1. States of Matter

2. Matter
S. Hawking: Big Bang
CyberChem: Big Bang

3. Mystery of our Universe: A Matter of Family?
Bosons – Force carriers
Fermions - Particles
Strong (gluon)
Weak (+W , -W , Z)
Electromag. (photon)
Gravity (graviton)
Quarks
Leptons
Hadrons neutron proton
e- - - [  ]
nuclides
atoms
Three families
u d e- e
c s - 
t b  - 
elements
compounds
mixtures
molecules
complexes
homogeneous
heterogeneous

4. Mystery of our Universe: Quarks
Big B T physics: QM Gravity vs. strings
Particle Hunters

5. The Ideal Gas Equation Boyle’s Law:
We can combine these into a general gas law:
Boyle’s Law:
Charles’s Law:
Avogadro’s Law:

6. The Ideal Gas Equation R = gas constant, then
The ideal gas equation is:
R = L·atm/mol·K = J/mol·K
J = kPa·L = kPa·dm3 = Pa·m3
Real Gases behave ideally at low P and high T.

7. Calculate the number of air molecules in 1
Calculate the number of air molecules in 1.00 cm3 of air at 757 torr and 21.2 oC.
Mathcad

8. Calculate the number of air molecules in 1
Calculate the number of air molecules in 1.00 cm3 of air at 757 torr and 21.2 oC.
F12
Mathcad

9. Low P  Ideal

10. High T  Ideal

11. Density of an Ideal-Gas
Mathcad
Gas Densities and Molar Mass
The density of a gas behaving ideally can be determined as follows:
The density of a gas was measured at 1.50 atm and 27°C and found to be 1.95 g/L. Calculate the molecular weight of the gas? If the gas is a homonuclear diatomic, what is this gas?
Plotting data of density versus pressure (at constant T) can give molar mass.

12. Density of an Ideal-Gas
Derivation of :

13. Plotting data of density versus pressure (at constant T) can give molar mass.

14. The density of a gas was measured at 1
The density of a gas was measured at 1.50 atm and 27°C and found to be 1.95 g/L. Calculate the molecular weight of the gas?
If the gas is a homonuclear diatomic, what is this gas?

15. Deviation of Density from Ideal
Molar Mass of a Non-Ideal Gas
Generally, density changes with P at constant T, use power series:
First-order approximation:
Plotting data of ρ/P vs. P (at constant T) can give molar mass.

16. Plotting data of ρ/P vs. P (at constant T) can give molar mass.

17. Ideal Gas Mixtures and Partial Pressures
Dalton’s Law: in a gas mixture the total pressure is given by the sum of partial pressures of each component:
Each gas obeys the ideal gas equation:
Density?

18. Density?

19. Ideal Gas Mixtures and Partial Pressures
Partial Pressures and Mole Fractions
Let ni be the number of moles of gas i exerting a partial pressure Pi , then
where χi is the mole fraction.
CyberChem (diving) video:

21. Real Gases: Deviations from Ideal Behavior
The van der Waals Equation
General form of the van der Waals equation:
Corrects for molecular volume
Corrects for molecular attraction

22. Real Gases: Deviations from Ideal Behavior
Berthelot
Dieterici
Redlick-Kwong

24. The van der Waals Equation
Calculate the pressure exerted by 15.0 g of H2 in a volume of 5.00 dm3 at 300. K .

25. The van der Waals Equation
Calculate the molar volume of H2 gas at 40.0 atm and 300. K .

26. The van der Waals Equation
Can solve for P and T , but what about V?
Let: Vm = V/n { molar volume , i.e. n set to one mole}
Cubic Equation in V, not solvable analytically!
Use Newton’s Iteration Method:
Mathcad: Text Solution
Mathcad: Matrix Solution

29. Picture

30. Kinetic Molecular Theory
Postulates:
Gases consist of a large number of molecules in constant random motion.
Volume of individual molecules negligible compared to volume of container.
Intermolecular forces (forces between gas molecules) negligible.
Kinetic Energy =>
Root-mean-square Velocity =>

31. Kinetic Molecular Model – Formal Derivation
Preliminary note: Pressure of gas caused by collisions of molecules with rigid wall. No intermolecular forces, resulting in elastic collisions.
Consideration of Pressure:
Identify F=(∆p/∆t) ≡ change in momentum wrt time.

