Notes: Ideal Gases

CHAPTER 13 &14 NOTES PACKET THE BEHAVIOR OF GASES Big Picture Idea: Gases are affected by temperature, pressure, and volume changes.

Big Picture Question: How are gases affected by temperature, pressure and volume? Suggested Resources… Homework Assignments Classwork Assignments Laboratory Activities Formative Assessments Textbook pages: Chapter 14 Websites: www.webelements.com Key Terms: 6. Molar volume 12.Boyle’s Law 1. Diffusion 7. Partial pressure 13.Charles’ Law 2. Elastic collision 8. Ideal gas 14.Gay Lussac’s Law 3. Kinetic molecular 9. Real gas 15.Graham’s Law theory 10.Gas constant 16.Dalton’s Law of par- 4. STP 11.PV=nRT (Ideal gas tial pressures 5. Absolute zero Law) 17.Combined Gas Laws Directions: Use this information as a general reference tool to guide you through this unit. Don’t hesitate to ask your teacher for help By the conclusion of this unit, you should know By the conclusion of this unit, you should be able to the following: do the following:

1. The kinetic molecular theory explains 1. Convert between different temperature, the behavior of gases. pressure and volume units. 2. Gases are affected by temperature, 2. Solve problems using the Combined pressure and volume changes. Gas Law and the Ideal Gas Law. 3. Relationships between temperature, pressure, and volume. 4. How gas and atmospheric pressure are measured. 5. The total pressure of a system of two or more gases would equal the sum of each gas’s partial pressure. GASES

Properties of Gases:

Kinetic Theory:

The particles in a gas are assumed to be small, hard spheres with an insignificant volume

The motion of particles in a gas is rapid and random.

All collisions between gas particles are perfectly elastic.

Pressure:

Definition: 2 Ch 13 & 14 Notes What creates pressure?

Atmospheric Pressure: Barometer

Pressure Units: 1 atmosphere = 760 mmHg = 101.3kPa

Make the following pressure conversions

4.3 atm to mmHg

2.25atm to kPa

450mmHg to kPa

Volume:

Definition:

Units: 1000 mL = 1 L = 1 dm3

3 Ch 13 & 14 Notes Kinetic Energy and Temperature:

Kinetic Energy:

Temperature:

Why Kelvin Temperature?

What is Absolute Zero?

What is STP?

Kelvin Temperature:

Units: 1 K = 1 °C K = °C +273

Make the following temperature conversions:

100°C to K 323 K to °C

4 Ch 13 & 14 Notes a. Which point on each curve represents the average kinetic energy? (label on diagram)

b. Which point on each curve represents the slowest moving particles? (label on diagram)

c. Which point on each curve represents the fastest moving particles? (label on diagram)

d. What do you think would happen to the first shape of the curve if the temperature were even lower?

RELATIONSHIPS BETWEEN PRESSURE, VOLUME & TEMPERATURE OF A GAS

Charles’s Law – Volume and Temperature Type of relationship? Temp. (K) Volume (L) 100 200 Equation 400 800

Practice problem: If a gas occupies 10.0 L at 50°C, what volume will it occupy at 150°C? Temperature MUST be in Kelvins (K = ºC + 273)

You Try: If a gas occupies 33.7 L at 16°C, what temperature will it be when it occupies a volume of 67.4 L?

5 Ch 13 & 14 Notes Gay-Lussac’s Law - Pressure and Temperature

Temp. (K) Pressure (atm) Type of relationship? 100 200 Equation 400 800

Practice problem: If a gas exerts a pressure of 2.5 atm at 100°C, what pressure would it exert at 200°C?

Temperature MUST be in Kelvins (K = ºC + 273)

You Try: The pressure of a gas is 650mmHg at 23°C. At what temperature will its pressure drop to 425mmHg?

Boyle’s Law-Pressure and Volume

Volume (mL) Pressure ( ) 60 50 40 30 20 10

Practice problem: A gas occupies a volume of 7.5 L at 550 mmHg. What volume will it occupy at 850 mmHg?

6 Ch 13 & 14 Notes You Try: A gas occupies a volume of 7.5 L at 550 mmHg. What is the pressure of a gas that has a volume of 8.50 L?

