1. Kinetic Theory of Gases

3. Gas Phase

4. Kinetic Molecular Theory (KMT)-Ideal Gases
The particles are in constant motion.
The volume of the individual particles of a gas are negligible compared to the distances between them.
The particles are assumed not to exert attracting or repelling forces (no intermolecular forces) on each other.
The collisions are perfectly elastic. No kinetic energy is lost before and after the collision.
The collisions of the particles with the walls of the container cause pressure.
*Real gases DO have volume & intermolecular forces!

5. State Variables of a Gas: describe the State of a Gas (PVT)
SI Unit
Pressure (P) Pascals Pa
Volume (V) m3
Temperature (T) Kelvin
Amount of gas molecules mol (n)

6. Simulation

7. Standard Temperature and Pressure (STP)
1 atm =760mmHg (torr) = kPa
273K =0 0C

8. Pressure
P= F A Units of Pressure: pascal, mmHg, atm 1 Pa = 1 N/m2 CONVERSION: 1 atm =760mmHg (torr) = kPa

9. Factors Affecting Gas Pressure
Number of Moles (Amount of gas)
As the number of particles increases, the number of collisions with the container wall increases (more force).
Volume
The smaller the volume, the greater the pressure exerted on the container (less area).
Temperature
As temperature increases, kinetic energy increases, increasing the frequency of collisions AND the forcefulness of each collision (MORE IMPORTANT). Thus pressure increases (more force). .

10. Manometer- Open End
PC=PB PA= Atmospheric Pressure PB=PA+ PAB PAB is measured in mmHg (torr) PAB is called gauge pressure.
Gas Sample

11. Manometer- Closed End “Barometer”
Gas Sample
PC=PB
PA= 0 atm
PB= PAB

12. Temperature How hot – cold Average kinetic energy of molecules.
The average kinetic energy of a gas is directly proportional to the Kelvin temperature.
KE = (3/2)RT

13. Temperature Scales Celsius 0 100 Kelvin 273 373 Fahrenheit 32 212
Freezing Point of Water Boiling Point of Water
Celsius
Kelvin
Fahrenheit
K=273+C (absolute zero: 0 K)
F=(9/5)C +32
When you increase T by one degree C, how many K do you increase by?
THE SAME!!!! The Kelvin & Celsius scale are the same, it’s just the numeric values in Kelvin are higher.

14. Kinetic Energy KE= ½ m v2 KE = 3/2 RT (for 1 mole of gas)
Average speed, v = √((3RT)/MM)
v speed, m mass
Example: speed of oxygen molecule at 25oC = 443 m/s

15. Molecular speed… The “Maxwell-Boltzmann distribution”
Inversely related to MASS (lighter molecules are faster)
Directly related to TEMPERATURE (hotter molecules are faster)
*Remember, even though a lighter molecule may be FASTER, it has the SAME KINETIC ENERGY as a heavier molecule if they are at the SAME TEMPERATURE (because kinetic energy is related to both velocity (aka speed) AND mass; when one goes up, the other goes down!)
Bell-curve distribution with an average speed ….particles are NOT ALL at the same speed
COMPARISON OF MASS
COMPARISON OF TEMPERATURE

16. Gas Laws

17. Ideal Gas Law vs. P V = n R T Van der Waals equation
P = pressure Pa = N/m2 V = volume measured in L n =# of moles T = temperature K R=Universal gas constant =8.314 kPa L / (mol K) = L atm/(mol K) =62.3 mmHg L/(mol K)
correction for molecular attraction (increases pressure as the concentration of molecules increases)

18. Ideal Gas Laws mostly hold at:
Low pressure
High temperature

19. If Mass and Temp are Constant

20. If Mass and Pressure are Constant

21. Boyle’s Law P1V1=P2V2 T constant P vs V hyperbola # moles constant
Isotherm
High Temp P V

22. Charles Law
V1 = V2 P constant T1 T2 # Moles constant
Isobar V
T (K)

23. Gay-Lussac
P1 = P2 V constant T1 T2 # moles Constant isochoric P T

24. Combined Gas Law
P1V1 = P2V2_
T T2

25. -Diffusion -Graham’s Law of Effusion -Dalton’s Law of Partial Pressures

26. Diffusion

27. Diffusion
The process in which particles of matter move from areas of high concentration to areas of low concentration.

