Pressure, Volume, Temperature
The Gas Laws
Learning Objectives
• Understand the qualitative relationship between pressure
(P) and volume (V) and temperature (T), when you have a
gas
• Learn the three gas laws and how to apply then
mathematically to solve problems
• Combine the gas laws into one equation, and solve
problems where P, V, and T are no longer constant.
Boyle’s Law
• Robert Boyle, studied the relationship
between pressure, p, and volume, V, in the
mid-1600s.
• When he doubled the pressure on a sample
of gas at constant temperature, its volume
was reduced by one-half.
pressure
volume
Boyle’s Law: Graphically
-constant temperature
-inverse relationship
Connection To Your Math Class
Asymptote- A line that continually approaches a given curve
but does not meet it at any finite distance.
Greek word that means “not falling together”
Boyle’s Law: Formula
P1V1 = P2V2
P1 = initial pressure
V1 = initial volume
P2 = final pressure
V2 = final volume
If you know three of the four, you can
calculate the fourth.
Boyle’s Law: Sample Problems
P1V1 = P2V2
Standard Problem
A sample of oxygen gas has a volume of 150. ml when its
pressure is 0.947 atm. What will the volume of the gas be at a
pressure of 0.987 atm if the temperature does not change?
More Difficult Problem
It is hard to begin inflating a balloon. A pressure of 800.0 kPa
is required to initially inflate the balloon 225.0 mL. What is the
final pressure in mm Hg when the balloon has reached it's
capacity of 1.2 L??
Boyle’s Law: Sample Problem
P1V1 = P2V2
A sample of oxygen gas has a volume of 150. ml when its pressure is
0.947 atm. What will the volume of the gas be at a pressure of 0.987 atm if
the temperature does not change?
P1 = 0.947 atm
V1 = 150. ml
P2 = 0.987 atm
V2 = what problem is looking for
P1V1 = P2V2
P2 = P2
P1V1 = V2
P2
V2 = (0.947)(150.) = 144 ml of O2
(.987)
Charles’ Law
• Jacques Charles discovered the relationship
between volume and temperature in 1787.
• The law states that the volume of a sample
of gas at constant pressure varies directly
with Kelvin temperature.
temperature
volume
1783 - 1st hydrogen balloon
Charles’s Law: Graphically
-constant pressure
-directly proportional
Charles’s Law: Formula
V1 = V2
T1
T2
V1 = initial volume
T1 = initial temperature
V2 = final volume
T2 = final temperature
If you know three of the four, you can
calculate the fourth.
Charles’s Law: Sample Problem
V1 = V2
T1
T2
A sample of neon gas occupies a volume of 752 ml
at 25oC. What volume will the gas occupy at 50oC if
the pressure remains constant?
T2V1
T2V2
=
T1
T2
T2V1 = V2
T1
V2 = (752)(273 +50) = 815 ml Ne
(273 + 25)
Gay-Lussac’s Law
•
Joseph Gay-Lussac is credited with discovering
relationship between pressure and temperature, but
the discovery should actually go to Guillaume
Amontons (1699).
•
The law states that the pressure of a sample of gas
at constant volume varies directly with Kelvin
temperature.
temperature
pressure
Gay-Lussacs Law: Graphically
-constant volume
-direct relationship
Gay-Lussac’s Law: Formula
P1 = P2
T1
T2
P1 = initial pressure
T1 = initial temperature
P2 = final pressure
T2 = final temperature
If you know three of the four, you can
calculate the fourth.
Gay-Lussac’s Law: Sample Problem
P1 = P2
T1
T2
The gas in an aerosol can is at a pressure of 3.00 atm at 25oC. The can
warns not to allow the temperature to get above 52oC. What would the
pressure of the can be at 52oC?
T2P1 = T2P2
T1
T2
T2P1 = P2
T1
P2 = (3.00)(273 +52) = 3.27 atm
(273 + 25)
LAW
RELATIONSHI
P
LAW
CONSTANT
Boyle’s
P V
P1V1 = P2V2
T, n
Charles’
V T
V1/T1 = V2/T2
P, n
GayLussac’s
P T
P1/T1 = P2/T2
V, n
The Combined Gas Law
The combined gas law expresses the
relationship between pressure, volume
and temperature of a fixed amount of
gas.
P1V1 P2V2

T1
T2
Sample Combined Gas Law Problem
A sample of helium gas has a volume of 0.180 L, a
pressure of 0.800 atm and a temperature of 29°C.
What is the new temperature (°C) of the gas at a
volume of 90.0 mL and a pressure of 3.20 atm?
Set up Data Table
P1 = 0.800 atm
V1 = 180 mL
P2 = 3.20 atm
V2= 90 mL
604 K - 331oC
T1 = 302 K
T2 = ??
Pressure, Volume, Temperature
Let’s see what we already know about these three variables …
Gas Law Program
NOVA: Race for Absolute Zero
Try not to lose your head when you are
doing chemistry
and
Why you should always wear your safety
goggles