Combined Gas Law

Equation:

Practice Problem: If a gas occupies 5.0 L at 1.25 atm and 75°C, what volume will it occupy at 0.5 atm and 125°C ?

GAS LAW PRACTICE PROBLEMS

Before beginning, write out all four formulas in the box below:

1. A gas occupies 450mL at 23C. Determine its volume at 75C if the pressure remains constant. Do you expect volume to go up or down? Formula:

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2. A gas in an expandable container has a pressure of 1.2atm when the volume is 10.0L. Determine its volume if the pressure is reduced to 0.85atm and the temperature remains constant. Do you expect volume to go up or down? 7 Ch 13 & 14 Notes Formula:

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3. A gas exerts a pressure of 106kPa in a sealed, rigid container at 25C. At what temperature will it exert a pressure of 149kPa? Do you expect temperature to go up or down? Formula:

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8 Ch 13 & 14 Notes 4. A gas exerts a pressure of 1.2atm in a 525mL container. Find the pressure of the same gas in a 2.5L container.

Do you expect pressure to go up or down? Formula:

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5. The temperature of a gas sample at standard pressure is 25°C. Find its pressure if it is heated to 98°C.

Do you expect pressure to go up or down? Formula:

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6. A gas occupies 240mL at 23°C and 650mmHg. It is transferred to a 375mL container at 30°C. Find the pressure in the new container.

Formula:

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7. A gas occupies 525mL at 30°C and 1.2 atm. What volume will it occupy at STP?

Formula:

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9 Ch 13 & 14 Notes Ideal Gas Law : Adding in the Mole

 moles and pressure

 moles and volume

 moles and temperature

Ideal Gas Law equation:

Determining “R”:

Other values for “R”: 8.31 kPa . L 0.0821 L . atm 62.4 mHg . L mol . K mol . K mol . K Example: 1. What volume is occupied by 0.250 mol of carbon dioxide gas at 250C and 371mm Hg?

2. Find the mass of oxygen in a 750mL container at 745mmHg and 23°C.

3. At what temperature will 12.0g of nitrogen occupy 32.0L if the pressure is 100kPa?

10 Ch 13 & 14 Notes GAS STOICHIOMETRY

Avogadro’s law shows that the mole ratio of two gases at the same temperature and pressure is the same as the volume ratio of the two gases.

2. Write the balanced equation when sodium reacts with water:

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What type of reaction is this? ______

How many liters of hydrogen gas will be produced at 280.0 K and 96.0 kPa if 40.0 g of sodium react with excess water?

Given:

3. Write the balanced that occurs when aluminum carbonate decomposes to form aluminum oxide and carbon dioxide.

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What type of reaction is this? ______

What volume of carbon dioxide, at 295.0 K and 880 mmHg, will be formed if 50.0g of aluminum carbonate decompose?

Given:

11 Ch 13 & 14 Notes USING THE IDEAL GAS LAW TO FIND MOLAR MASS AND DENSITY

Molar Mass = mass of gas moles of gas

What is the molar mass of the element that has a mass of 89.78g and occupies 45 L at 2.5 atm and 35oC.? Identify the element.

TRY: Find the molar mass of a gas if 0.75g of the gas fill a 500mL flask at 23°C and 747mmHg.

Density = mass of gas L of gas

What is the density of carbon disulfide (gas) at STP?

What is the density of nitrogen gas at 102kPa and 45°C?

12 Ch 13 & 14 Notes MOVEMENT OF GAS PARTICLES: MAXWELL-BOLTZMAN DISTRIBUTION

a. If both samples contain the same gas, which sample is at a higher temperature? b. If both samples are at the same temperature, which gas has the higher molar mass?

GRAHAM’S LAW: PARTICLE SPEED AND MASS

Temperature is the average kinetic energy of particles in a sample. Kinetic energy is related to particle speed and mass. If two particles are at the same temperature, the lighter one will have the higher speed.

If a sample of hydrogen and a sample of nitrogen are each is a sealed 1.0L container at the same temperature and the same pressure:

a. which sample contains more molecules? ______

b. which sample is heavier? ______

c. which sample has the greater average kinetic energy? ______

d. in which sample are the particles moving faster? ______

13 Ch 13 & 14 Notes DALTON’S LAW AND PARTIAL PRESSURE OF GASSES

H N 2 2 H 2 CO H 2 2 N 2 CO 2 H N 2 2

DALTON’S LAW:

a. The container above contains 4.0moles of hydrogen, 3.0 moles of nitrogen and 2.0 moles of carbon dioxide. The total pressure of the container is 450mmHg.

