1. Chapter 14 The Behavior of Gases 14.2 The Gas Laws
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. Boyle’s Law
Do Now:
If I have 10 L of gas at a pressure of 1 atm and double the pressure, what will the new volume of the gas be?
250 L of gas is in a sealed container at a pressure of 1.5 atm. If I decrease the volume of the container to 100 L, what will the gas pressure be?
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3. Boyle’s Law
Boyle’s law states that for a given mass of gas at constant temperature, the volume of the gas varies inversely with pressure.
P1  V1 = P2  V2
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4. CHEMISTRY & YOU
A hot air balloon contains a propane burner onboard to heat the air inside the balloon. What happens to the volume of the balloon as the air is heated?
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5. Remember: T Kelvin = T Celsius + 273 V1 V2 T1 T2
Charles’s Law
Charles’s law: the volume of a fixed mass of gas is directly proportional to its Kelvin temperature if the pressure is kept constant.
Remember: T Kelvin = T Celsius + 273 V1 V2 T1 T2 =
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6. Interpret Graphs
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7. Sample Problem 14.2
Using Charles’s Law
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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8. Analyze List the knowns and the unknown.
Sample Problem 14.2
Analyze List the knowns and the unknown. 1
KNOWNS
UNKNOWN
V1 = 4.00 L
T1 = 24oC
T2 = 58oC
V2 = ? L
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9. Calculate Solve for the unknown.
Sample Problem 14.2
Calculate Solve for the unknown. 2
Because you will use a gas law, start by expressing the temperatures in kelvins.
T1 = 24oC = 297 K
T2 = 58oC = 331 K
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10. Calculate Solve for the unknown.
Sample Problem 14.2
Calculate Solve for the unknown. 2
Rearrange the equation to isolate V2.
V V2 =
T T2
Isolate V2 by multiplying both sides by T2: V1 T2 V2 T1 = 
V2 = T1
V1  T2
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11. Calculate Solve for the unknown.
Sample Problem 14.2
Calculate Solve for the unknown. 2
Substitute the known values for T1, V1, and T2 into the equation and solve.
V2 =
297 K
4.00 L  331 K
V2 = 4.46 L
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12. Evaluate Does the result make sense?
Sample Problem 14.2
Evaluate Does the result make sense? 3
The volume increases as the temperature increases.
This result agrees with both the kinetic theory and Charles’s law.
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13. What is the temperature of a 2
What is the temperature of a 2.3 L balloon if it shrinks to a volume of L when it is dipped into liquid nitrogen at a temperature of 77 K?
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14. What is the temperature of a 2
What is the temperature of a 2.3 L balloon if it shrinks to a volume of L when it is dipped into liquid nitrogen at a temperature of 77 K?
T1 = V2
V1  T2
0.632 L
2.3 L  77 K
T1 = 280 K
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15. Gay-Lussac’s Law
Gay-Lussac’s law: pressure of a gas is directly proportional to the Kelvin temperature if the volume remains constant. P1 P2 T1 T2 =
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16. Gay-Lussac’s Law
Food cooks faster in a pressure cooker because trapped steam becomes hotter than it would under atmospheric pressure.
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17. Using Gay-Lussac’s Law
Sample Problem 14.3
Using Gay-Lussac’s Law
The gas in a used aerosol can is at a pressure of 103 kPa at 25oC. If the can is thrown onto a fire, what will the pressure be when the temperature reaches 928oC?
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18. Analyze List the knowns and the unknown.
Sample Problem 14.3
Analyze List the knowns and the unknown. 1
KNOWNS
UNKNOWN
P1 = 103 kPa
T1 = 25oC
T2 = 928oC
P2 = ? kPa
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19. Calculate Solve for the unknown.
Sample Problem 14.3
Calculate Solve for the unknown. 2
Convert temperatures to Kelvin.
T1 = 25oC = 298 K
T2 = 928oC = 1201 K
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20. Calculate Solve for the unknown.
Sample Problem 14.3
Calculate Solve for the unknown. 2
Rearrange the equation to isolate P2.
P P2 =
T T2
Isolate P2 by multiplying both sides by T2: P1 T2 P2 T1 = 
P2 = T1
P1  T2
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21. Calculate Solve for the unknown.
Sample Problem 14.3
Calculate Solve for the unknown. 2
P2 =
298 K
103 kPa  1201 K
P2 = 415 kPa
P2 = 4.15  102 kPa
Does the result make sense?
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22. A pressure cooker containing kale and some water starts at 298 K and 101 kPa. The cooker is heated, and the pressure increases to 136 kPa. What is the final temperature inside the cooker?
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23. A pressure cooker containing kale and some water starts at 298 K and 101 kPa. The cooker is heated, and the pressure increases to 136 kPa. What is the final temperature inside the cooker?
T2 = P1
P2  T1
101 kPa
136 kPa  298 K
T2 = 400 K
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24. The Combined Gas Law P1  V1 T1 T2 P2  V2 =
This assumes the amount of gas is constant
You can derive the other gas laws from this by holding a variable constant
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25. Using the Combined Gas Law
Sample Problem 14.4
Using the Combined Gas Law
The volume of a gas-filled balloon is 30.0 L at 313 K and 153 kPa pressure. What would the volume be at standard temperature and pressure (STP)?
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26. Analyze List the knowns and the unknown.
Sample Problem 14.4
Analyze List the knowns and the unknown. 1
KNOWNS
UNKNOWN
V1 = 30.0 L
T1 = 313 K
P1 = 153 kPa
T2 = 273 K (standard temperature)
P2 = kPa (standard pressure)
V2 = ? L
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27. Calculate Solve for the unknown.
Sample Problem 14.4 2
Calculate Solve for the unknown.
Rearrange the equation to isolate V2. =
T T2
P2  V2
P1  V1
Isolate P2 by multiplying both sides by T2: T2 P2 =
T T2
P2  V2
P1  V1 
V2 =
P2  T1
V1  P1  T2
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28. Calculate Solve for the unknown.
Sample Problem 14.4
Calculate Solve for the unknown. 2
Substitute the known quantities into the equation and solve.
V2 =
101.3 kPa  313 K
30.0 L  153 kPa  273 K
V2 = 39.5 L
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29. If I have a container with an internal pressure of 1
If I have a container with an internal pressure of 1.5 atm and temperature of 250 C, what will the pressure be if I heat the container to 1500 C?
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30. If I have a container with an internal pressure of 1
If I have a container with an internal pressure of 1.5 atm and temperature of 250 C, what will the pressure be if I heat the container to 1500 C?
2.13 atm
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31. END OF 14. 2 https://phet. colorado
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