1. Chapter 13 Kinetic Theory (Kinetikos- “Moving”)
Based on the idea that particles of matter are always in motion
The motion has consequences
Behavior of Gases
Physical Properties of Gases
Ideal Gas – an imaginary gas that conforms perfectly to all assumptions

2. Five Assumptions of the KMT
Gases consist of large numbers of tiny particles
The Particles are in Constant Motion, moving in straight lines.
The collisions between particles & w/ the container wall are elastic.
There are no forces of attraction or repulsion between the particles of a gas.
The average K.E. of the particles is directly proportional to the Kelvin Temperature.
KE = ½ mv2

3. Measuring Gases Four factors that can affect the behavior of a gas.
Amount of gas (n) = moles
Volume (V), 1000 cm3 = 1000mL = 1L
Temperature (T), Celsius and Kelvins
Kelvins = oC + 273
Pressure(P), atmospheres(atm), mmHg, or kPa

4. Atmospheric Pressure
Pressure exerted by the column of air in the atmosphere.
Result of the earth’s gravity attracting the air downward.
Barometer – device used to measure the atmospheric pressure on earth.
Manometer – device used to measure the pressure of a gas in an enclosed container.

5. Nature of Gases 1 mole of any gas at STP equals 22.4L of volume.
STP is defined at sea level.
Standard Temperature = 0oC = 273K
Standard Pressure = 1 atm = kPa = 760mmHg = 760 torrs
Normal boiling point of water is 100oC at sea level.
Higher elevation lower boiling points.
Less Pressure above the surface of water.

6. Physical Properties of Gases
Gases have mass
Easily compressed
Fill their containers completely
Different gases move easily through each other.
Diffusion – more mass = slower gas
Gases exert pressure
Pressure of a gas depends on temperature
Volumes of gas particles themselves are assumed to be zero and exert no force on each other.

7. 13.2 - Summary Pressure = Force / Area P = F/A
Reduce the area - Increase the Pressure
Increase the force - Increase the Pressure
S.I Unit for Force - N (Newton)
S.I Unit for Area m2
S.I Unit for Pressure - Pa (Pascal) = 1 N/ m2

8. Pressure and Volume at Constant Temperature
Pressure is exerted by gas particles colliding with walls of its container.
What would happen when a gas in a 1-liter container is placed into a 1/4 liter container?
Less space = More collisions
More collisions = Greater Pressure
Conclusion
Volume Decreases - Pressure Increases.
Inverse Relationship
Boyle’s Law

9. 13.3- Boyle’s Law: Pressure-Volume Relationship
2 Conditions
P1V1 = k
P2V2 = k
Then
P1V1 = P2V2
If you know 3 you can find the 4th
Boyle’s Law - the volume of a fixed gas varies inversely with the pressure at constant temperature.

10. Algebraic Equations for Boyle
P1V1 = P2V2

11. Sample Problem
A sample of gas collected occupies a volume of 150mL when its pressure is 720 mmHg.
What volume will it occupy if its pressure is changed to 750 mmHg?
Given V1 = 150 mL V2 = ?
P1 = 720 mmHg P2 = 750 mmHg
Equation
P1V1 = P2V2 (720)(150) = (750) X
X = (720 x 150) / (750) = 144 mL

12. Charles’ Law: Temperature-Volume Relationship
The volume of a fixed amount of gas varies directly with the Kelvin temperature at constant pressure.
V1 / T1 = V2 / T2
V1 T2 = V2 T1

13. Charles’ Law Temperature must be in Kelvin!
Absolute Zero - lowest possible temperature, all kinetic energy ceases °C

14. Sample Problem
A sample of neon gas occupies a volume of 752 mL at 25 °C. What volume will it occupy at 50 °C. P, n are constant.
V1= 752 mL V2= ?
T1 = 25 °C +273 = 298 K T2 = 50 °C = 323 K
V1 T2 = V2 T1
X = (752)(323) / 298 = mL

15. Gay-Lussac’s Law
The pressure of a fixed gas varies directly with the temperature at constant volume.
Mathematically
P = k T or P / T = k
P1T2 = P2T1

16. Sample Problem (3.0)( 325) = X (298) X = (325)(3.0) / 298 = 3.27 atm
The gaseous contents in an aerosol can are under a pressure of 3.00 atm at 25 °C. If the temperature is increased to 52 °C, what would the pressure of the can be?
P1= 3.00 atm T1 = = 298 K
P2= ? T2 = = 325 K
P1T2 = P2T1
(3.0)( 325) = X (298)
X = (325)(3.0) / 298 = 3.27 atm

