States of Matter

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 • 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 = 0.08206 L·atm/mol·K = 8.3145 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 1.00 cm3 of air at 757 torr and 21.2 oC. Mathcad

8. 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 1.50 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. Wall of Unit Area A z y x Consider only x-direction: ( m=molecule ) ( w=wall )

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