CHEM 10113, Quiz 7 December 7, 2011

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1 CHEM 10113, Quiz 7 December 7, 2011 Name (please print) All equations must be balanced and show phases for full credit. Significant figures count, show charges as appropriate, and please box your answers! IA Periodic Table of the Elements VIIIA (1) (18) H IIA IIIA IVA VA VIA VIIA He (2) (13) (14) (15) (16) (17) Li Be B C N O F Ne Na Mg IIIB IVB VB VIB VIIB VIIIB IB IIB Al Si P S Cl Ar (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe Cs Ba La Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn Fr Ra Ac Rf Db Sg Bh Hs Mt Ds Uuu Uub Uug (261) (262) (266) (264) (270) (268) (281) Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr (6 points) SHOW ALL WORK. You are given a small bar of an unknown metal X. You find the density of the metal to be 10.5 g/cm 3. An X-ray diffraction experiment measures the edge of the face-centered cubic unit cell as 4.09 x m. Identify X. Density = mass = 10.5 g/cm 3 V Volume = l 3 = (4.09 x m x 1 cm ) 3 = x cm g/cm 3 = mass of unit cell x cm 3 mass of unit cell = x g Since there are four atoms per unit cell, the mass of one atom is unit cell mass/4, then convert the mass of one atom to the mass of one mole:

2 7.184 x g = x g x (6.022 x atoms) = 108 g/mol 4 atoms atom x = Ag 2. (4 points) Name two (2) differences between molecular solids and network solids. Held together by: MP Molecular Solids LDF, dipole-dipole, Low dipole-induced dipole and/or H-bonding Network Solids Covalent bonds High 3. (7 points) These questions concern band theory. a.) Draw a labeled band diagram ( 3 labels) for an insulator. b.) Use the band model to explain why increasing the temperature increases the conductivity of a semiconductor. a) Conduction band Empty Band Gap Valence band Full b) Conductivity is a product of the movement of electrons transitioning from the highest occupied molecular orbital into higher energy empty molecular orbitals. As a semiconductor is heated, electrons become sufficiently excited to cross the band gap and enter the conduction band. 4. (3 points) X-rays from a copper X-ray tube ( = 154 pm) were diffracted at an angle of degrees by a crystal of silicon. Assuming first-order diffraction (n = 1 in the Bragg equation), what is the interplanar spacing in silicon? Bragg s Law: n =2sin D= n = 1(154 pm) = 1(154 pm) = 313 pm 2sin 2 sin(14.22) 2(0.2456)

3 5. (1 point) Cubic closest packing describes the same crystal structure as the hexagonal unit cell. 6. (4 points) A drawing of the NaCl unit cell is shown below. The larger ions are chlorides, the smaller ones are sodium ions. a. What is the edge length (in pm) of the unit cell? The ionic radius of Na + is 97 pm, and the ionic radius of Cl is 181 pm. l = 2r Cl - + 2r Na + = 2(181 pm) + 2(97 pm) = 556 pm b. How many chloride ions are inside the unit cell? Simple cubic 4 chloride ions CHEM 10113, Quiz 7 December 7, 2011 Name (please print) All equations must be balanced and show phases for full credit. Significant figures count, show charges as appropriate, and please box your answers! IA Periodic Table of the Elements VIIIA (1) (18) H IIA IIIA IVA VA VIA VIIA He (2) (13) (14) (15) (16) (17) Li Be B C N O F Ne Na Mg IIIB IVB VB VIB VIIB VIIIB IB IIB Al Si P S Cl Ar (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe Cs Ba La Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn Fr Ra Ac Rf Db Sg Bh Hs Mt Ds Uuu Uub Uug (261) (262) (266) (264) (270) (268) (281) Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr

4 1. (6 points) SHOW ALL WORK. You are given a small bar of an unknown metal X. You find the density of the metal to be 8.95 g/cm 3. An X-ray diffraction experiment measures the edge of the face-centered cubic unit cell as pm. Identify X. Density = mass = 8.95 g/cm 3 V Volume = l 3 = ( pm x cm ) 3 = x cm 3 pm 8.95 g/cm 3 = mass of unit cell x cm 3 mass of unit cell = x g Since there are four atoms per unit cell, the mass of one atom is mass of unit cell/4, then convert the mass of one atom to the mass of one mole: x g = x g x (6.022 x atoms) = 63.6 g/mol 4 atoms atom x = Cu 2. (4 points) Name two (2) differences between ionic solids and network solids. Held together by: Composite unit of: Ionic Solids Electrostatic interactions Formula units (cations and anions) Network Solids Covalent bonds atoms 3. (7 points) These questions concern band theory. a.) Draw a labeled band diagram ( 3 labels) for a conductor. b.) Use the band model to explain why adding a dopant increases the conductivity of a semiconductor. a) Conduction Band Valence Band Empty Full

