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Gas Laws
Chapters 13.1 + 14
Review
TemperatureAverage kinetic energy
PressureCollisions of gas particles between
each other and container walls Volume
Amount of space
Ideal Gas
Don’t exist
Model to explain behavior of all gases
Kinetic Molecular Theory
The particles in a gas are constantly moving in rapid, random, straight-line motion.
Gas particles have no volume compared to the volume of the gas.
No attraction between particles All collisions are completely elastic
Gas Laws
Boyle’s Law Charles’s Law Amontons’s Law Combined Gas Law Avogadro’s Law Dalton’s Law of Partial Pressures Ideal Gas Law
Boyle’s Law
Relationship between pressure and volumeConstant Temperature
Mathematical relationshipsAs pressure is increasing, volume is
decreasingAs pressure is decreasing, volume is
increasing
Boyle’s Law
V
P
Boyle’s Law
PV = constant Temperature remains constant
PV PV1 1 2 2
Example
A 40 L sample of gas at 1atm of pressure is compressed to 10 L. What is the new pressure of the gas?
P1V1 = P2V2
(1atm)*(40L) = P2*(10L)
P2 = 4 atm
Example
The pressure of a 25 L sample is changed from 2 atm to 0.4 atm. What is the new volume of the gas?
P1V1 = P2V2
(2atm)*(25L) = (0.4atm)*V2
V2 = 125 L
Real Life
Charles’s Law
Relationship between volume and temperatureConstant Pressure
Mathematical relationshipsAs temperature is increasing, volume
is increasingAs temperature is decreasing, volume
is decreasing
Charles’s Law
T
V
Charles’s Law
V/T = constantPressure remains constant
Temperature must be in Kelvin
V
T
V
T1
1
2
2
Example
A 4L sample of gas at 300K is heated to 600K. What is the new volume?
K
V
K
L
600300
4 2V
T
V
T1
1
2
2
LV 82
Example
A gas occupying 45L at 27°C is cooled until its volume is 15L. What is the new temperature of the gas?
2
15
300
45
T
L
K
LV
T
V
T1
1
2
2
CKT 1731002
Amontons's Law
In the winter the tire sensors on my wife’s car beep, indicating that there is low pressure in the tires. Why?
What factor is changing with the weather?
What factor is responding to this change?
Which factor(s) remain constant?
Amontons's Law
Mathematical relationshipsAs temperature increases, pressure
increasesAs temperature decreases, pressure
decreases
Amontons's Law
T
P
Amontons's Law
P/T = constant Volume remains constant (rigid
container) Temperature must be in Kelvin
P
T
P
T1
1
2
2
Example
In a pressure cooker, a sample of gas at 1 atm and 300K is heated to 400K. What is the pressure at this temperature?
P
T
P
T1
1
2
2
K
P
K
atm
400300
1 2
atmP 33.12
Example
A sample of gas at 101.3 kPa and 27°C is heated until its pressure is 3.5atm. What is the new temperature?
P
T
P
T1
1
2
2
2
5.3
300
1
T
atm
K
atm
KT 10502
Combined Gas Law
GoalUnderstands how to use the gas laws
to predict the behavior of gases.• Pressure vs. volume (Boyle)• Volume vs. temperature (Charles)• Volume, temperature, and pressure
(Combined)
Review
Boyle’s Law
Charles’s Law
Amontons's Law
PV PV1 1 2 2
V
T
V
T1
1
2
2
P
T
P
T1
1
2
2
Question
How often do only 2 properties of a gas change while the other remains constant?Rarely
Need a gas law that incorporates all three properties (PTV) changing
Combined Gas Law
Combines Boyle’s, Charles’s, and Amontons's Laws together
PV
T
PV
T1 1
1
2 2
2
Example
Example
Worksheet
Combined Gas Law
GoalUnderstands how to use the gas laws
to predict the behavior of gases.• Pressure vs. volume (Boyle)• Volume vs. temperature (Charles)• Volume, temperature, and pressure
(Combined)
Review
1 mole of ANY gas occupies 22.4L of volume at STP
Avogadro’s Law
Relationship between the amount of gas and the volume of the gas
Mathematical relationshipsAs the amount of gas increases,
volume increasesAs the amount of gas decreases,
volume decreases
Avogadro’s Law
n
V
Avogadro’s Law
V/n = constantPressure and Temperature remains
constant
V
n
V
n1
1
2
2
Avogadro’s Law
Equal volumes of gas at the same Temperature and Pressure have the same number of particles
At the same temperature and pressure, which sample contains the same number of moles of particles as 1 liter of O2(g)?
A. 1 L Ne(g) B. 0.5 L SO2(g)
C. 2 L N2(g) D. 4 L H2O(g)
Dalton’s Law
Demonstration Assume each jelly bean represents 1
mole of gas How many moles are in the flask? What fraction is green? Does color make a difference in
pressure when shaken?
Dalton’s Law
Mole Fraction (XA)Moles of one gas divided by total
moles of gas
Partial Pressure (PA)Pressure exerted by one gas in a
sample of gas
Dalton’s Law of Partial Pressures
How does partial pressure relate to total pressure?
Sum of partial pressures equals total pressure
PT = PA + PB + PC…
Dalton’s Law of Partial Pressures How can we relate mole fraction to partial
pressure and total pressure?
XP
PAA
T
ATA PPX *
Example
A container has 1 mol of hydrogen, 1 mol of nitrogen, and 1 mol of oxygen. What is the mole fraction of hydrogen?
3
1Moles of Hydrogen
Total Moles
Example
A container has 1 mol of hydrogen, 1 mol of nitrogen, and 1 mol of oxygen. If the total pressure is 6 atm, what is the partial pressure of nitrogen?
ATA PPX *
APatm6*3
1atmPA 2
Moles of Nitrogen
Total Moles
Review
Boyle’s Law
Charles’s Law
Amontons's Law
Avogadro’s Law
PV PV1 1 2 2
V
T
V
T1
1
2
2
P
T
P
T1
1
2
2
2
2
1
1
n
V
n
V
All Together Now
If we add Avogadro’s Law into the Combined Gas Law:
PV
nT Constant
PV
nTR
22
22
11
11
Tn
VP
Tn
VP
Ideal Gas Law
PV = nRTR = Universal Gas Constant
Ideal Gases follow assumptions of the Kinetic Molecular Theory
Kinetic Theory of Gases
The particles in a gas are constantly moving in rapid, random, straight-line motion.
Gas particles have no volume compared to the volume of the gas.
No attraction between particles All collisions are completely elastic
Ideal Gases
When do real gases act most like an ideal gas? High Temperature Low Pressure
When do real gases act least like an ideal gas? Low Temperature High Pressure
Gas Laws
Boyle’s Law Charles’s Law Amontons's Law Combined Gas Law Avogadro’s Law Dalton’s Law of Partial Pressures Ideal Gas Law
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