International Chemistry Olympiad

IChO 2000

Copenhagen, Denmark · 6 theory problems with complete solutions

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  1. Problem 1: Synthesis of Compounds with Wound Healing Properties

    Figure 1

    Shikonin is a red compound found in the roots of the plant Lithospermum erythrorhizon which grows in Asia. Extracts of the root have been used for centuries in folk medicine and are used today in ointments for healing of wounds.

    Figure 2

    Shikonin

    1.1 How many stereoisomers of Shikonin are possible ?

    1.2 Do all stereoisomers of Shikonin have the same melting point? Mark with an X.

    yes no

    The following sequence is part of a synthetic route to Shikonin:

    Figure 3

    1.3 Draw the structural formula of reagent A.

    1.4 Indicate (by means of an X in the appropriate check-box) the correct IUPAC name for reagent A.

    2-Methyl-2-pentenoyl chloride ☐
    1-Chloro-4-methyl-3-pentene ☐
    4-Methyl-3-pentenoyl chloride ☐
    4-Methyl-3-pentene-1-ol ☐
    4,4-Dimethyl-3-butenoyl chloride ☐

    1.5 Write the molecular formula of reagent C.

    Numerous Shikonin analogues have been synthesized with a view to obtaining more potent compounds. One reaction sequence is shown below:

    Figure 4

    1.6 Draw the structural formula of compound E.

    1.7 How many stereoisomers of compound E, if any, are possible

    Another route to useful Shikonin analogues is the following:

    Figure 5

    1.8 Draw the structural formula of compound F.

    1.9 Draw the structural formula of compound G.

    Official English text of the problem.

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  2. Problem 2: Bridge between Denmark and Sweden

    Figure 1

    On July 1, 2000, the combined tunnel and bridge connecting Denmark and Sweden was officially opened. It consists of a tunnel from Copenhagen to an artificial island, and a bridge from the island to Malmö in Sweden. The major construction materials employed are concrete and steel. This problem deals with chemical reactions relating to production and degradation of such materials.

    Concrete is produced from a mixture of cement, water, sand and small stones. Cement consists primarily of calcium silicates and calcium aluminates formed by heating and grinding of clay and limestone. In the later steps of cement production a small amount of gypsum, \(\ce{CaSO4 * 2H2O}\), is added to improve subsequent hardening of the concrete. The use of elevated temperatures during the final production may lead to formation of unwanted hemihydrate, \(\ce{CaSO4 * 1/2H2O}\). Consider the following reaction:

    Figure 2

    The following thermodynamic data apply at 25 °C, standard pressure: 1.00 bar:

    Compound \(\Delta_{\mathrm f}H^\circ\) (\(\mathrm{kJ\,mol^{-1}}\)) \(S^\circ\) (\(\mathrm{J\,K^{-1}\,mol^{-1}}\))
    \(\ce{CaSO4 * 2H2O(s)}\) −2021.0 194.0
    \(\ce{CaSO4 * 1/2H2O(s)}\) −1575.0 130.5
    \(\ce{H2O(g)}\) −241.8 188.6

    Gas constant: \(R=8.314\ \mathrm{J\,mol^{-1}\,K^{-1}}=0.08314\ \mathrm{L\,bar\,mol^{-1}\,K^{-1}}\)

    \(0\ ^\circ\mathrm C=273.15\ \mathrm K.\)

    2.1 Calculate \(\Delta H^\circ\) (in kJ) for transformation of 1.00 kg of \(\ce{CaSO4 * 2H2O(s)}\) to hemihydrate \(\ce{CaSO4 * 1/2H2O(s)}\). Is this reaction endothermic or is it exothermic?

    2.2 Calculate the equilibrium pressure (in bar) of water vapour in a closed vessel containing \(\ce{CaSO4 * 2H2O(s)}\), \(\ce{CaSO4 * 1/2H2O(s)}\) and \(\ce{H2O(g)}\) at 25 °C.

    2.3 Calculate the temperature at which the equilibrium water vapour pressure is 1.00 bar in the system described in problem 2-2. Assume that \(\Delta H^\circ\) and \(\Delta S^\circ\) are temperature independent.

    Corrosion of metals is associated with electrochemical reactions. This also applies for the formation of rust on iron surfaces, where the initial electrode reactions usually are:

    Figure 3

    An electrochemical cell in which these electrode reactions take place is constructed. The temperature is 25 °C. The cell is represented by the following cell diagram:

    Figure 4

    Standard electrode potentials (at 25 °C):

    Figure 5

    Nernst factor: \(RT\ln 10/F=0.05916\) volt (at 25 °C)

    Faraday constant: \(F=96485\ \mathrm{C\,mol^{-1}}\)

    2.4 Calculate the standard electromotive force (the standard cell voltage), \(E^\circ\), at 25 °C.

    2.5 Write down the overall reaction which takes place during discharge of the cell under standard conditions.

    2.6 Calculate the equilibrium constant at 25 °C for the overall cell reaction.

    2.7 The overall reaction referred to above is allowed to proceed for 24 hours under standard conditions and at a constant current of 0.12 A. Calculate the mass of \(\ce{Fe}\) converted to \(\ce{Fe^2+}\) after 24 hours. Oxygen and water may be assumed to be present in excess.