5 b) When doping occurs, extra energy levels become available that allow electrons to conduct without having to reach all the way across the band gap. 4. (3 points) X-rays from an X-ray tube ( = pm) were diffracted at an angle of degrees by a crystal of aluminum. Assuming first-order diffraction (n = 1 in the Bragg equation), what is the interplanar spacing in aluminum? Bragg s Law: n =2sin D= n = 1(131.5 pm) = 1(131.5 pm) = pm 2sin 2 sin(25.25) 2(0.4267) 5. (1 point) The body-centered cubic unit cell contains a total of 2 particles per unit cell. 6. (4 points) A drawing of the NaF unit cell is shown below. The larger ions are fluorides, the smaller ones are sodium ions. a. What is the edge length (in pm) of the unit cell? The ionic radius of Na + is 97 pm, and the ionic radius of F is 136 pm. l = 2r F - + 2r Na + = 2(136 pm) + 2(97 pm) = 466 pm b. How many fluoride ions are inside the unit cell? Simple cubic 4 fluoride ions CHEM 10113, Quiz 7 December 7, 2011 Name (please print) All equations must be balanced and show phases for full credit. Significant figures count, show charges as appropriate, and please box your answers!

6 IA Periodic Table of the Elements VIIIA (1) (18) H IIA IIIA IVA VA VIA VIIA He (2) (13) (14) (15) (16) (17) Li Be B C N O F Ne Na Mg IIIB IVB VB VIB VIIB VIIIB IB IIB Al Si P S Cl Ar (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe Cs Ba La Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn Fr Ra Ac Rf Db Sg Bh Hs Mt Ds Uuu Uub Uug (261) (262) (266) (264) (270) (268) (281) Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr (6 points) SHOW ALL WORK. You are given a small bar of an unknown metal X. You find the density of the metal to be g/cm 3. An X-ray diffraction experiment measures the edge of the face-centered cubic unit cell as 495 pm. Identify X. Density = mass = g/cm 3 V Volume = l 3 = (495 pm x cm ) 3 = x cm 3 pm g/cm 3 = mass of unit cell x cm 3 mass of unit cell = x g Since there are four atoms per unit cell, the mass of one atom is mass of unit cell/4, then convert the mass of one atom to the mass of one mole: x g = x g x (6.022 x atoms) = 207 g/mol 4 atoms atom x = Pb

7 2. (4 points) Name two (2) differences between molecular solids and metallic solids. Molecular Solids Metallic Solids Held together by: LDF, dipole-dipole, dipole-induced dipole and/or H-bonding metallic bonds; electron sea model Composite unit of: molecules atoms 3. (7 points) These questions concern band theory. a.) Draw a labeled band diagram ( 3 labels) for a semiconductor. b.) Use the band model to explain why increasing the temperature does not increase the conductivity of a conductor. a) Empty Band Gap Full b) Conductivity is a product of the movement of electrons transitioning from the highest occupied molecular orbital into higher energy empty molecular orbitals. Since metals have no band gap, raising temp does not increase electrons' access to the conduction band. Indeed, raising the temp lowers the conductivity slightly due to increased vibrations of the atoms and a disruption of the lattice structure. 4. (3 points) X-rays from a molybdenum X-ray tube ( = 71.0 pm) were diffracted at an angle of 7.23 degrees by a crystal of germanium. Assuming first-order diffraction (n = 1 in the Bragg equation), what is the interplanar spacing in germanium? Bragg s Law: n =2sin D= n = 1(71.0 pm) = 1(71.0 pm) = 282 pm 2sin 2 sin(7.23) 2(0.1256)

8 5. (1 point) The hexagonal closest packing crystal structure consists of alternating layers in an ABAB pattern. 6. (4 points) A drawing of the SnTe unit cell is shown below. The larger ions are tellurides, the smaller ones are tin ions. a. What is the edge length (in pm) of the unit cell? The ionic radius of Sn 2+ is 71 pm, and the ionic radius of Te 2 is 221 pm. l = 2r Te r Sn 2 + = 2(221 pm) + 2(71 pm) = 584 pm b. How many telluride ions are inside the unit cell? Simple cubic 4 telluride ions

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