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Ideal Gas Don’t exist Model to explain behavior of all gases
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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 Gay-Lussac’s Law Combined Gas Law Avogadro’s Law Ideal Gas Law
Boyle’s Law
Relationship between pressure and volumeConstant Temperature and amount of
gas Mathematical relationships
As pressure is increasing, volume is decreasing
As 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
Charles’s Law
Relationship between volume and temperatureConstant Pressure and amount of gas
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
VT
VT
1
1
2
2
Example
A 4L sample of gas at 300K is heated to 600K. What is the new volume?
KV
KL
6003004 2
VT
VT
1
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
1530045
TL
KL
VT
VT
1
1
2
2
CKT 1731002
Gay-Lussac'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?
Gay-Lussac's Law
Mathematical relationshipsAs temperature increases, pressure
increasesAs temperature decreases, pressure
decreases
Gay-Lussac's Law
T
P
Gay-Lussac's Law
P/T = constant Volume remains constant (rigid
container) and amount of gas Temperature must be in Kelvin
PT
PT
1
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?
PT
PT
1
1
2
2
K
PK
atm400300
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?
PT
PT
1
1
2
2
2
5.33001
Tatm
Katm
KT 10502
Review
Boyle’s Law
Charles’s Law
Gay-Lussac's Law
PV PV1 1 2 2
VT
VT
1
1
2
2
PT
PT
1
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 Gay-Lussac's Laws together
PVT
PVT
1 1
1
2 2
2
Example
A gas at 5atm is heated and compressed from 10L at 100K to 5L at 200K. What is the new pressure?
PVT
PVT
1 1
1
2 2
2
KLP
KLatm
200)5)((
100)10)(5( 2
atmP 202
Example
A gas at 2atm and 27°C occupies 10L of space. What is the new volume when it is cooled to STP?
PVT
PVT
1 1
1
2 2
2
KVatm
KLatm
273))(1(
300)10)(2( 2
LV 2.182
Real Life
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
Vn
Vn
1
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)
Review
Boyle’s Law
Charles’s Law
Gay-Lussac’s Law
Avogadro’s Law
PV PV1 1 2 2
VT
VT
1
1
2
2
PT
PT
1
1
2
2
2
2
1
1
nV
nV
All Together Now
If we add Avogadro’s Law into the Combined Gas Law:
PVnT
Constant
PVnT
R
22
22
11
11
TnVP
TnVP
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