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Theoretical Problems 44th International Chemistry Olympiad July 26, 2012 United States of America Name: Code: Instructions Write your name and code on each page This examination has problems and Periodic Table on 49 pages You have hours to work on the exam problems Begin only when the START command is given Use only the pen and the calculator provided All results must be written in the appropriate boxes Anything written elsewhere will not be graded Use the back side of the exam sheets if you need scratch paper Write relevant calculations in the appropriate boxes when necessary Full marks will be given for correct answers only when your work is shown When you have finished the examination, put your papers into the envelope provided Do not seal the envelope You must stop working when the STOP command is given Do not leave your seat until permitted by the supervisors The official English version of this examination is available on request only for clarification th The 44 IChO – Theoretical Examination The official English version Name: Code: Physical Constants, Formulas and Equations Avogadro's constant, NA = 6.0221 1023 mol–1 Boltzmann constant, kB = 1.3807 10–23 J∙K–1 Universal gas constant, R = 8.3145 J∙K–1∙mol–1 = 0.08205 atm∙L∙K–1∙mol–1 Speed of light, c = 2.9979 108 m∙s–1 Planck's constant, h = 6.6261 10–34 J∙s Mass of electron, me = 9.10938215 10–31 kg Standard pressure, P = bar = 105 Pa Atmospheric pressure, Patm = 1.01325 105 Pa = 760 mmHg = 760 Torr Zero of the Celsius scale, 273.15 K nanometer (nm) = 10–9 m picometer (pm) = 10–12 m Equation of a circle, x2 + y2 = r2 r2 r r3/3 r2 Bragg's Law of Diffraction: sin = n/2d th The 44 IChO – Theoretical Examination The official English version Name: Code: 1 1.00794 18 4.00260 H 0.28 He 13 6.941 9.01218 Li Atomic number 1.00794 Be H 0.28 Atomic weight Na 10.811 Atomic symbol Covalent radius, Å 11 12 22.9898 24.3050 14 15 1.40 17 16 10 12.011 14.0067 15.9994 18.9984 20.1797 B C N O F Ne 0.89 0.77 0.70 0.66 0.64 1.50 13 14 15 16 17 18 26.9815 28.0855 30.9738 32.066 35.4527 39.948 Mg Al Si P S Cl Ar 1.17 1.10 1.04 0.99 1.80 10 11 12 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 39.0983 40.078 44.9559 47.867 50.9415 51.9961 54.9381 55.845 58.9332 58.6934 63.546 65.39 69.723 72.61 74.9216 78.96 79.904 83.80 K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr 1.46 1.33 1.25 1.37 1.24 1.25 1.24 1.28 1.33 1.35 1.22 1.20 1.18 1.14 1.90 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 85.4678 87.62 88.9059 91.224 92.9064 95.94 (97.905) 101.07 102.906 106.42 107.868 112.41 114.818 118.710 121.760 127.60 126.904 131.29 Rb Sr Y 55 56 57-71 132.905 137.327 Cs Fr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe 1.43 1.37 1.36 1.34 1.34 1.37 1.44 1.49 1.67 1.40 1.45 1.37 1.33 2.10 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 178.49 180.948 183.84 186.207 190.23 192.217 195.08 196.967 200.59 204.383 207.2 208.980 (208.98) (209.99) (222.02) Ba La-Lu 87 88 89-103 (223.02) (226.03) Zr 1.60 Ra Ac-Lr Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po 1.59 1.43 1.37 1.37 1.35 1.36 1.38 1.44 1.50 1.70 1.76 1.55 1.67 At Rn 2.20 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 (261.11) (262.11) (263.12) (262.12) (265) (266) (271) (272) (285) (284) (289) (288) (292) (294) (294) Rf Db Sg Bh Hs Mt Ds Rg Cn Uut Fl Uup Lv Uus UUo 2.25 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 138.906 140.115 140.908 144.24 (144.91) 150.36 151.965 157.25 158.925 162.50 164.930 167.26 168.934 173.04 174.04 La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu 1.87 1.83 1.82 1.81 1.83 1.80 2.04 1.79 1.76 1.75 1.74 1.73 1.72 1.94 1.72 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 (227.03) 232.038 231.036 238.029 (237.05) (244.06 (243.06) (247.07) (247.07) (251.08) (252.08) (257.10) (258.10) (259.1) (260.1) Ac Th Pa U Np 1.88 1.80 1.56 1.38 1.55 ) Pu Am Cm Bk Cf Es 1.73 1.74 1.72 1.99 2.03 Fm Md No Lr 1.59 th The 44 IChO – Theoretical Examination The official English version Name: Code: PROBLEM a–i 7.5% of the total a–ii a-iii b