Determine the partial pressure of each gas.

P H2 = P N2 = P CO2=

b. The pressure of nitrogen in the classroom is approximately 0.82atm. The pressure of oxygen in the room is approximately 0.20atm and the pressure of water vapor in the room is approximately 0.02atm.

a. The total pressure in the room is 1.10atm. Assuming carbon dioxide is the only other gas present, find the pressure of carbon dioxide in the room.

b. Find the number of moles of oxygen in the room if the room holds 8500 moles of air.

14 Ch 13 & 14 Notes COLLECTING GASSES OVER WATER.

Oxygen gas is collected by water displacement in a 250mL flask at 30ºC and a barometric pressure of 95.00kPa. The vapor pressure of water at 30ºC is 31.82kPa.

Determine the pressure of the dry oxygen in the flask.

Determine the number of moles of dry oxygen in the flask.

15 Ch 13 & 14 Notes EDMODO HOMEWORK #1: MIXED GAS LAWS

SHOW ALL WORK FOR ALL PROBLEMS

1.0 atm = 760 mmHg = 101.3 kPa And 0C = 273 K

Change the following units:

359 kPa = ______atm 10C = ______K

6.2 atm = ______mmHg 10K = ______C

FOR EACH PROBLEM, WRITE OUT THE FORMUA YOU ARE USING. WRITE YOUR ANSWER IN THE SPACE PROVIDED.

1. The gas in a sealed can is at a pressure of 3.00 atm at 25C. A warning on the can tells the user not to store the can in a place where the temperature will exceed 52C. What would the gas pressure in the can be at 52C?

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2. A sample of hydrogen exerts a pressure of 0.829 atm at 47C. At what temperature will the pressure raise to 1.5atm.

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16 Ch 13 & 14 Notes 3. A sample of neon gas occupies a volume of 752 mL at 25C. What volume will the gas occupy at standard temperature if the pressure remains constant?

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4. A sample of oxygen gas has a volume of 150 mL when its pressure is 440 mmHg. If the pressure is increased to standard pressure and the temperature remains constant, what will the new gas volume be?

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5. Ralph had a helium balloon with a volume of 4.88 liters at 150 kPa of pressure. If the volume is changed to 3.15 liters, what would be the new pressure in atm?

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6. 536 mL of nitrogen gas are at -25C. At what temperature will it expand to 2.2L if the pressure remains constant.

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17 Ch 13 & 14 Notes EDMODO HOMEWORK #2: COMBINED GAS LAW/MIXED 1. A gas has a pressure of 725mmHg in a 2.0L container at 33C. Determine its pressure in a 3.5L container at 100.0C.

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2. A gas occupies 550mL at 98C and 890mmHg. Determine its volume at STP.

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3. Determine the temperature of a gas at 650mmHg in a 5.0L container if it occupies 875mL at 23C and 425mmHg.

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4. A gas expands to 4.4L at 65°C. At what temperature will it contract to 950mL.

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5. Find the volume of a gas at 1.2atm if its volume is 650mL at 600mmHg.

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6. A gas occupies 855mL at 32°C and 455mmHg. At what temperature will it occupy 1.8L at 99kPa?

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7. Find the volume of a gas at STP if it occupies 2.3L at 29°C and 1.1atm.

______18 Ch 13 & 14 Notes EDMODO HOMEWORK #3: IDEAL GAS LAW

8.31 kPa . L 0.0821 L . atm 62.4 mHg . L mol . K mol . K mol . K

1) How many moles of a gas at 100°C does it take to fill a 1.00 L flask to a pressure of 1.50 atm?

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2) A camping stove uses a 2.0L propane tank that holds 30g of liquid C3H8. Find the pressure in the tank at 25°C.

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3) What volume would be occupied by 100 g of oxygen gas at a pressure of 1.50atm and a temperature of 25°C?