32. Before After pm=mu pm’=-mu pw=0 pw’=? Wall of Unit Area A z y x
Consider only x-direction: ( m=molecule ) ( w=wall )
Before
After
pm=mu
pm’=-mu
pw=0
pw’=?

33. Assumption: On average, half of the molecules are hitting wall and other not.
In unit time => half of molecules in volume (Au) hits A
If there are N molecules in volume V, then number of collisions with area A in unit time is:
And since each collision transfers 2mu of momentum, then
Total momentum transferred per unit time = pw’ x (# collisions)

34. Mean Square Velocity:
In 3-D, can assume isotropic distribution:
Substituting [eqn 3] into [eqn 2b] gives:

36. Mathcad

37. Kinetic Molecular Theory
Molecular Effusion and Diffusion
The lower the molar mass, M, the higher the rms.

38. Concept of Virial Series
Define: Z = compressibility factor
Virial Series: Expand Z upon molar concentration [ n/V ] or [ 1/Vm ]
B=f(T) => 2nd Virial Coeff., two-molecule interactions
C=f(T) => 3rd Virial Coeff., three-molecule interactions
Virial Series tend to diverge at high densities and/or low T.

39. Concept of Virial Series – vdw example

41. Phase Changes

43. Phase Changes Critical Temperature and Pressure
Gases liquefied by increasing pressure at some temperature.
Critical temperature: the minimum temperature for liquefaction of a gas using pressure.
Critical pressure: pressure required for liquefaction.

44. Phase Changes
Critical Temperature and Pressure

45. Phase Diagrams

46. Phase Diagrams
The Phase Diagrams of H2O and CO2

47. Reduced Variables

50. PVT Variations among Condensed Phases
Brief Calculus Review

51. PVT Variations among Condensed Phases

52. PVT Variations among Condensed Phases

54. Brief Calculus Review – F15 -1
Mathcad

55. Brief Calculus Review – F15 -2
Mathcad

56. Brief Calculus Review – F15 -3
Mathcad

57. Brief Calculus Review – F15 -4
Mathcad

58. Brief Calculus Review – F15 - 5
Mathcad

59. Brief Calculus Review – F15 - 6
Mathcad

60. Brief Calculus Review – F15 - 7
Mathcad

61. Exact and Partial Differentials: Tutorial
A right-circular cylinder has a base radius ( r ) of 2.00 cm and a height ( h ) of 5.00 cm.
(a) Find the “approximate change” in the volume ( V ) of the cylinder if r is increased by 0.30 cm and h is decreased by 0.40 cm. Express the answer in terms of  cm3 . This is the “differential” volume change. Then compare to the “real” volume change from algebraic calculations of initial and final volumes.
Repeat for r increase of 0.10 cm and h decrease of 0.10 cm.
Repeat for r increase of cm and h decrease of cm.
What is your conclusion regarding the comparisons?

62. A right-circular cylinder has a base radius ( r ) of 2
A right-circular cylinder has a base radius ( r ) of 2.00 cm and a height ( h ) of 5.00 cm.

63. Mathcad-file

64. A right-circular cylinder has a base radius ( r ) of 2
A right-circular cylinder has a base radius ( r ) of 2.00 cm and a height ( h ) of 5.00 cm.

65. Differential
Algebra
r / cm
h / cm
Dr / cm
Dh / cm
DV / p*cm3 V1 V2
V'=V2-V1
Diff
Diff%
2.00
5.00
6.6000E-02
1.52E+00
9.0000E-03
5.59E-01
3.3600E-04
7.64E-02
9.9000E-05
6.18E-02
3.0360E-06
6.90E-03
E-03
E-03
3.0036E-08
6.83E-04
E-04
3.0003E-10
6.82E-05
3.00E-06
-4.00E-06
E-05
2.9994E-12
6.82E-06
3.00E-07
-4.00E-07
E-06
3.3846E-14
7.69E-07
3.00E-08
-4.00E-08
E-07
2.6741E-15
6.08E-07

66. States of Matter