C 10 Problem 20 7.5% a Boron Hydrides and Other Boron Compounds Boron hydride chemistry was first developed by Alfred Stock (1876-1946) More than 20 neutral molecular boron hydrides with the general formula B xHy have been characterized The simplest boron hydride is B2H6, diborane i Using the data below derive the molecular formulae for two other members of this series of boron hydrides, A and B (A and B) Substance A B State (25 ˚C, bar) Mass Percent Boron Liquid Solid 83.1 88.5 A = _ B5H11 _ Molar mass (g/mol) 65.1 122.2 B = B10H14 points each = points th The 44 IChO – Theoretical Examination The official English version Name: Code: ii William Lipscomb received the Nobel Prize in Chemistry in 1976 for “studies on the structures of boron hydrides illuminating the problems of chemical bonding.” Lipscomb recognized that, in all boron hydrides, each B atom has a normal 2-electron bond to at least one H atom (B–H) However, additional bonds of several types occur, and he developed a scheme for describing the structure of a borane by giving it a styx number where: s = number of B–H–B bridges in the molecule t = the number of 3-center BBB bonds in the molecule y = the number of two-center B–B bonds in the molecule x = the number of BH2 groups in the molecule The styx number for B2H6 is 2002 Propose a structure for tetraborane, B4H10, with a styx number of 4012 H H H H B H B H H B H B B H H H actual structure H H H B H H B H H B H H unknown but acceptable structure points for either of these structures th The 44 IChO – Theoretical Examination The official English version Name: Code: iii A boron-based compound is composed of boron, carbon, chlorine, and oxygen (B4CCl6O) Spectral measurements indicate the molecule has two types of B atoms, with tetrahedral and trigonal planar geometry, in a 1:3 ratio, respectively These spectra are also consistent with a CO triple bond Given that the molecular formula of the compound is B4CCl6O, suggest a structure for the molecule Structure: O C Cl2B Cl2B B BCl2 points Not required to show the stereochemistry th The 44 IChO – Theoretical Examination The official English version Name: Code: b Thermochemistry of Boron Compounds Estimate the B-B single bond dissociation enthalpy in B2Cl4(g) using the following information: Bond Bond Dissociation Enthalpy (kJ/mol) B–Cl 443 Cl–Cl 242 Compound BCl3(g) B2Cl4(g) fH° (kJ/mol) –403 –489 A Born-Haber cycle gives a B-B bond dissociation enthalpy of 327 kJ/mol 2B + 6Cl rHo = -4 x 443 - 242 kJ - BB rHo = x 443 kJ B2Cl4 + Cl2 2BCl3 rHo = +317 kJ points th The 44 IChO – Theoretical Examination The official English version Name: Code: c Chemistry of Diborane Give the structure for each numbered compound in the scheme below Each numbered compound is a boron-containing compound NOTES: a The boiling point of compound is 55 ˚C b Excess reagents used in all reactions c The freezing point depression for 0.312 g of compound in 25.0 g of benzene is 0.205 ˚C The freezing point depression constant for benzene is 5.12 ˚C/molal th The 44 IChO – Theoretical Examination The official English version Name: Code: Number Molecular Structure of Compound OCH3 B H3CO B(OCH3)3 C6H5 B O O B OCH3 C6H5 B O C6H5 A dimer or tetramer [C6H5BO]x are also acceptable (x = 2, 4) Cl B BCl3 Cl H BNH6 H H B N H H Cl H Formal charges not necessary H H H B N H6 B N N B B N H H H Formal charges not necessary 10 points, points each but only point for formula only th The 44 IChO – Theoretical Examination The official English version ... The 44 IChO – Theoretical Examination The official English version Name: Code: gases, the solution reacts with excess KI solution, turning yellow-brown This solution can be titrated with thiosulfate... under Ar; titration of this solution required 1.696 10-4 mol thiosulfate to reach the endpoint i Calculate the number of moles of Cu in each of these samples of YBCO nCu = nthiosulfate in the first... 10–4 g gold points 16 th The 44 IChO – Theoretical Examination The official English version Name: Code: PROBLEM 7.5 % of the Total a b 12 c-i c-ii 12 Problem 34 7.5% Thiomolybdate ions are derived