Transcript Chapter 7 Gases - College of San Mateo

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 the pressure (P)
increases, then the
volume decreases
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PV Constant in Boyle’s Law
Boyle’s law
• if 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
•
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 obtain V2, divide both sides by P2.
P1V1 = P2V2
P2
P2
P1V1
P2
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=
V2
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P and V in Inhalation
During inhalation,
• the lungs expand
• the pressure in the
lungs decreases
• air flows toward
the lower pressure
in the lungs
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P and V in 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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Using the Gas Laws
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Example of Using 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 initially
at 550 mmHg after its pressure is changed to 2200 mmHg
at constant T?
STEP 1 Organize the data in a table of initial and final
conditions.
Conditions 1
Conditions 2
Know
Predict
P1 = 550 mmHg P2 = 2200 mmHg P increases
V1 = 8.0 L
V2 = ?
V decreases
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Example of Using Boyle’s Law
(continued)
STEP 2 Rearrange the gas law for the unknown.
Solve Boyle’s law for V2. When pressure
increases, volume decreases.
P1V1 = P2V2
V2
= V1P1
P2
STEP 3 Substitute values into the gas law to
solve for the unknown.
V2
= 8.0 L x 550 mmHg = 2.0 L
2200 mmHg
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 the helium in a cylinder has a volume of 120
mL and a pressure of 850 mmHg, what is the new
volume if the pressure changes to 425 mmHg
inside the cylinder?
1) 60 mL
2) 120 mL
3) 240 mL
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Solution
STEP 1 Organize the data in a table of initial and final
conditions.
Conditions 1
Conditions 2
Know
Predict
P1 = 850 mmHg
P2 = 425 mmHg P decreases
V1 = 120 mL
V2 = ?
V increases
STEP 2 Rearrange the gas law for the unknown.
Solve Boyle’s law for V2:
P1V1 = P2V2
V2
= V1P1
P2
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Solution (continued)
STEP 3 Substitute values into the gas law to
solve for the unknown.
V2 = P1V1
P2
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=
120 mL x 850 mmHg = 240 mL (3)
425 mmHg
Pressure ratio
increases volume
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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
and n 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 and n constant), the
new volume is represented by the smaller
balloon A.
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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 and n constant)?
1) 3.2 L
2) 6.4 L
3) 12.8 L
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Solution
STEP 1 Organize the data in a table of initial and final
conditions.
Conditions 1
Conditions 2
Know
Predict
P1 = 0.70 atm
V1 = 6.4 L
P2 = 1.40 atm
V2 = ?
P increases
V decreases
STEP 2 Rearrange the gas law for the unknown.
Solve Boyle’s law for V2.
P1V1 = P2V2
V2 = V1P1
P2
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Solution (continued)
STEP 3 Substitute values into the gas law to
solve for the unknown.
V2 =
6.4 L x 0.70 atm
1.40 atm
=
3.2 L (1)
Volume decreases when there is an increase in
the pressure (at constant T and n).
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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
A gauge indicates the pressure
of a gas in a tank.
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Solution
STEP 1 Organize the data in a table of initial and final
conditions.
Conditions 1
Conditions 2 Know
Predict
P1 = 600 mmHg
P2 = ?
P decreases
V1 = 12.0 L
V2 = 36.0 L
V increases
STEP 2 Rearrange the gas law for the unknown.
P1V1 = P2V2
P2
= P1 V1
V2
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Solution (continued)
STEP 3 Substitute values into the gas law to solve for
the unknown.
600. mmHg x 12.0 L = 200. mmHg (1)
36.0 L
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