES Name: _____________________________________________Period: _____Date:__________

6 assumptions on which the kinetic-molecular theory (KMT) of GASES is based:

1. Gases are composed of large numbers of tiny particles, usually atoms or

molecules. 2. Gas particles are relatively far apart from one another; between the gas particles is empty

space; therefore, the volume of gas particles is insignificant compared to the volume of a gas.

3. ______attractive or repulsive forces exist between the gas particles. 4. Gas particles move in continuous, rapid, random motion (in straight paths); gas

particles therefore possess kinetic energy. (The energy an object has because of its motion is called kinetic energy.)

5. Collisions between gas particles and between particles and container walls are

perfectly elastic; an elastic collision is one in which there is no net loss of kinetic energy; kinetic energy is transferred between two particles during a collision, but the total kinetic energy of the two particles remains the same.

6. The average kinetic energy of gas particles is directly proportional to the Kelvin temperature

of the gas.

Ideal Gases: • ______________________= an imaginary gas that conforms perfectly to all the

assumptions of the kinetic-molecular theory ⇒ We will assume that the gases used for the gas law problems are ____________.

• Why do we talk about an ideal gas if it does not exist?

⇒ _________________________________________________________

_________________________________________________________

_________________________________________________________

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Real Gases vs. Ideal Gases: • Remember: An ideal gas is an imaginary gas that conforms perfectly to all the assumptions

of the kinetic-molecular theory • Gas Laws do __________work for real gases • ______________= a gas that does not behave completely according to the assumptions of

the kinetic-molecular theory. • All real gases deviate to some degree from ideal gas behavior. However, most real gases

behave nearly ideally when their particles are sufficiently far apart and have sufficiently high kinetic energy.

• Causes of non-ideal behavior:

1. ___________pressure (low volume): • space taken up by gas particles becomes significant • intermolecular forces are more significant between gas particles that are closer

together

2. _________temperature: • gas particles move slower so intermolecular forces become more important

3. The kinetic-molecular theory is more likely to hold true for gases whose particles have ____________attraction for each other.

The Kinetic-Molecular Theory & the Nature of Gases: • Be able to explain each of the following properties of gases using the kinetic-molecular

theory. 1. Gases ___________to fill the volume and shape of their container:

• Gases have _____definite shape and volume • Gases expand to fit the shape and volume of their container • KMT - gas particles move rapidly in all directions without significant attraction or

repulsion between particles 2. Gases have___________:

• Gas particles can glide easily past one another (Flow) • KMT - No significant attraction or repulsion between gas particles

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3. Gases have a____________________: • Gaseous substance is about 1/1000 the density of the same substance in the liquid or

solid state • KMT - particles are so much father apart in the gas state

4. Gases can be _____________________into much smaller volumes:

• Gases can be compressed and the volume of the gas sample can be decreased • KMT - gas particles are far apart from one anther with room to be “squished” together

5. Gases exhibit diffusion:

• ___________________= spontaneous mixing of the particles of two substances caused by their random motion

• KMT – gas particles move in continuous, rapid, random motion

6. Gases exhibit effusion:

• ____________________= a process by which gas particles pass through a tiny opening

• KMT- gas particles move in continuous, rapid, random motion

Pressure of Gases: • __________________= the force per unit area on a surface • Units of pressure:

o millimeter of mercury (mmHg) o torr o kilopascal (kpa) o atmosphere (atm)

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1 atm = 760 mmHg (exact conversion) 1 atm = 760 torr (exact conversion) 1 atm = 101.325 kpa

• If a gas exerts a pressure of 635 torr, what pressure does it exert in atmospheres?

• Why do gases exert pressure? o ___________________________________________________________

___________________________________________________________

______________________________________________________________________________________________________________

Atmospheric Pressure:

• The atmosphere is a blanket of air surrounding the earth. It is composed of about 78% nitrogen, 21% oxygen, and 1% other gases.

