1. Chapter 14 The Behavior of Gases 14.3 Ideal Gases
14.1 Properties of Gases
14.2 The Gas Laws
14.3 Ideal Gases
14.4 Gases: Mixtures and Movements
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2. How can you blanket a stage with fog?
CHEMISTRY & YOU
How can you blanket a stage with fog?
Solid carbon dioxide, or dry ice, can be used to make stage fog.
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3. Ideal Gas Law
Ideal Gas Law
1. How can you calculate the amount of a contained gas when the pressure, volume, and temperature are specified?
Used the Ideal Gas Law
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4. Ideal Gas Law
2. Suppose you want to calculate the number of moles (n) of a gas in a fixed volume at a known temperature and pressure.
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5. Ideal Gas Law
Suppose you want to calculate the number of moles (n) of a gas in a fixed volume at a known temperature and pressure.
The volume occupied by a gas at a specified temperature and pressure depends on the number of particles.
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6. Ideal Gas Law
Suppose you want to calculate the number of moles (n) of a gas in a fixed volume at a known temperature and pressure.
The volume occupied by a gas at a specified temperature and pressure depends on the number of particles.
The number of moles of gas is directly proportional to the number of particles.
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7. Ideal Gas Law
Suppose you want to calculate the number of moles (n) of a gas in a fixed volume at a known temperature and pressure.
The volume occupied by a gas at a specified temperature and pressure depends on the number of particles.
The number of moles of gas is directly proportional to the number of particles.
Moles must be directly proportional to volume.
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8. Ideal Gas Law
You can introduce moles into the combined gas law by dividing each side of the equation by n.
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9. Ideal Gas Law
You can introduce moles into the combined gas law by dividing each side of the equation by n.
This equation shows that (P  V)/(T  n) is a constant.
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10. Ideal Gas Law
You can introduce moles into the combined gas law by dividing each side of the equation by n.
This equation shows that (P  V)/(T  n) is a constant.
This constant holds for what are called ideal gases—gases that conform to the gas laws.
P1  V P2  V2
T1  n1
T2  n2 =
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11. Ideal Gas Law
4. If you know the values for P, V, T, and n for one set of conditions, you can calculate a value for the ideal gas constant (R).
P  V
T  n
R =
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12. Ideal Gas Law
4. If you know the values for P, V, T, and n for one set of conditions, you can calculate a value for the ideal gas constant (R).
Recall that 1 mol of every gas occupies 22.4 L at STP (101.3 kPa and 273 K).
P  V
T  n
R =
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13. Ideal Gas Law
4. If you know the values for P, V, T, and n for one set of conditions, you can calculate a value for the ideal gas constant (R).
Recall that 1 mol of every gas occupies 22.4 L at STP (101.3 kPa and 273 K).
Insert the values of P, V, T, and n into (P  V)/(T  n).
P  V
T  n
R = =
101.3 kPa  22.4 L
273 K  1 mol
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14. Ideal Gas Law
4. If you know the values for P, V, T, and n for one set of conditions, you can calculate a value for the ideal gas constant (R).
A. Recall that 1 mol of every gas occupies 22.4 L at STP (101.3 kPa and 273 K).
B. Insert the values of P, V, T, and n into (P  V)/(T  n).
P  V
T  n
R = =
101.3 kPa  22.4 L
273 K  1 mol
R = 8.31 (L·kPa)/(K·mol)
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15. Ideal Gas Law
6. The gas law that includes all four variables—P, V, T, n—is called the ideal gas law.
P  V = n  R  T
PV = nRT or
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16. Ideal Gas Law
7. When the pressure, volume, and temperature of a contained gas are known, you can use the ideal gas law to calculate the number of moles of the gas.
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17. Sample Problem 14.5
Using the Ideal Gas Law
8. At 34oC, the pressure inside a nitrogen-filled tennis ball with a volume of L is 212 kPa. How many moles of nitrogen gas are in the tennis ball?
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18. Analyze List the knowns and the unknown.
Sample Problem 14.5
Analyze List the knowns and the unknown. 1
Use the ideal gas law (PV = nRT) to calculate the number of moles (n).
KNOWNS
UNKNOWN
P = 212 kPa
V = L
T = 34oC
R = 8.31 (L·kPa)/(K·mol)
n = ? mol N2
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19. Calculate Solve for the unknown.
Sample Problem 14.5
Calculate Solve for the unknown. 2
Convert degrees Celsius to kelvins.
T = 34oC = 307 K
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20. Calculate Solve for the unknown.
Sample Problem 14.5
Calculate Solve for the unknown. 2
State the ideal gas law.
P  V = n  R  T
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21. Calculate Solve for the unknown.
Sample Problem 14.5
Calculate Solve for the unknown. 2
Rearrange the equation to isolate n.
P  V = n  R  T
Isolate n by dividing both sides by (R  T): =
R  T
n  R  T
P  V
n =
R  T
P  V
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22. Calculate Solve for the unknown.
Sample Problem 14.5
Calculate Solve for the unknown. 2
Substitute the known values for P, V, R, and T into the equation and solve.
n =
R  T
P  V
n =
8.31 (L·kPa) / (K·mol)  307 K
212 kPa  L
n = 1.23  10–2 mol N2
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23. 10. Evaluate Does the result make sense?
Sample Problem 14.5
10. Evaluate Does the result make sense? 3
A. A tennis ball has a small volume and is not under great pressure.
B. It is reasonable that the ball contains a small amount of nitrogen.
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24. Sample Problem 14.6
Using the Ideal Gas Law
11. A deep underground cavern contains 2.24 x 106 L of methane gas (CH4) at a pressure of 1.50 x 103 kPa and a temperature of 315 K. How many kilograms of CH4 does the cavern contain?