17. Avogadro’s Law
Equal volumes of gases at the same temperature and pressure contain equal number of gas particles.
At STP, 22.4L = 1 mol
V1n2 = V2n1

18. Sample Problem
Determine the number of moles of helium that are held in a 250mL container. Consider that 2.0 moles can be held in a 3L container.
V1 = 250mL V2 = 3000mL
n1 = ? n2 = 2.0moles

19. The Combined Gas Law
Expresses the relationship between P,T, & V of a fixed amount of gas.
Mathematically
PV/T = k
P1V1T2 = P2V2T1

20. Sample Problem
A helium-filled balloon has a volume of 50.0 L at 25°C and 820 mmHg. What volume will it occupy at 650 mmHg and 10 °C?
P1 = 820 mmHg P2 = 650 mmHg
V1 = 50 L V2 = ?
T1 = 298 K T2 = 283 K
V2 = (820)(50)(283)
(650)(298)
V2= 59.9 L

21. Dalton’s Law of Partial Pressure
The total pressure of a mixture of gases is equal to the sum of all the partial pressures.
Partial pressure - pressure of one gas in a mixture of gases
PT = P1 + P2 + P3 + …

22. Sample Problem
Determine the pressure of oxygen gas in a container that is under 1 atm of pressure and contains carbon dioxide and nitrogen.
Note: PCO2 = .285mmHg, PN2 = 594mmHg
760 mmHg = PO mmHg + 594mmHg
PO2 = mmHg

23. 13-4 : Ideal Gas Law
Describes the physical behavior of an ideal gas in terms of pressure, volume, temperature and number of moles.
The combination of all 4 gas laws from the previous section.

24. Derived Equation for the Ideal Gas Law
Needed an Ideal Gas Law Constant (R).
The second conditions were set at STP to equal the ideal behavior.

25. Ideal Gas Constant

26. Practice Problem
A camping stove uses a propane tank that holds 4.0 moles of liquid C3H8. How many liters will be needed to hold the same amount of propane at 25oC and 3atm?
V = ? n = 4 mol T = 25oC = 298K
P = 3 atm R = .0821

27. Gas Density at STP
The density of a gas at STP is constant, due to the standard molar volume of a gas.
Note: Molar Volume = 22.4L/mol

28. Gas Density Problems Determine the density of CO2 at STP.
What is the molar mass of gas that has a density of 1.28g/L at STP?

29. Molar Mass and Ideal Gas Law
Considering that moles are in the Ideal Gas Law equation, we can substitute the equivalent of moles(n) into the equation.

30. Density and the Ideal Gas Law
Now that mass(m) is in the equation we can substitute density(d) into the equation.

31. Molar Mass not at STP Using the previous equations : Example:
A 1.25g sample of gas was found to have a volume of 350mL at 20oC and 750mmHg. What is the molar mass of this gas?

32. Classwork
What is the molar mass of a gas that has a density of 2.08g/L at STP?
What is the density at STP of NO2?
What is the molar mass of a gas, if a 1.39g sample of gas has a volume of 375mL at 22oC and 755mmHg?
46.6g/mol
2.05g/L
90.4 g/mol

33. Ratm = RmmHg = RkPa = 8.314

34. Corrected Vapor Pressure
When a gas is collected through water displacement, there is always a trace of water vapor in the container.
To correctly use the gas laws you must subtract the water vapor pressure from the atmospheric pressure.
Pgas = Patm – PH2O

35. Water Displacement
A sample of methane gas that was collected through water displacement had a volume of 350mL at 27.0oC and 720mmHg. What is the volume at 2.0oC and 600.2mmHg?
T1 = 300 K T2 = 275K
P1 = 720mmHg P2 = 600.2mmHg
V1 = 350mL V2= ?
V2 = P1V1T2
T1 P2

36. Solution
P1=720mmHg –26.7 mmHg = 693.3mmHg

37. Graham’s Law
Diffusion – Tendency of gas particles to travel toward areas of lower concentration.
Effusion – Gas escapes a tiny opening in a container. (one way diffusion)
Graham’s Law
Rate of effusion of a gas is inversely proportional to the square root of its molar mass.
Less mass = faster gas

38. Graham’s Law Problems
Which gas will diffuse into a container faster? CO2 or NH3? Why?
Compare the rates of effusion for F2 and Cl2.
NH3, has less mass.

39. At a certain temperature and pressure, Cl2 has a velocity of. 038m/s
At a certain temperature and pressure, Cl2 has a velocity of .038m/s. What is the velocity of SO2 at the same condition?

40. Determining the Molar Mass
An unknown gas was placed into a container with N2 gas. The nitrogen was found to travel 1.2 times faster than the unknown gas. What is the molar mass of this unknown gas?