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Logarithm Review

Logarithm Review. Definition. log a c = b. a b = c, (a > 0, a ≠ 1). If a = 10, it is called common logarithm. log c = log 10 c. If a = e = 2.718281828459045 ∙ ∙ ∙, it is called n atural l ogarithm. ln c = log e c. Keys on your calculator. Properties of Logarithm. x > 0, y > 0.

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Logarithm Review

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  1. Logarithm Review Definition logac = b ab = c, (a > 0, a ≠ 1) If a = 10, it is called common logarithm logc = log10c If a = e = 2.718281828459045 ∙ ∙ ∙, it is called natural logarithm lnc = logec Keys on your calculator

  2. Properties of Logarithm x > 0, y > 0 ln(xy) = ln(x) + ln(y) ln(x/y) = ln(x) − ln(y) ln(xm) = m ln(x) Also see Appendix I B

  3. Chapter 11 Liquids, Solids and Intermolecular Forces continued

  4. Chemistry, continue on Vapor Pressure

  5. Surface Molecules

  6. Temperature: T Temperature: T

  7. GA, 760 torr = 1 atm H2O 100 °C Normal Boiling Point

  8. Tibet, 480 torr < 1 atm H2O 85 °C Normal Boiling Point

  9. (a) The Vapor Pressure of Water, Ethanol, and Diethyl Ether as a Function of Temperature. (b) Plots of In(Pvap) versus 1/T for Water, Ethanol, and Diethyl Ether T is in K! 1/T (K−1)

  10. Linear relation: y = kx + C y slope: k = tg θ θ x C: intercept

  11. 1/T (K−1) Linear relation: y = kx + C ln P = k(1/T) + C

  12. Heat of vaporization ∆Hvap: energy needed to convert one mole of liquid to gas. Unit: J/mol or kJ/mol. ∆Hvap > 0

  13. x y slope k < 0

  14. ln (P) 1 ln (P1) 2 ln (P2) 1/T1 1/T2 1/T (K−1)

  15. Clausius-Clapeyron Equation

  16. The vapor pressure of water at 25 °C is 23.8 torr, and the heat of vaporization of water is 43.9 kJ/mol. Calculate the vapor pressure of water at 50 °C. Five: T1, T2, P1, P2, ∆Hvap Four known, calculate the other.

  17. Units in ideal gas law PV = nRT Option 1 Chem 1211 P — atm, V — L, n — mol, T — K R = 0.082 atm · L · mol−1 · K−1 Option 2 P — Pa, V — m3, n — mol, T — K R = 8.314 J · mol−1 · K−1 Clausius-Clapeyron equation

  18. Carbon tetrachloride, CCl4, has a vapor pressure of 213 torr at 40 °C and 836 torr at 80 °C. What is the normal boiling point of CCl4? ( Please try to work on this question by yourself. Will review next week)

  19. Liquid potassium has a vapor pressure of 10.00 torr at 443 °C • and a vapor pressure of 400.0 torr at 708 °C. Use these data • to calculate • The heat of vaporization of liquid potassium; • The normal boiling point of potassium; • The vapor pressure of liquid potassium at 100. °C. ( Please try to work on this question by yourself. Will review next week)

  20. Clausius-Clapeyron Equation

  21. x y slope k < 0

  22. Linear relation: y = kx + C y slope: k = tg θ θ x C: intercept

  23. y a d c b x Lines tilt to the right have positive slopes (a and b), left negative (c and d). Steeper line has greater absolute value of slope. In this graph, the order of slopes is a > b > 0 > c > d

  24. What is the order of heat of vaporization for these three substances?

  25. Solids

  26. Glass (SiO2)

  27. Crystal Solid Noncrystal

  28. Basis Crystal structure

  29. The basis may be a single atom or molecule, or a small group of atoms, molecules, or ions. NaCl: 1 Na+ ion and 1 Cl− ion Cu: 1 Cu atom Zn: 2 Zn atoms Diamond: 2 C atoms CO2: 4 CO2 molecules

  30. = Use a point to represent the basis:

  31. Lattice Lattice point:

  32. Unit cell: 2-D, at least a parallelogram Unit cell is the building block of the crystal

  33. How many kinds of 2-D unit cells can we have?

  34.                                                           

  35. Extend the concept of unit cell to 3-D, the real crystals.

  36. : 3-D, at least a parallelepiped

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