Transcript 7.3_Pressure_and_Volume_(Boyle`s_Law)

Chapter 7
Gases
7.3
Pressure and Volume
(Boyle’s Law)
General, Organic, and Biological Chemistry
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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 the pressure (P)
increases, then the
volume (V) decreases
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PV Constant in Boyle’s Law
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)
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Solving for a Gas Law Factor
The equation for Boyle’s law can be rearranged to
solve for any factor.
P1V1 = P2V2
Boyle’s Law
To solve for V2 , divide both sides by P2.
P1V1
= P2V2
P2
P2
V1 x P1
P2
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=
V2
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Boyle’s Law and Breathing:
Inhalation
During inhalation,
 the lungs expand
 the pressure in the
lungs decreases
 air flows towards
the lower pressure
in the lungs
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Boyle’s Law and Breathing:
Exhalation
During 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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Guide to Calculations with Gas Laws
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Calculation with Boyle’s Law
Freon-12, CCl2F2, is used in refrigeration systems. What
is the new volume (L) of an 8.0 L sample of Freon gas
after its pressure is changed from 550 mmHg to 2200
mmHg at constant T?
STEP 1 Set up a data table:
Conditions 1
Conditions 2
P1 = 550 mmHg
V1 = 8.0 L
P2 = 2200 mmHg P increases
V2 = ?
V decreases
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Know
Predict
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Calculation with Boyle’s Law
(continued)
STEP 2 Solve Boyle’s law for V2. When pressure
increases, volume decreases.
P1V1 = P2V2
V2
= V1 x P1
P2
STEP 3 Set up problem
V2
= 8.0 L x 550 mmHg =
2200 mmHg
2.0 L
pressure ratio
decreases volume
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Learning Check
For a cylinder containing helium gas, 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 gas, indicate if cylinder
A or cylinder B represents the new volume for the
following changes (n and T are constant):
1) Pressure decreases (cylinder B)
2) Pressure increases (cylinder A)
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Learning Check
If a sample of helium gas has a volume of 120 mL
and a pressure of 850 mmHg, what is the new
volume if the pressure is changed to 425 mmHg?
1) 60 mL
2) 120 mL
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3) 240 mL
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Solution
3) 240 mL
Conditions 1
P1 = 850 mmHg
V1 = 120 mL
Conditions 2
P2 = 425 mmHg
V2 = ?
Know
Predict
P decreases
V increases
V2 = V1 x P1 = 120 mL x 850 mmHg = 240 mL
P2
425 mmHg
Pressure ratio
increases volume
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Learning Check
A sample of helium gas in a balloon has a volume of
10. L at a pressure of 0.90 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
10. L at a pressure of 0.90 atm. At a higher pressure
(T constant), the new volume is represented by the
smaller balloon.
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Learning Check
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
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Solution
A) 3.2 L
STEP 1 Set up data table (conditions)
Conditions 1 Conditions 2
Know
P1 = 0.70 atm
V1 = 6.4 L
P increases
P2 = 1.40 atm
V2 = ?
Predict
V decreases
STEP 2 Solve for Boyles law for V2
V2 = V1 x P1
P2
STEP 3 Set up problem
V2 = 6.4 L x 0.70 atm = 3.2 L
1.40 atm
Volume decreases when there is an increase in the pressure
(temperature is constant).
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Learning Check
A sample of oxygen gas has a
volume of 12.0 L at 600 mmHg.
What is the new pressure when
the volume changes to 36.0 L?
(T and n constant)
1) 200 mmHg
2) 400 mmHg
3) 1200 mmHg
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Solution
1) 200 mmHg
Conditions 1
Conditions 2
P1 = 600 mmHg
V1 = 12.0 L
P2 = ?
V2 = 36.0 L
Know
Predict
P decreases
V increases
P2 = P1 x V1
V2
600 mmHg x 12.0 L = 200 mmHg
36.0 L
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