28. Effusion
The passage of gases through a small hole or pores of a membrane.

29. Note
Gases of lower molar mass diffuse and effuse faster than gases of higher molar mass.

30. Graham’s Law of Effusion
________ va= √ MMb vb MMa v = rate of effusion = (1/ time) MM= molar mass -The rate of effusion of a gas is inversely proportional to the square root of its molar mass.

31. Example
Compare the rates of effusion of CO2 to oxygen gas.

32. Dalton’s Law of Partial Pressures
Ptot=P1+P2+….
Total pressure of a mixture of gases in a container is the sum of the individual pressures (partial pressures) of each gas, as if each took up the total space alone.

33. Dalton’s Law of Partial Pressures

34. Dalton’s Law of Partial Pressures:
The total pressure in a gas mixture is the sum of the partial pressures of each individual gas.
Ptotal = Pgas 1 + Pgas 2 + Pgas 3 + …
Pgas 1 = ( 𝑚𝑜𝑙𝑒𝑠 𝑜𝑓 𝑔𝑎𝑠 1 𝑡𝑜𝑡𝑎𝑙 𝑚𝑜𝑙𝑒𝑠 𝑜𝑓 𝑔𝑎𝑠 ) (Ptotal)

35. Partial Pressure of a Gas:
The pressure that the gas would exert if it were the only gas present in the container.

36. Liquids

37. Liquids Intermolecular attractions hold molecules of liquids together.
Incompressible, definite volume.
More dense than gases.
Molecules have kinetic energy.

38. Vaporization
Change of phase from a liquid to a gas

39. Evaporation Vaporization occurring at the surface of the liquid.
Responsible for the vapor pressure, Pvapor , of a liquid.

40. Evaporation example: Bromine
Gas (Vapor)
Liquid

41. Evaporation in a Closed Container

42. Evaporation in a Closed Container
Liquid  Vapor  When the rate of evaporation equals the rate of condensation the system is in Equilibrium

43. Vapor Pressure
The pressure resulting from the gas that would evaporate from a liquid
at a specific given temperature,
in an equilibrium situation (closed container).

44. What happens to the rate of evaporation as the liquid is heated?
The rate of evaporation increases.
As T increases, more particles have the minimum speed to escape the liquid surface (Pvapor increases…).
Minimum speed to escape liquid surface

45. The vapor pressure increases with increasing temperature.
Why? Because the kinetic energy of the liquid molecules increases and more leave the liquid and collide with the walls of the container.

46. Evaporation is a cooling process
Why?
The particles with the higher kinetic energy escape the liquid first; the process of evaporation still requires the breaking of IMFs (absorption of energy).

47. Boiling
Vaporization occurring beneath the liquid’s surface (i.e. throughout the liquid).
This only occurs when the Pvapor = Pexternal.
Pvapor = vapor pressure of liquid
Pexternal = pressure above liquid from atmosphere, etc.

48. Boiling Point
The temperature at which a liquid boils.

49. Pvapor < Pexternal = no boiling
When the external pressure is greater than the vapor pressure of the bubbles in the liquid the bubbles cannot come to the surface. Boiling does not happen.

50. Pvapor = Pexternal, then boiling!
When the external pressure is equal to the vapor pressure of the bubbles in the liquid, boiling occurs.

52. Why does water boil at a lower temperature at high altitudes?
Because the external pressure is lower.

53. Normal Boiling Point
The boiling point at 1 atm or 101.3kPa

54. Solids

55. Solids
Atoms vibrate about fixed positions.

56. Properties of Solids
Depend on their arrangement of their atoms.

57. Melting Points Temperature at which a solid changes to a liquid.
Vibrations of particles are strong enough to overcome the attraction that holds them in fixed locations.
Melting point is same as freezing points.

58. Melting Points of Ionic and Molecular Solids
Ionic Solids have high melting points because strong forces are holding the particles together.
Molecular Solids have lower melting points.
Not all solids melt (ex. Wood, cane sugar, some plastics)

59. Most Solids are Crystalline
Unit cell : the smallest group of particles that retains the shape of the crystal.
Crystal Lattice: a repeating array of unit cells.

60. Simple Cubic,Body-Centered and Face-Centered

62. Allotropes
Two or more different molecular forms of the same element in the same physical state.

63. Allotropes of Carbon
Diamond
Graphite
Bucky Balls

64. Buckminsterfullerene “Bucky Ball”

65. Amorphous Solids No order internal structure
Examples: glass, plastics, asphalt

67. Formula for calculating heat input for kinetic energy changes: q = mC∆T
Formula for calculating heat transfer for potential energy changes: q = m∆Hfus or vap

69. Phase diagram of water