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4) On a warm day, a very large amusement park balloon is filled with 47.8 g of helium. The temperature is 33°C and the pressure in the balloon is 785mmHg. Calculate the volume of the balloon.

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19 Ch 13 & 14 Notes 5) A ten-liter gas cylinder contains 380 g of nitrogen. What pressure, in kPa, is exerted by the nitrogen at 25°C?

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6) A drum used to transport crude oil has a volume of 162 L. How many water molecules, as steam, are required to fill the drum at 1.00 atm and 100°C?

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7) How many moles of air are there in a 125 mL erlenmeyer flask if the pressure is 755 mm Hg and the temperature is 20°C?

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20 Ch 13 & 14 Notes EDMODO HOMEWORK #4: GAS STOICHIOMETRY, ETC

1. Write the balanced equation for the reaction that occurs when chlorine gas is bubbled through a solution of sodium iodide.

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a. Use stoichiometry to predict the volume of chlorine gas, at STP, needed to react with 45.0g of sodium iodide.

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b. Use stoichiometry and gas laws to predict the volume of chlorine gas, at 32°C and 750mmHg, needed to react with 125g of sodium iodide.

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2. Write the balanced equation for the combustion of ethylene, C2H2.

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What mass of ethylene must burn in order to form 2.2L of carbon dioxide, at 98kPa and 25°C?

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3. After the reaction, a student measures the volume of carbon dioxide actually formed. He measures 1.8L. Determine the percent yield and percent error.

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21 Ch 13 & 14 Notes EDMODO HOMEWORK #5: MIXED GAS LAWS 1. A container holds 1 mole of nitrogen, 6 moles of methane and 5 moles of carbon dioxide. The total pressure in the container is 800mmHg. Find the pressure of each individual gas.

PN2 = ______PCH4 = ______PCO2 = ______

2. a) A student collects oxygen over water at 23°C. The atmospheric pressure is 755mmHg. The water vapor pressure at this temperature is 21.1mmHg. Find the pressure of the dry oxygen gas.

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***b. The student collected a total of 5.0moles of gas. Using your answer from part a, how many moles of oxygen did he collect?

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3. Find the temperature of a gas sample that contains 54g of oxygen in a 32L container at 1.2atm.

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4. A gas exerts a pressure of 88kPa in a 3.0L container. The container expands to 4.5L. Assuming the temperature remains constant, what is the new pressure of the gas?

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5. A gas occupies 250mL at 60°C and 425mmHg. Determine its volume at STP.

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6. A student has a 500mL flask filled with NO2 at 1.2atm and 25°C. He fills a second 500mL flask with O2 at 1.2atm and 25°C.

a. Which flask is heavier? ______b. Which flask has more molecules? ______c. Which flask has the higher average kinetic energy? ______d. In which flask are the molecules moving faster? ______

22 Ch 13 & 14 Notes EDMODO HOMEWORK #6: CHAPTER 13-14 REVIEW 1. A gas occupies a volume of 6.25 liters at 25.0C. What volume would it occupy at –25.0C?

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2. If a gas occupies a volume of 3.75 liters and exerts a pressure of 925 mm Hg at 95.0C, what pressure would it exert at 75.0C and in a volume of 1.90 liters?

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3. Find the density of carbon monoxide at 600mmHg and 33°C.

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4. If a gas occupies a volume of 125 ml at a pressure of 0.415 atm, what pressure will the gas exert in a 79.0 ml container?

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5. What mass of chlorine gas will occupy 1250 ml and exert a pressure of 2100 mm Hg at 100.0C?

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6. What volume will 1.85 moles of xenon occupy at 1025 mm Hg and 100.0C?

23 Ch 13 & 14 Notes 7. 70.4g of a gas occupies 40.0L at 23°C and 745mmHg. Find the molar mass of the gas.

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8. Write the reaction for the decomposition of sodium chlorate to form sodium chloride and oxygen.

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What volume of oxygen, at 755mmHg and 25°C, will be formed by the complete decomposition of 125g of sodium chlorate?

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9. A container holds 2.5moles of nitrogen and 5.5 moles of helium at STP. The total pressure of the container is 600mmHg. Find the pressure of the helium.

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Which gas is moving faster, the helium or the nitrogen? ______

24 Ch 13 & 14 Notes