• Since the atmosphere is a mixture of gases, it exerts a pressure!

• Average atmospheric pressure at sea level at 0°C is 760 mm Hg (1 atm).

• Atmospheric pressure depends on elevation and weather conditions.

Barometers: • ____________________= a device used to measure atmospheric pressure • How does a barometer measure atmospheric pressure?

o The Hg in the tube pushes downward b/c of its weight, which is due to the________________________________.

o The Hg in the tube thus falls until the pressure exerted by its

weight is equal to the pressure exerted by the atmosphere

o The _____________of the Hg in the tube depends on the _____________

The pressure of the atmosphere is proportional to the height of the Hg column, so the height of the Hg can be used to measure atmospheric pressure!

GAS LAWS:

• To find the volume of a gas, you need to know both the temperature and the pressure.

Remember to convert ALL temperatures to K. (_________________)

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~Remember values for STP are: 273 K 101.3 kPa 1 atm 0 °C 760 mm Hg 760 torr

Pressure and Volume of a Gas at Constant Temperature: _______________________– states that if the temperature is constant, volume and pressure are inversely proportional. If the pressure increases, the volume decreases! • Ex: If you squeeze a balloon, it gets smaller, but the pressure increases and if it increases

too much, it will pop. The reverse is also true, if the pressure decreases, the volume will increase.

• Ex: Halving the volume leads to twice the rate of collisions and a doubling of the pressure

• KMT Explanation: o As volume______________, gas particles

have_______ frequent collisions with container walls causing _____________pressure

o As volume _____________gas particles have

________frequent collisions with container walls causing _____________pressure.

• If the volume (V) is doubled, what happens to the pressure

(P)? o __________________________________

• If P is reduced by 1/3, what happens to the V?

o _____________________________ • Formula: P1V1 = P2V2

o The subscript 1 means the starting (___________)value o The subscript 2 means the ending (___________) value

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Ex #1: 242cm3 of oxygen gas is collected in a container and has a pressure of 87.6 kPa and a constant temperature. What volume will the same gas occupy @ STP (101.3 kPa)? Ex #2: Suppose a 30mL container of helium gas has a pressure 109 kPa. Calculate the pressure of the gas when it has a volume of 135.7mL. Assume constant temperature.

BBOOYYLLEE’’SS LLAAWW PPRROOBBLLEEMMSS Solve each of the following problems. Show all work. Units should be included on all numbers. Be sure to include the formula solved for the correct variable before inserting numbers. 1) You decide to climb to the tops of some of the tallest mountains. Before you are about to leave on your epic

journey a friend gives you a balloon with a volume of 800.0 mL that was inflated under standard pressure. You climbed two different mountains with this balloon:

Mt. Everest: 29,028 ft above sea level, which has an average atmospheric pressure of 221 mmHg Mt. McKinley: 20,320 ft above sea level, which has an average atmospheric pressure of 345 mmHg

Predict on which mountain the balloon will have the largest volume before doing calculations. Calculate the volume of the balloon on EACH mountaintop. 2) Explain why climbers of tall mountains (such as Mt. Everest and Mt. McKinley) need to carry oxygen with them

near the top of the mountain. How does this relate to the low pressures found on the tops of these mountains?

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3) A 50.0 mL soap bubble is blown at standard pressure. When a thunderstorm passes later in the day, the pressure becomes 700.0 mmHg. Will the bubble get bigger or smaller? Calculate the new volume of the bubble.

4) A balloon was inflated to a volume of 5.0 L at a pressure of 0.90 atm. It rises to an altitude where its volume

becomes 25.0 L. Will the pressure increase or decrease? What was the new pressure? 5) A SCUBA diver inflates a balloon to 10.0 L at the surface (where there is standard pressure- 760 mmHg) and

takes it on a dive. At a depth of 100.0 ft the volume is 2.5L. What was the new pressure of the balloon? 6) A balloon has a volume of 68.5mL at the bottom of a mountain. At the top of the mountain the balloon is

95.4mL and the pressure is 78 kPa. What was the pressure when the balloon was at the bottom of the mountain?

