1. Pressure, Volume, Temperature The Gas Laws

2. 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 them mathematically to solve problems
Combine the gas laws into one equation, and solve problems where P, V, and T are no longer constant.

3. 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

4. Boyle’s Law: Graphically
constant temperature
-inverse relationship

5. 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”

6. P1V1 = P2V2 Boyle’s Law: Formula
P1 = initial pressure
V1 = initial volume
P2 = final pressure
V2 = final volume
If you know three of the four, you can calculate the fourth.

7. Boyle’s Law: Sample Problems
P1V1 = P2V2
Standard Problem
A sample of oxygen gas has a volume of 150. ml when its pressure is atm. What will the volume of the gas be at a pressure of atm if the temperature does not change?
More Difficult Problem
It is hard to begin inflating a balloon. A pressure of kPa is required to initially inflate the balloon mL.  What is the final pressure in mm Hg when the balloon has reached it's capacity of 1.2 L??

8. Boyle’s Law: Sample Problem
P1V1 = P2V2
A sample of oxygen gas has a volume of 150. ml when its pressure is atm. What will the volume of the gas be at a pressure of atm if the temperature does not change?
P1 = atm
V1 = 150. ml
P2 = atm
V2 = what problem is looking for
P1V1 = P2V2
P2 = P2
P1V1 = V2 P2
V2 = (0.947)(150.) = 144 ml of O2
(.987)

9. 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.
volume
temperature
st hydrogen balloon

10. Charles’s Law: Graphically
constant pressure
-directly proportional

11. Charles’s Law: FormulaV1 T1 V2 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.

12. Charles’s Law: Sample ProblemV1 T1 V2 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?
T2V T2V2
T T2
T2V1 T1 = = V2
V2 = (752)( ) = 815 ml Ne
( )

13. 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).
There is a Gay-Lussac's law but it has to do with the ratio of the volumes of gases in a chemical reaction, the "law of combining volumes".
pressure
temperature

14. Gay-Lussacs Law: Graphically
constant volume
-direct relationship

15. Gay-Lussac’s Law: FormulaP1 T1 P2 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.

16. Gay-Lussac’s Law: Sample ProblemT1 P2 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?
T2P T2P2
T T2
T2P1 T1 = = P2
P2 = (3.00)( ) = atm
( )

17. Summary Boyle’s P V P1V1 = P2V2 T, n Charles’ V T V1/T1 = V2/T2
LAW
RELATIONSHIP
CONSTANT
Boyle’s
P V
P1V1 = P2V2
T, n
Charles’
V T
V1/T1 = V2/T2
P, n
Gay-Lussac’s
P T
P1/T1 = P2/T2
V, n

18. The Combined Gas Law
The combined gas law expresses the relationship between pressure, volume and temperature of a fixed amount of gas.

19. Sample Combined Gas Law Problem
A sample of helium gas has a volume of L, a pressure of 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 = atm V1 = 180 mL T1 = 302 K
P2 = atm V2= 90 mL T2 = ??

20. Pressure, Volume, Temperature
Let’s see what we already know about these three variables …
Gas Law Program

21. 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