1. Kinetic Molecular Theory

2. THE KINETIC-MOLECULAR THEORY of GASES (the particle view)
The Kinetic Molecular Theory is used to explain the behavior of gases.
The kinetic molecular theory shows how individual gas particles interact with one another.

3. The Five Tenants of KMT
1. The gas consists of large numbers of very small particles that are far apart relative to their size. (Gases are mostly empty space)
2. Collisions between molecules and the sides of the container are perfectly elastic. (No energy is gained or lost during the collision).
3. Gas molecules are in constant, random motion. (They have kinetic energy and hold to Newton’s Laws.)
4. There are no attractive or repulsive forces between the molecules or between the particles and the walls of the container. (The molecules do not interact with each other)
5. The average kinetic energy of the gas particles depends only on the temperature of the gas.

4. #5 explained
The average kinetic energy of the gas particles depends only on the temperature of the gas.
KE= 1/2 m v2
Since all of the gas particles are the same, the mass of each does not vary so the KE depends only on speed.
Speed increases as temperature increases, so KE increases as temperature increases.
All gases at the same temperature have the same average KE, so lighter gas particles have higher velocities.
Gas Properties - Gas, Pressure, Volume - PhET

5. To fully describe a gas four conditions must be measured:
volume
Temperature
number of molecules
Pressure

6. Standard Temperature and Pressure (STP)
STP = 0°C and 1 atm pressure

7. The Gas Laws –The macroscopic view
The mathematical relationships between pressure, temperature, volume and the amount of a gas.
Three different laws, Boyle’s Law, Charles’s Law and Gay-Lussac’s Law, are manipulated to form the Combined Gas Law.

8. Boyle’s Law
A volume of a fixed mass of gas varies inversely with the pressure at constant temperature. (As one value increases the other value will decrease.)
PV = k
Pressure * Volume = k
k is constant for a given sample of a gas.
If volume increases then pressure will decrease proportionally and vice versa.

9. Boyle’s Law can be used to compare changing conditions in a system as long as temperature remains constant.
P1V1 = k P2V2 = k therefore P1V1=P2V2
Try this:
If I have 5.6 liters of gas in a piston at a pressure of 1.5 atm and compress the gas until its volume is 4.8 L, what will the new pressure inside the piston be?
P1V1 = P2V2
(1.5 atm)(5.6 L) = (P2)(4.8 L)
P2 = 1.8 atm
I have added 15 L of air to a balloon at sea level (1.0 atm). If I take the
balloon with me to Denver, where the air pressure is 0.85 atm, what will
the new volume of the balloon be?
(1.0 atm)(15 L) = (0.85 atm)(V2)
V2 = 18 L

10. Charles' Law
Charles determined through his studies that when the temperature of a gas changes, the volume changes.
If the volume or temperature of the gas changes , you get the same constant.  From this, Charles came up with this statement: V1/T1 = V 2/T2
Temperature, needs to be given in Kelvin. Why?

11. If we have 2. 00 L of methane gas at a temperature of 40
If we have 2.00 L of methane gas at a temperature of 40.0° Celsius, what will the volume be if we heat the gas to 80.0 ° Celsius?
The first thing we have to do is convert the temperatures to Kelvins (by adding 273).
The initial temperature is = 313 K
The final temperature is = 353 K.
V1/T1 = V2/T2
2 L / 313 K = V2 / 353 K
V2 = 2.26 L

12. Try these:
If I have 45 liters of helium in a balloon at 25° C and increase the temperature of the balloon to 55 ° C, what will the new volume of the balloon be?
Calcium carbonate decomposes at 1200°C to form carbon dioxide and calcium oxide. If 25 liters of carbon dioxide are collected at 1200°C, what will the volume of this gas be after it cools to 25°C?

13. Gay-Lussac's Law This law relates pressure to temperature: P α T
P1/T1 = P2/T2 This gas law explains that if you increase the temperature of a container with fixed volume, the pressure inside the container will increase.  This explains why you shouldn't leave cans of spray paint in your trunk - the pressure might get so high that the propellant will blow the can up.

14. Try these:
A cylinder contain a gas which has a pressure of 125kPa at a temperature of 200 K. Find the temperature of the gas which has a pressure of 100 kPa.
T2 = 160K
Find the final pressure of gas at 150 K, if the pressure of gas is 210. kPa at 120 K.
P2 = 262. kPa

15. The Combined Gas Law The combined gas law combines the previous laws.
(P1V1) / T 1 = (P2V2) / T2
In this equation, all of the terms are exactly the same as in the preceding equations. 
Whenever you're changing the conditions of pressure, volume, and/or temperature for a gas, you just plug the numbers into this equation.   
If one of these variables isn't mentioned in the problem, just ignore it entirely. 
Suppose that the temperature of the gas didn't change while you were making your change.  Since the first temperature term and the second are the same, they cancel out.

16. Example:
If we have two liters of a gas at a temperature of 420 K and decrease the temperature to 350 K, what will the new volume of the gas be?
To solve this problem, use the combined gas law to find the answer.  Since pressure was never mentioned in this problem, just ignore it.  As a result, the equation will be:
V1/T1 = V 2/T Charles's law

17. Try this:
2.00 L of a gas is collected at 25.0 °C and mmHg. What is the volume at STP?
Set up a table:
Solve for V2.
Write the combined gas law equation: P1V1 / T1 = P2V2 / T2 Rearrange the equation by first cross-multiplying:
P1V1T2 = P2V2T1 then dividing:
V2 = (P1V1T2) / (P2T1) Solve it!
1.80L
P1 = mmHg
P2 = 760 mm Hg
V1 = 2.00 L
V2 = ???
T1 = 25.0 °C + 273
T2 = 0 °C + 273

18. Home Fun
Practice Problems– The Gas Laws