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7) Suppose a soap bubble is blown at 2.67atm and has a volume of 4.5mL. When a thunderstorm passes later in the day, the pressure becomes 1.3 atm. Calculate the new volume of the bubble.

8) A fountain pen that has been used frequently has an ink volume of 1.2 cm3 at the surface where the pressure

is 780.0 mmHg. The pen is put in a pilot’s pocket and the pilot flies to an altitude where the pressure is 520.0 mmHg. What would be the volume of the pen in the pilot’s pocket? Would it be wise for the pilot to wear a pocket protector?

Volume and Temperature of a Gas at Constant Pressure: ____________________ - States that if the pressure is constant, volume and the Kelvin temperature are directly proportional. If the temperature increases, the volume increases, and if the temperature decreases, so does the volume. • KMT Explanation:

o As temp.________________, gas particles move _____________and collide with walls of their container with _________force; to maintain constant pressure--frequency of collisions must ________________(volume increases)

o As temp.__________________, gas particles move

_______________and collide with walls of their container with _____________force; to maintain constant pressure – frequency of collision must ______________(volume decreases)

• If temp. doubles, what happens to the volume?

o __________________________________

• If the volume decreases by ½, what happens to the temp.? o __________________________________

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• Formula: V1_ = V2__ T1 T2 • Charles’ Law can be used to extrapolate ______________________(theoretically the lowest

possible temperature when molecular motion stops and particles have zero kinetic energy). Absolute zero is ____________________________

Ex#1: 225cm3 volume of gas is collected at 58°C. What volume would this sample of gas occupy at standard temperature? Assume constant pressure. Ex#2: A balloon is inflated in a room at 24°C and has a volume of 4.00 L. The balloon is heated and the new volume is 6.2 L. What temperature was the balloon heated to? Assume that the pressure remains constant.

CCHHAARRLLEESS’’ LLAAWW PPRROOBBLLEEMMSS Solve each of the following problems. Show all work. Units should be included on all numbers. Be sure to include the formula solved for the correct variable before inserting numbers. 1) A 50.0 mL soap bubble is blown in at 27°C room. It drifts out an open window and lands in a snow bank at

−3°C. What is its new volume? 2) A balloon is inflated to a volume of 5.0 L at a temperature of 7°C. It landed in an oven and was heated to

147°C. What is its new volume?

*REMEMBER TO CONVERT ALL TEMPERATURES TO KELVIN! K = °C + 273

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3) During the day at 27°C a cylinder with a sliding top contains 20.0 L of air. At night it only holds 19.0 L. What is the temperature at night?

4) A 113 L sample of helium gas at 27°C is cooled to −78°C. Calculate the new volume of the helium gas. 5) On all aerosol cans you see a warning telling you to keep the can away from heat because of the danger of

explosion. What is the potential volume of the gas contained in a 500.0 mL can at 25°C if it were heated to 54°C? In other words, if the can could expand to allow the gas to take up a greater volume, what would be the new volume of the gas when heated as previously described?

6) a) A CO2 bubble is formed in cake batter at 27°C. In the oven it gets heated to 177°C and has a volume of

0.64mL. What was the size of the CO2 bubble before it was baked?

7) A 655 mL glass filled with air is placed into water up side down while at 23°C. Then the water is cooled to

-2.3°C. What is the volume of the gas when it is cooled?

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8) At one point in history people could measure temperature by looking at the volume of a sample of gas. Suppose a sample in a gas thermometer has a volume of 135 mL at 11°C. What temperature would correspond to each of the following volumes: a) 113 mL b) 142 mL

CCoommbbiinneedd GGaass LLaaww:: • The combined gas law expresses the relationship between pressure, volume, and

temperature of a fixed amount of gas. It is a combination of the previous laws. • Formula: _P1V1 = __P2V2 T1 T2 Ex #1: A gas filled balloon occupies 31 L at 41°C and 1028 mmHg. What volume would the balloon occupy at STP?

