RSPT 1060
MODULE C
Lesson #4
GAS LAWS
OBJECTIVES
•
At the end of this module, the student should be able to…
•
Define terms associated with gas laws.
•
Define Boyle’s Law.
•
Describe the relationship between volume, pressure,
mass and temperature.
•
Describe how Boyle’s Law can be used to explain normal
ventilation.
•
Given appropriate information, use the mathematical
formula for Boyle’s Law to solve for an unknown.
•
Define Charles’s Law.
•
Describe the relationship between volume, pressure,
mass and temperature.
•
State a clinical example of when Charles Law is applied
in respiratory therapy.
•
Given appropriate information, use the mathematical
formula for Charles’s Law to solve for an unknown.
OBJECTIVES
•
At the end of this module, the student should be
able to…
•
•
•
•
•
•
•
Define Gay Lussac’s Law.
Describe the relationship between volume, pressure,
mass and temperature.
Give a clinical example of when Gay-Lussac's Law is
applied in respiratory therapy
Given appropriate information, use the mathematical
formula for Gay-Lussac's Law to solve for an unknown.
State the combined gas law.
Given appropriate information, use the mathematical
formula for the Combined Gas Law to solve for an
unknown.
State the Universal (Ideal) Gas Law.
SUPPORTIVE READINGS
• Egan: Gas Behavior Under Changing
Conditions, pgs. 109 – 111
• Sibberson’s Math for RC:
• Chapter 2 – Boyle’s Law, pgs. 17 – 19, Sample Problems
Fourth Set.
• Chapter 2 – Charles’s Law, pgs. 19 – 20, Sample Problems
Fifth Set.
• Chapter 2 – Gay Lussac’s Law, pgs. 20 – 21, Sample Problems
Sixth Set.
• Chapter 2 – Combined Gas Law, pgs. 22 – 26, Sample
Problems Seventh & Eighth Set.
• Chapter 2 – Practice Exercises, pgs. 29 – 32, #21 – 60.
Web Sites
• http://www.grc.nasa.gov/WWW/K12/airplane/boyle.html
Gas Laws
• Laws describing the behavior of gases.
• Supported by the Kinetic Molecular Theory
• Six assumptions
• Applies to most situations.
• Exceptions to these laws may occur when there is…
• Extremely high pressures
• Extremely low temperatures
Physical Properties
Compared in the Gas Laws
• Mass – “amount of matter”
• Pressure – “The force per unit of surface area” (pounds per
square inch or psi). Results from molecular collisions.
• Temperature – measurement of the degree of molecular
activity
• Volume – “space occupied by matter” For a gas it is the
volume of the container because gases will always fill the
container.
Gas Law - Summary Table
Boyle’s
Charles’s
Gay
Lussac’s
Combined
Formula:
P1xV1=P2xV2
V1 = V2
T1
T2
P1 = P2
T1
T2
P1xV1 = P2xV2
T1
T2
Constant:
Temperature
& Mass
Pressure &
Mass
Volume &
Mass
Mass
Relationship:
Inverse:
P
= V
Direct:
T
= V
Direct:
T
= P
Variable
Rearranged:
V2=P1xV1
P2
V2=V1xT2
T1
P2=P1xT2
T1
V2=V1xP1xT2
P2xT1
P2=V1xP1xT2
V2xT1
T2=P2xV2xT1
P1xV1
Law:
P2=P1xV1
V2
Memory Game
“What remains constant?”
• Boyle’s = “Boiling”
• (Temperature constant)
• Charles’s = Charlie watches TV.
• (Pressure constant)
• Gay Lussac’s = GV
• (Volume constant)
Gas volume
Boyle’s Law
• Constants: Mass & Temperature
• Measured under Isothermic conditions
• Constant temperature
• Difficult to accomplish
P1 x V1 = P2 x V2
• Opposite of Isothermic: “Adiabatic”
• means a varying temperature
Boyle’s Law
• Inverse relationship:
P1 x V1 = P2 x V2
• As pressure exerted on a gas is increased,
volume will decrease.
• As pressure exerted on a gas is
decreased, volume will increase.
Boyle’s Law
• Solve for the unknown :
P1 x V1 = P2 x V2
P1 x V1
(both known)
=
P2 x V2
(one known & one unknown)
NBRC Question
•
You have 3 liters of gas at 770 mmHg. The volume is
changed to 2.5 liters. (The mass and temperature are
constant.) Which of the following statements would
be true concerning this situation?
I.
II.
III.
IV.
V.
The pressure has increased
The pressure has decreased
The pressure is now 924 mmHg
The pressure is now 641.7
The pressure has not changed
Calculation
• P1 x V1 = P2 x V2
• V1 = 3 liters of gas
• P1 = 770 mmHg
• V2 = 2.5 liters (volume decrease)
increase or
• P2 = ______________?
decrease?
Rearrange the formula
P2 = P1xV1 =
V2
Choose an answer
•
•
•
•
•
I
The pressure will increase
II
The pressure will decrease
III The pressure will be 924 mmHg
IV The pressure will be 641.7
V
The pressure will not change
a. I & II
b. I & III
c. II & III
d. II & IV
e. V only
Practice
• Sibberson’s Practical Math for RC:
• Chapter 2: Boyle’s Law, pgs, 17-19,
Sample Problems Fourth Set.
Problem #1
• P1 x V1 = P2 x V2
•
•
•
•
V1=6.4L
P1 = 720 mmHg
V2 = 4.75L
P2 = __________? increase or decrease?
Rearrange the formula
P2 = P1xV1 =
V2
Examples
• Closed syringe
• Close off the end of a syringe and pull back.
• Vacuum is formed with pressure decrease and
volume increase.
• Normal breathing
• Muscle contraction and inspiration causes
decreased pressure in the pleural space and lungs.
• Decreased pressure yields volume movement into
the lungs and increase in volume.
Temp
constant
Pressure
change =
Volume
change
Charles’s Law
V1  V2

