#### Transcript The 14 Bravais lattices 7 crystal systems

Logarithm Review Definition ab = c, (a > 0, a ≠ 1) logac = b If a = 10, it is called common logarithm log c = log10c If a = e = 2.718281828459045 ∙ ∙ ∙, it is called natural logarithm ln c = logec Keys on your calculator 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 Chapter 11 Liquids, Solids and Intermolecular Forces continued Chemistry, continue on Vapor Pressure Surface Molecules Temperature: T Temperature: T GA, 760 torr = 1 atm H2O 100 °C Normal Boiling Point Tibet, 480 torr < 1 atm H2O 85 °C Normal Boiling Point (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) Linear relation: y = kx + C y slope: k = tg θ θ x C: intercept 1/T (K−1) Linear relation: y = kx + C ln P = k(1/T) + C Heat of vaporization ∆Hvap: energy needed to convert one mole of liquid to gas. Unit: J/mol or kJ/mol. ∆Hvap > 0 ln P H va p 1 R y slope k < 0 T x C ln (P) ln P H va p 1 R C T 1 ln (P1) 2 ln (P2) 1/T1 1/T2 1/T (K−1) Clausius-Clapeyron Equation ln P H va p 1 R C T H vap 1 1 ln P2 R T1 T 2 P1 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. H vap 1 1 ln P2 R T1 T 2 P1 Five: T1, T2, P1, P2, ∆Hvap Four known, calculate the other. 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 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? H vap 1 1 ln P2 R T1 T 2 P1 ( Please try to work on this question by yourself. Will review next week) 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 (a) The heat of vaporization of liquid potassium; (b) The normal boiling point of potassium; (c) The vapor pressure of liquid potassium at 100. °C. ( Please try to work on this question by yourself. Will review next week) Clausius-Clapeyron Equation ln P H va p 1 R C T H vap 1 1 ln P2 R T1 T 2 P1 ln P H va p 1 R y slope k < 0 T x C Linear relation: y = kx + C y slope: k = tg θ θ x C: intercept 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 What is the order of heat of vaporization for these three substances? Solids Glass (SiO2) Crystal Solid Noncrystal Basis Crystal structure 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 Use a point to represent the basis: = Lattice Lattice point: Unit cell: 2-D, at least a parallelogram Unit cell is the building block of the crystal How many kinds of 2-D unit cells can we have? Extend the concept of unit cell to 3-D, the real crystals. : 3-D, at least a parallelepiped How many kinds of 3-D unit cells can we have? 1. triclinic a≠b≠c α≠β≠γ 2. monoclinic c a a≠b≠c b c a b The 14 Bravais lattices 3. orthorhombic 7 crystal systems α = β = γ = 90° 5. rhombohedral (trigonal) 4. tetragonal a=b=c 90° ≠ α = β = γ < 120° a=b≠c α = β = γ = 90° 7. cubic 6. hexagonal a=b≠c α = β = 90° ,γ = 120° γ a=b=c α = β = γ = 90° (Simple cubic) Chem 1212: assume a lattice point is a single atom Information of a cubic unit cell • Size of the cell X-ray diffraction The Wave Nature of Light Information of a cubic unit cell • Size of the cell X-ray diffraction • Size of the atoms • Number of atoms in a cell Soon Now! C D B A C D E B A F Number of atoms in a unit cell = ¼ x 4 = 1 Number of Atoms in a Cubic Unit Cell 1 2 4 The body-centered cubic unit cell of a particular crystalline form of iron is 0.28664 nm on each side. Calculate the density (in g/cm3) of this form of iron. d = 7.8753 g/cm3 The body-centered cubic unit cell of a particular crystalline form of an element is 0.28664 nm on each side. The density of this element is 7.8753 g/cm3. Identify the element. The face-centered cubic unit cell of a particular crystalline form of platinum is 393 pm on each side. Calculate the density (in g/cm3) of this form of platinum. d = 21.4 g/cm3 Closest Packing a a b c a b c a b c b a b c c b c a b c a a b a c a c b a b a c a a b a c a a a b c a a · · · abab · · · · · · abab · · · 1. triclinic 2. monoclinic a≠b≠c a≠b≠c α≠β≠γ The 14 Bravais lattices 3. orthorhombic 7 crystal systems α = β = γ = 90° 5. rhombohedral (trigonal) 4. tetragonal a=b=c 90° ≠ α = β = γ < 120° a=b≠c α = β = γ = 90° 7. cubic 6. hexagonal a=b≠c α = β = 90° ,γ = 120° γ a=b=c α = β = γ = 90° · · · abcabc · · · abcabc = Cubic Closest Packing e.g. Ag, 1 atoms (1 lattice point) in a unit cell Information of a unit cell • Size of the cell X-ray diffraction • Size of the atoms • Number of atoms in a cell Soon Now! Now! Example 11.7, page 494 Al crystallizes with a face-centered cubic unit cell. The radius of a Al atom is 143 pm. Calculate the density of solid Al in g/cm3. d = 2.71 g/cm3 L r L 8 r 2r L r What about simple cubic? L r Simple Cubic L = 2r What about body-centered cubic? Body centered cubic Body diagonal D = 4r L D L L D L F L Body diagonal D = 4r L 4 3 r Pythagorean theorem Titanium metal has a body-centered cubic unit cell. The density of titanium is 4.50 g/cm3. Calculate the edge length of the unit cell and a value for the atomic radius of titanium in pm. L = 328 pm r = 142 pm 100-mL container 50 mL 70 mL 50 % 70 % 1 52 % L = 2r 2 4 68 % 74 % prove L 4 3 r L 8 r Packing Efficiency: fraction of volume occupied by atoms