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CCOOMMBBIINNEEDD GGAASS LLAAWW PPRROOBBLLEEMMSS:: Solve each of the following problems. Show all work. Units should be included on all numbers. Be sure to include the formula solved for the correct variable before inserting numbers. 1) A balloon is filled with helium to a volume of 4.0 L when the pressure is 1.0 atm and the temperature is 27˚C.

It escapes and rises until the pressure is 0.25 atm and the temperature is −23˚C. What is the new volume? 2) When a bubble escapes from a sunken ship, it has a pressure of 42 atm and a temperature of −3˚C. It

reaches the surface where it is 4,842 cm3 and the temperature is 27˚C. The pressure at the surface is 1.10 atm. What was the original volume of the bubble?

3) A CO2 bubble in some bread dough had an original volume of 0.30 mL when it formed at 27˚C and 750. mmHg

of pressure. While baking, its temperature rose to 177˚C and a thunderstorm moved through dropping the pressure to 725 mmHg. What is the new volume of the bubble?

4) Suppose an air balloon holds 3.10 x 102 mL of air at standard pressure. The balloon is heated to 67˚C and rises

to where the pressure is 755 mmHg and is now 3.54 x 102 mL. What was the original temperature of the gas?

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5) A SCUBA diver’s tank holds 235 liters of air at 27˚C and 150 atm. What would the volume of the gas be when the diver is at a pressure of 40 atm and the temperature is 7˚C?

6) You drive to school in a hurricane where the pressure is 720 mmHg, which is abnormally low. However, when

you get out of your car you notice that the volume of your tires seems normal: 5.00 liters. During the day a high pressure, bright sunshine system moves overhead changing the pressure to 780 mmHg. When you come back outside you notice your tires seem a little flat. What is the new volume of your tires?

7) During the day at 25˚C a cylinder with a sliding top contains 20.0 L of air. At night it only holds 18.0 L of air.

None of the air leaked out. What is the temperature at night? (Assume pressure doesn’t change significantly over the entire day.)

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Dalton’s Law of Partial Pressures: • Dalton’s Law of partial pressures = The total pressure of a mixture of gases is equal to

the sum of the partial pressures of the component gases. • _____________________________= The pressure of each gas in a mixture is called the

partial pressure of that gas. • Formula: PT = P1 + P2 + P3 + . . . Ex: Suppose the pressure of three unknown gases is 3.23 atm, 3.89 atm, and 2.33 atm. What is the total pressure of the three gases?

Dalton’s Law of partial pressures & Gases collected by water displacement:

• Gases collected in the lab are often

collected over water. The collected gas will mix with water vapor. Water vapor, like other gases, exerts a pressure known as water vapor pressure. If the collection bottle is adjusted so the levels of water inside and outside the bottle are the same, the pressure of the collected gas will equal that of atmospheric pressure.

• The total pressure of the gas can be found using the following formula:

Ptotal = Pdry gas + Pwater vapor

OR

Pdry gas = Ptotal − Pwater vapor

• Once you find Pdry gas –this is now P1 for the Combined Gas Law!

• You will have to use a chart (see last page of packet) to find the vapor pressure of water. Use the temperature given and look up the value for the Pwater (be sure to use the correct pressure units)

• Dalton’s Law will also be used with the Combined Gas Law

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Ex#1: Suppose that a sample of potassium chlorate is decomposed by heating. Suppose that 720 mL of oxygen gas is produced and collected over water at 25˚C and 755.0 mmHg. Calculate the volume of the dry oxygen gas at STP. Ex#2: Suppose that 3.67 L of hydrogen gas is produced and collected over water at STP. Calculate the volume of the dry hydrogen gas at 45 ˚C and 98.3 kPa.