T1  T2
• Constants: Mass &
Pressure
Direct Relationship – as
temperature increases,
volume increases
Charles’s Law
• Rearrange the
formula to find V2
V1 V2

T1 T2
NBRC Question
• If you have 2 liters of a gas at 37°C and 752 mmHg and you
change the temperature to 68°C without changing the pressure
(constant pressure is Charles’s Law), what is the new volume of
gas? Do you expect the volume to increase or decrease?
•
•
•
•
•
A
B
C
D
E
2.2 Liters
1.8 liters
2 liters
2.4 liters
1.6 liters
Temperature Scales
• When working with gas laws – always
convert temperature to Kelvin.
• °Celsius (C) + 273° = °Kelvin (K)
Calculation
V1 V2

T1 T2
V1  2 lite rsof gas
T1  37 C  273 K  310 K
T2  68 C  273 K  341 K
V2  UNKNOWN incre as e /de cre ase
Practice
• Sibberson’s Practical Math for RC:
• Chapter 2: Charles’s Law, pgs, 19 - 20,
Sample Problems Fifth Set.
Examples
• Balloon filled with air
• Put in refrigerator and it shrinks
• Put by heater and it expands
• Pulmonary Function Testing
• Patient exhales warm gas (37° C) into cold
spirometer (room temp).
• Measured gas volume will be less than actual
volume in the lungs.
• Measured volume must be corrected from ATPS to
BTPS.
Gay-Lussac’s Law
• Constants: Mass &
Volume
Direct Relationship
– as temperature
increases, pressure
increases
P1  P2

T1  T2
Gay-Lussac’s Law
• Rearrange the formula to find P2
P1 P2

T1 T2
NBRC Question
• You have 1.5 liters of a gas at 40° C and 750 mmHg pressure.
The temperature of the gas is changed to 25° C without changing
the volume (constant volume is Gay-Lussac’s Law), what is the
new pressure of gas? Do you expect the pressure to increase or
decrease?
•
•
•
•
•
A
B
C
D
E
The new pressure will increase by a factor of 25
The new pressure will increase by a factor of 15
417 mmHg will be the new pressure
714 mmHg will be the new pressure
There will not be a pressure change
Temperature Scales
• When working with gas laws – always
convert temperature to Kelvin.
• °Celsius (C) + 273° = °Kelvin (K)
Calculation
P1 P2

