Gas Laws
A. Characteristics of Gases
• Gases expand to fill any container.
– random motion, no attraction
• Gases are fluids (like liquids).
– no attraction
• Gases have very low densities.
– no volume = lots of empty space
B. Characteristics of Gases
• Gases can be compressed.
– no volume = lots of empty space
• Gases undergo diffusion & effusion.
– random motion
C. Temperature
• Always use absolute temperature
(Kelvin) when working with gases.
ºF
-459
ºC
-273
K
0
C  F  32
5
9
32
212
0
100
273
373
K = ºC + 273
D. Pressure
• KEY UNITS AT SEA LEVEL
101.325 kPa (kilopascal)
1 atm
760 mm Hg
760 torr
14.7 psi
N
kPa  2
m
E. STP
STP
Standard Temperature & Pressure
0°C
273 K
-OR-
1 atm
101.325 kPa
Units
STP is Standard Temperature and Pressure. STP is 0 °C and 1 atm of
pressure. Gases properties can be compared using STP as a reference.
Temperature:
Celsius and Kelvin
0 ◦C = 273 K
Pressure Units
• 1 atm
• 760 mmHg
• 101.3 kPa
• 760 torr
Using dimensional analysis to convert pressure units
• What is 475 mm Hg expressed in atm?
475 mmHg
1 atm
= 0.625 atm
760 mm Hg
Charles's Law
Charles's Law can be stated as the volume occupied by any sample of gas at a constant pressure is
directly proportional to the absolute temperature.
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V is the volume
T is the absolute temperature (measured in Kelvin)
Charles's Law can be rearranged into:
V1 / T1 = V2 / T2
V1 is the initial volume
T1 is the initial temperature
V2 is the final volume
T2 is the final temperature
Sample Problem
You have a gas that has a volume of 2.5 liters and a temperature of 250 K. What would be
the final temperature if the gas has a volume of 4.5 liters?
V1 / T1 = V2 / T2
V1 = 2.5 liters
T1 = 250 K
V2 = 4.5 liters
T2 = ?
Solving for T2, the final temperature equals 450 K.
So, increasing the volume of a gas at constant pressure from 2.5 to 4.5 liters results in a
temperature increase of 200 K.
Important: Charles's Law only works when the pressure is constant.
Note: Charles's Law is fairly accurate but gases tend to deviate from it at very high and low pressures.
Boyle's Law
• Boyle's Law states the volume of a definite quantity of dry gas is
inversely proportional to the pressure, provided the temperature
remains constant.
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Mathematically Boyle's law can be expressed as P1V1 = P2V2
V1 is the original volume
V2 is the new volume
P1 is original pressure
P2 is the new pressure
Sample Problem
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Suppose you have a gas with 45.0 ml of volume and has a pressure of
760.mmHg. If the pressure is increased to 800mmHg and the temperature
remains constant then according to Boyle's Law the new volume is 42.8 ml.
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(760mmHg) * (45.0ml) = (800mmHg) * (V2)
800 mmHg
800 mmHg
V2 = 42.8ml
To solve for V2, divide both
sides by 800 mmHg. Cancel
800 mm Hg on the right side.
Then multiply 760 by 45.0.
Divide your answer by 800
and you should get 42.8
Gay-Lussac’s Law
• P and T are directly Proportional
P1 = P2
T1
T2
or
P1T2 = P2T1
Sample problem
The pressure inside a container is 770 mmHg at a temperature of 57 C.
What would the pressure be at 75 C?
P1= 770 mmHg
T1 = 57°C
T2= 75°C
P2 = ?
Combined Law
• The combined gas law is a combination of Boyle's Law and
Charles's Law; hence its name the combined gas law. Since for a
given amount of gas there is a constant then we can write-P1V1 / T1 = P2V2 / T2.
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P1 is the initial pressure
V1 is the initial volume
T1 is the initial temperature (in Kelvin)
P2 is the final pressure
V2 is the final volume
T2 is the final temperature (in Kelvin)
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For example if you have 4.0 liters of gas at STP, and you want to know the
volume of the gas at 2.0 atm of pressure and 30 °C, the equation can be
setup as follows:
(1.0)(4.0) / 273 = (2.0)(V2) / 303
(V2)(2)(273) = (1)(4)(303)
V2 = 2.2
Therefore the new volume is 2.2 liters
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