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DDAALLTTOONN’’SS LLAAWW PPRROOBBLLEEMMSS Solve each of the following problems. Show all work. Units should be included on all numbers. Be sure to include the formula solved for the correct variable before inserting numbers. 1) Suppose that 100 mL of neon gas is collected over water at 27°C and 785.5 mmHg. At what Celsius

temperature would the dry gas occupy 50.0 mL at 711.4 mmHg? 2) If 120 mL of argon is collected over water at 25°C and 780.0 mmHg, compute the volume of the dry argon at

STP. 3) A sample of oxygen gas is collected over water in a 175 mL container at 50.°C and 100.9 kPa. What volume

would the dry gas occupy at 15°C and 98.1 kPa?

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4) A 135 mL sample of oxygen gas is collected over water at a temperature of 35°C and a total pressure of 742.0 mmHg. At what temperature would the dry oxygen gas occupy 146.34mL at 765.5 mmHg?

5) If 222 mL of helium is collected over water at 50.°C and 103.0 kPa, compute the volume of the dry helium at

STP.

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Vapor Pressure of Water in mmHg Temperature Pressure Temperature Pressure

(C) (mmHg) (C) (mmHg) -5 3.00 25.5 24.5 0 4.58 26 25.2 5 6.45 26.5 26.0 8 8.03 27 26.7 10 9.22 27.5 27.5 12 10.5 28 28.4 14 12.0 28.5 29.2 16 13.7 29 30.1 18 15.5 29.5 31.0 20 17.6 30 31.8 20.5 18.1 35 42.4 21 18.7 40 55.4 21.5 19.2 50 92.3 22 19.8 60 149 22.5 20.4 70 234 23 21.1 80 354 23.5 21.7 90 525 24 22.4 100 760 24.5 23.1 200 11660 25 23.8

Vapor Pressure of Water in kPa

Temperature Pressure Temp. Pressure Temp. Pressure (C) (kPa) (C) (kPa) (C) (kPa) 0 0.6 21 2.5 30 4.2 5 0.9 22 2.6 35 5.6 8 1.1 23 2.8 40 7.4 10 1.2 24 3.0 50 12.3 12 1.4 25 3.2 60 19.9 14 1.6 26 3.4 70 31.2 16 1.8 27 3.6 80 47.3 18 2.1 28 3.8 90 70.1 20 2.3 29 4.0 100 101.3

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GGAASSEESS HHOOMMEEWWOORRKK:: Answer the following question based on your notes and classroom activities. 1. Describe particle spacing and motion of a gas. 2. According to KMT, describe the shape and volume of gases. Be specific! 3. Why can gases be compressed while solids cannot? 4. What is the difference between diffusion and effusion when dealing with a gas? 5. What causes a gas to exert pressure?

6. List 2 ways atmospheric pressure can be affected? 7. What does a barometer measure? ___________________________________ 8. What force is pulling down on the column of mercury in a barometer? ________________ 9. How can the height of the Hg be used to measure atmospheric pressure in a Hg barometer? 10. What will happen to the column of mercury if atmospheric pressure decreases? 11. Using the KMT, explain what happens to the volume and pressure of a gas when the volume decreases?

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12. Using the KMT, explain what happens to the temperature and volume of a gas when the temperature increases and pressure is constant?

13. What is the difference between a real gas and an ideal gas?

a. Which gas is used in the study of the different gas laws? _____________________________ 14. List the values for STP. 15. What is the difference between Boyle’s Law and Charles’ Law? 16. What are 2 causes of non-ideal behavior of gases? 17. Look at the two graphs below. Determine which one represents Boyle’s Law and which one represents Charles’ Law.

a. Graph A = _________________________ • How do you know?

b. Graph B = _________________________ • How do you know?