T1 T2
P1  750mmHg
T1  40 C  273 K  313 K
T2  25  C  273 K  298 K
P2  UNKNOWN incre as e /de cre ase
Calculation
P1  T2
P2 
T1
Choose an answer
A.
B.
C.
D.
E.
The new pressure will increase by a factor of 25
The new pressure will increase by a factor of 15
417 mmHg will be the new pressure
714 mmHg will be the new pressure
There will not be a pressure change
Practice
• Sibberson’s Practical Math for RC:
• Chapter 2: Gay Lussac’s Law, pgs, 20 - 21,
Sample Problems Sixth Set.
Examples
• Gas cylinder
• Exposure to increased temperatures will
cause the pressure in the cylinder to rise
• Bicycle tires
• On a hot day the tire pressure will be
higher than the pressure on a cold day
• Automobile tires
• After driving a car for a while the tire
pressure will increase as the tires heat up.
Combined Gas Law
P1V1 P2V2

T1
T2
• Mass is the
only constant
• This formula
can replace all
previous.
Temperature & Pressure & Volume Relationships
Guidelines
• Before doing any calculations
• Must correct temperature to Kelvin
• Before doing any calculations
• Must subtract water vapor
• Use the “Temperature & Humidity Chart”
Sibberson Math Book – page 24
Sibberson Math Book – page 25
Set up a chart before you set up
your formula
• P1 – PH2O = ___
• P2 – PH2O = ___
• V1 = ___
• V2 =___
• T1
• T2(convert to ° K) = ____
(convert to °K) = ____
Fill in chart then set up formula:
P1V1 P2V2

T1
T2
NBRC Question
• A gas is at 42° C and 760 mmHg pressure. It
occupies a volume of 2.5 liters. The
temperature is decreased to 37° C and the
volume decreases to 2 liters. What is the new
pressure? (decreased or increased?)
•
•
•
•
•
Set up the table
Change temp. to Kelvin
Subtract PH2O (if indicated)
Rearrange formula
Solve for unknown
Set up a chart before you set up
your formula
• P1 – PH2O = ___
• P2 – PH2O = ___
• V1 = ___
• V2 =___
• T1
• T2(convert to ° K) = ____
(convert to °K) = ____
Fill in chart then set up formula:
P1V1 P2V2
P1V1T2


 P2
T1
T2
V2T1
Practice
• Sibberson’s Practical Math for RC:
• Chapter 2: Combined Law, pgs, 22 - 26,
Sample Problems Seventh & Eighth Set.
• Seventh set is dry gases
• Eighth set is gases with water vapor
Problem #1
page 26 (vapor)
On hand is a gas volume of 5.8 L, at a temp. of 32C, and an
atmospheric pressure of 722 mmHg, ATPS. Find the new volume
if the gas was measured at STPD.
• P1 – PH2O = ___
• V1 = ___
• T1
• P2 – PH2O = ___
P1V1 P2V2

T1
T2
(convert to °K) = ____
• V2 =___
• T2(convert to ° K) = ____
5. Universal Gas Law
• P1xV1 = nRT
• n = Gram molecular weight (mass)
• R = 22.4 L (molar volume)
• All parameters can vary
•
•
•
•
Pressure
Temperature
Volume
Mass
• Used in situations where mass is varying
• Not used in Respiratory Therapy
Gas Law - Summary Table
Boyle’s
Charles’s
Gay
Lussac’s
Combined
Formula:
P1xV1=P2xV2
V1 = V2
T1
T2
P1 = P2
T1
T2
P1xV1 = P2xV2
T1
T2
Constant:
Temperature &
Mass
Pressure &
Mass
Volume &
Mass
Mass
Relationship:
Inverse:
P
= V
Direct:
T
= V
Direct:
T
= P
Variable
Rearranged:
V2=P1xV1
P2
V2=V1xT2
T1
P2=P1xT2
T1
V2=V1xP1xT2
P2xT1
P2=V1xP1xT2
V2xT1
T2=P2xV2xT1
P1xV1
Law:
P2=P1xV1
V2