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Chapter 11 Gases
11.3 Pressure and Volume (Boyle’s Law)
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Boyle’s Law
Boyle’s Law states that
• The pressure of a gas is inversely related to its volume when T and n are constant.
• If volume decreases, the pressure increases.
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In Boyle’s Law• The product P x V is constant as long as T and n
do not change.
P1V1 = 8.0 atm x 2.0 L = 16 atm L
P2V2 = 4.0 atm x 4.0 L = 16 atm L
P3V3 = 2.0 atm x 8.0 L = 16 atm L
• Boyle’s Law can be stated as
P1V1 = P2V2 (T, n constant)
PV Constant in Boyle’s Law
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Solving for a Gas Law Factor
The equation for Boyle’s Law can berearranged to solve for any factor.
P1V1 = P2V2 Boyle’s Law
To obtain V2 , divide both sides by P2.
P1V1 = P2V2
P2 P2
P1V1 = V2
P2
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PV in Breathing
In inhalation,• The lungs expand.• The pressure in
the lungs decreases.
• Air flows towards the lower pressure in the lungs.
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PV in Breathing
In exhalation• Lung volume
decreases.• Pressure within
the lungs increases.
• Air flows from the higher pressure in the lungs to the outside.
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Freon-12, CCl2F2, is used in refrigeration systems. What is the new volume (L) of a 8.0 L sample of Freon gas initially at 550 mm Hg after its pressure is changed to 2200 mm Hg at constant T?
1. Set up a data tableConditions 1 Conditions 2 P1 = 550 mm Hg P2 = 2200 mm Hg
V1 = 8.0 L V2 =
(predict smaller
V2)
Calculation with Boyle’s Law
?
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2. Because pressure increases, we predict that the volume will decrease.
Solve Boyle’s Law for V2:
P1V1 = P2V2
V2 = V1P1
P2
V2 = 8.0 L x 550 mm Hg = 2.0 L
2200 mm Hg pressure ratio
decreases volume
Calculation with Boyle’s Law (Continued)
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Learning Check
For a cylinder containing helium indicate if cylinder A or cylinder B represents the new volume for the following changes (n and T are constant):
1) Pressure decreases
2) Pressure increases
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Solution
For a cylinder containing helium indicate if cylinder A or cylinder B represents the new volume for the following changes (n and T are constant):
1) Pressure decreases B
2) Pressure increases A
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Learning Check
If the helium in a cylinder has a volume of 120mL and a pressure of 850 mm Hg, what is the newvolume if the pressure is changed to 425 mm Hginside the cylinder?
1) 60 mL 2) 120 mL 3) 240 mL
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3) 240 mL P1 = 850 mm Hg P2 = 425 mm Hg
V1 = 120 mL V2 = ??
V2 = P1V1 = 120 mL x 850 mm Hg = 240 mL P2 425 mm Hg
Pressure ratio increases volume
Solution
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Learning Check A sample of helium gas in a balloon has a volume
of 6.4 L at a pressure of 0.70 atm. At 1.40 atm (T constant), is the new volume represented by A, B, or C?
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Solution
A sample of helium gas in a balloon has a volume of 6.4 L at a pressure of 0.70 atm. At a higher pressure (T constant), the new volume is represented by the smaller balloon A.
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If the sample of helium gas has a volume of 6.4 L at a pressure of 0.70 atm, what is the new volume when the pressure is increased to 1.40 atm (T constant)?
A) 3.2 L B) 6.4 L C) 12.8 L
Learning Check
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If the sample of helium gas has a volume of 6.4 L at a pressure of 0.70 atm, what is the new volume when the pressure is increased to 1.40 atm (T constant)?
A) 3.2 L
V2 = V1P1
P2 V2 = 6.4 L x 0.70 atm = 3.2 L
1.40 atmVolume decreases when there is an increase in the pressure (Temperature is constant.)
Solution
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A sample of oxygen gas has a volume of 12.0 L at 600. mm Hg. What is the new pressure when the volume changes to 36.0 L? (T and n constant).
1) 200. mm Hg
2) 400. mm Hg
3) 1200 mm Hg
Learning Check
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1) 200. mm Hg Data table Conditions 1 Conditions 2P1 = 600. mm Hg P2 = ??? (lower)
V1 = 12.0 L V2 = 36.0 L
P2 = P1 V1
V2
600. mm Hg x 12.0 L = 200. mm Hg 36.0 L
Solution