Graph A

Graph B

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PROBLEMS: 1. Neon is collected over water in a 35 ml flask. The temperature is 80°C and the pressure is 542

kPa. What will the volume of neon gas be at STP? 2. A 113 cm3 volume of gas is collected at 23°C. What will the volume of oxygen be at 46°C, if the

pressure remains the same? 3. Nitrogen gas occupies 236cm3 at 478 kPa. If the temperature remains constant, what will the

volume of nitrogen be at 890 kPa?

4. 312 ml of oxygen gas is collected in a container at 24°C and 1054 kPa, what will the volume be at 319K and 1329 kPa?

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5. A sample of oxygen gas is collected over water in a 175mL container at 50°C and 100.9 kPa. Calculate the pressure of the dry gas if it occupied 140mL at 15°C.

6. A 185 mL sample of hydrogen gas had it pressure changed from 75 kPa to 150 kPa, at a constant

temperature. Calculate the new volume. 7. A 42mL sample of air at 31°C and 1027mm Hg is collected. What volume would the air occupy at

STP? 8. Suppose a 50 cm3 sample of gas is collected at 25°C. Calculate the volume of the gas if it cooled

to -4°C under constant pressure.

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Unit Learning Map (9 days): Gases Mrs. Hostetter

Unit Essential Question(s): Instructional Tools:

Guided Notes Demo: balloon in flask, Cartesian diver, Can Crush Lab Materials: Boyle’s Law Lab Molar Volume Lab

How are do gas particles behave according to

KMT?

KMT & Gases Boyle’s Law & Charles’ Law

Combined Gas Law Dalton’s Law

1) How can KMT be used to describe certain properties of gases?

1) How are volume and pressure of a gas related?

2) How are pressure and temperature of a gas related?

1) How are volume, temperature and pressure of a gas related?

1) How can you determine the pressure of a gas when it is collected over water?

Ideal Gas Real gas Diffusion Effusion Pressure Atmospheric pressure Barometer

Boyle’s Law Charles’ Law

Combined Gas Law Dalton’s Law Water vapor

Vocabulary: Vocabulary: Vocabulary: Vocabulary:

Lesson Essential Question(s): Lesson Essential Question(s): Lesson Essential Question(s): Lesson Essential Question(s):

Concept: Concept: Concept: Concept:

Class: Academic Chemistry B -PA Standard: Predict the behavior of gases through the application of laws (e.g., Boyle’s law, Charles’ law, or ideal gas law.

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Gases Vocabulary:

1) Ideal gas = an imaginary gas that conforms perfectly to all the assumptions of the kinetic-molecular theory

2) Real gas = a gas that does not behave completely according to the assumptions of the kinetic-

molecular theory 3) Diffusion = spontaneous mixing of the particles of two substances caused by their random motion 4) Effusion = a process by which gas particles pass through a tiny opening 5) Pressure (P) = the force per unit area on a surface 6) Barometer = a device used to measure atmospheric pressure 7) BOYLE’S LAW – states that if the temperature is constant, volume and pressure are inversely

proportional. If the pressure increases, the volume decreases!

• Formula: P1V1 = P2V2 8) CHARLES’ LAW - States that if the pressure is constant, volume and the Kelvin temperature are

directly proportional. If the temperature increases, the volume increases, and if the temperature decreases, so does the volume

• Formula: V1_ = V2__ T1 T2 9) COMBINED GAS LAW = expresses the relationship between pressure, volume, and temperature of

a fixed amount of gas. It is a combination of the previous laws • Formula: _P1V1 = __P2V2

T1 T2 10) DALTON’S LAW OF PARTIAL PRESSURES = The total pressure of a mixture of gases is equal

to the sum of the partial pressures of the component gases

• Formula: Pdry gas = Ptotal − Pwater vapor

• Once you find Pdry gas –this is now P1 for the Combined Gas Law!

~Remember values for STP are: 273 K 101.3 kPa 1 atm 0 °C 760 mm Hg 760 torr