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25. Analyze List the knowns and the unknown.
Sample Problem 14.6
Analyze List the knowns and the unknown. 1
Calculate the number of moles (n) using the ideal gas law. Use the molar mass of methane to convert moles to grams. Then convert grams to kilograms.
KNOWNS
UNKNOWN
P = 1.50  103 kPa
V = 2.24  103 L
T = 315 K
R = 8.31 (L·kPa)/(K·mol)
molar massCH4 = 16.0 g
m = ? kg CH4
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26. Calculate Solve for the unknown.
Sample Problem 14.6
Calculate Solve for the unknown. 2
State the ideal gas law.
P  V = n  R  T
Rearrange the equation to isolate n.
n =
R  T
P  V
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27. Calculate Solve for the unknown.
Sample Problem 14.6
Calculate Solve for the unknown. 2
Substitute the known quantities into the equation and find the number of moles of methane.
n =
8.31 (L·kPa)/(K·mol)  315 K
(1.50  106 kPa)  (2.24  106 L)
n = 1.28  106 mol CH4
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28. Calculate Solve for the unknown.
Sample Problem 14.6
Calculate Solve for the unknown. 2
Do a mole-mass conversion.
1.28  106 mol CH4 
16.0 g CH4
1 mol CH4
= 20.5  106 g CH4
= 2.05  107 g CH4
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29. Calculate Solve for the unknown.
Sample Problem 14.6
Calculate Solve for the unknown. 2
Convert from grams to kilograms.
2.05  106 g CH4 
1 kg
103 g
= 2.05  104 kg CH4
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30. Evaluate Does the result make sense?
Sample Problem 14.6
Evaluate Does the result make sense? 3
Although the methane is compressed, its volume is still very large.
So it is reasonable that the cavern contains a large amount of methane.
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31. How would you rearrange the ideal gas law to isolate the temperature, T?PV nR
T = A. nR PV
T = C. PR nV
T = B. RV nP
T = D.
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32. How would you rearrange the ideal gas law to isolate the temperature, T?PV nR
T = A. nR PV
T = C. PR nV
T = B. RV nP
T = D.
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33. Ideal Gases and Real Gases
Under what conditions are real gases most likely to differ from ideal gases?
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34. Ideal Gases and Real Gases
15. An ideal gas is one that follows the gas laws at all conditions of pressure and temperature.
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35. Ideal Gases and Real Gases
An ideal gas is one that follows the gas laws at all conditions of pressure and temperature.
Its particles could have no volume.
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36. Ideal Gases and Real Gases
15. An ideal gas is one that follows the gas laws at all conditions of pressure and temperature.
A. Its particles could have no volume.
B. There could be no attraction between particles in the gas.
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37. Ideal Gases and Real Gases
There is no gas for which these assumptions are true.
So, an ideal gas does not exist.
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38. Ideal Gases and Real Gases
At many conditions of temperature and pressure, a real gas behaves very much like an ideal gas.
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39. Ideal Gases and Real Gases
At many conditions of temperature and pressure, a real gas behaves very much like an ideal gas.
The particles in a real gas have volume.
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40. Ideal Gases and Real Gases
At many conditions of temperature and pressure, a real gas behaves very much like an ideal gas.
The particles in a real gas have volume.
There are attractions between the particles.
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41. Ideal Gases and Real Gases
17. At many conditions of temperature and pressure, a real gas behaves very much like an ideal gas.
The particles in a real gas have volume.
There are attractions between the particles.
Because of these attractions, a gas can condense, or even solidify, when it is compressed or cooled.
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42. Ideal Gases and Real Gases
18. Real gases differ most from an ideal gas at low temperatures and high pressures.
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43. Interpret Graphs
This graph shows how real gases deviate from the ideal gas law at high pressures.
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44. What are the characteristics of an ideal gas?
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45. What are the characteristics of an ideal gas?
20. The particles of an ideal gas have no volume, and there is no attraction between them.
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46. CHEMISTRY & YOU
Certain types of fog machines use dry ice and water to create stage fog. What phase changes occur when stage fog is made?
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47. CHEMISTRY & YOU
Certain types of fog machines use dry ice and water to create stage fog. What phase changes occur when stage fog is made?
Dry ice doesn’t melt—it sublimes. As solid carbon dioxide changes to gas, water vapor in the air condenses and forms a white fog. Dry ice can exist because gases don’t obey the assumptions of kinetic theory at all conditions.
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48. Key Concepts and Key Equation
21. When the pressure, volume, and temperature of a contained gas are known, you can use the ideal gas law to calculate the number of moles of the gas.
22. Real gases differ most from an ideal gas at low temperatures and high pressures.
23. Key Equation: ideal gas law
P  V = n  R  T or PV = nRT
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49. Glossary Terms
24. ideal gas constant: the constant in the ideal gas law with the symbol R and the value 8.31 (L·kPa)/(K·mol)
25. ideal gas law: the relationship PV = nRT, which describes the behavior of an ideal gas
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50. BIG IDEA
Kinetic Theory
26. Ideal gases conform to the assumptions of kinetic theory.
27. The behavior of ideal gases can be predicted by the gas laws.
28. With the ideal gas law, the number of moles of a gas in a fixed volume at a known temperature and pressure can be calculated.
29. Although an ideal gas does not exist, real gases behave ideally under a variety of temperature and pressure conditions.
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51. END OF 14.3
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