    2.8 Calculate \(E\) for the cell at 25 °C for the following conditions :

    \[ [\ce{Fe^2+}]=0.015\ \mathrm M,\quad \mathrm{pH}_{\text{right-hand half-cell}}=9.00,\quad p(\ce{O2})=0.700\ \mathrm{bar}. \]

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  3. Problem 3: Bioinorganic Chemistry

    The square planar complex cis-diammine dichloroplatinum(II) is an important drug for the treatment of certain cancers.

    3.1 Draw the structures of cis- and trans-diammine dichloroplatinum(II) and label each structure as cis or trans.

    A number of ionic compounds also have the empirical formula \(\ce{Pt(NH3)2Cl2}\).

    3.2 Write molecular formulas for all possible ionic compounds which comply with the following conditions: each compound has

    1) empirical formula \(\ce{Pt(NH3)2Cl2}\), 2) an anion and a cation and is composed of discrete, monomeric square planar platinum(II) complex, 3) only one type of cation and one type of anion. The answer must clearly reveal the composition of each discrete platinum(II) complex entity in each compound

    3.3 How many \(5d\) electrons are there in the platinum(II) ion?

    The valence d-orbital energy splitting diagram for a square planar complex can be regarded as being derived from that for an octahedral complex in which the metal-ligand interactions due to the two ligands coordinated along the \(z\) axis vanish, while the bonds to the four remaining ligands (coordinated along the \(x\) and \(y\) axes) become stronger.

    3.4 Which of the five \(5d\) orbitals attain the highest energy (i. e. is the least likely to be occupied by electrons) in the general case of a square-planar \(\ce{Pt(II)}\) complex?

    Serum transferrin (abbreviated: Tf) is a monomeric protein whose main function in the human body is the transport of iron(III). Each transferrin molecule can bind up to two iron(III) ions with stepwise binding constants \(K_1\) and \(K_2\) at biological conditions except that the temperature is \(25\,^\circ\mathrm{C}\) corresponding to the reactions:

    Figure 1

    In the diferric protein, \(\ce{(Fe^{III})2Tf}\), the two iron(III) ions are bound at two similar, but non-identical sites, and the two possible monoferric protein products, \(\ce{(Fe^{III})Tf}\), can be denoted \(\{\ce{Fe^{III} . Tf}\}\) and \(\{\ce{Tf . Fe^{III}}\}\). Their relative abundance at equilibrium is given by the constant

    \[ K=[\{\ce{Tf . Fe^{III}}\}]\,[\{\ce{Fe^{III} . Tf}\}]^{-1}=5.9. \]

    3.5 Calculate the values of the two constants \(K_1'=[\{\ce{Fe^{III} . Tf}\}]\,[\ce{Fe^{III}}]^{-1}[\ce{Tf}]^{-1}\) and \(K_1''=[\{\ce{Tf . Fe^{III}}\}]\,[\ce{Fe^{III}}]^{-1}[\ce{Tf}]^{-1}\), respectively, corresponding to the formation of each monoferric form of transferrin.

    3.6 Calculate the values of the two constants \(K_2'=[\ce{(Fe^{III})2Tf}]\,[\ce{Fe^{III}}]^{-1}[\{\ce{Fe^{III} . Tf}\}]^{-1}\) and \(K_2''=[\ce{(Fe^{III})2Tf}]\,[\ce{Fe^{III}}]^{-1}[\{\ce{Tf . Fe^{III}}\}]^{-1}\) respectively, corresponding to the formation of diferric transferrin from each of the monoferric forms.

    The bound iron(III) ion at each binding site is surrounded by six donor atoms from various ligands. Thus, two oxygen atoms of a carbonate anion coordinate to the metal, and the following amino acid side chains from the protein primary structure also coordinate to the iron(III) ion with one potential donor atom each: one aspartate, one histidine and two tyrosine residues.

    3.7 What is the total number of oxygen donor atoms that surround a 6-coordinate iron(III) ion in transferrin?

    Official English text of the problem.

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  4. Problem 4: A Naturally Occurring Compound

    A naturally occurring compound A containing only \(\ce{C}\), \(\ce{H}\) and \(\ce{O}\) has the following elemental composition, percentage mass,

    \(\ce{C}\): 63.2 %, \(\ce{H}\): 5.3%, \(\ce{O}\): 31.5%.

    4.1 Derive the empirical formula of compound A.

    Figure 1

    Figure 1

    The mass spectrum of compound A is shown in Figure 1.

    4.2 What is the molecular formula for compound A?

    A solution of A in ether is shaken with an aqueous solution of \(\ce{NaOH}\). After this, no A remains in the ether phase. Another solution of A in ether is shaken with an aqueous solution of \(\ce{NaHCO3}\). A remains in the ether phase.

    4.3 Which of the following classes of compounds does A belong to according to these experiments? Mark with an X.

    alcohol □ phenol □ aldehyde □ ketone □
    acid □ ester □ ether □

    Compound A gave rise to formation of a silver mirror with Tollens’ reagent (\(\ce{Ag(NH3)2+}\)).

    4-1 Which of the following functional groups does this indicate the presence of in A? Mark with an X.

    hydroxy group of an alcohol □ hydroxy group of a phenol □
    carbonyl group of an aldehyde □ carbonyl group of a ketone □
    carboxylic group □ ester group □
    alkoxy group of an ether □
    Figure 2

    Figure 2a

    The \({}^{1}\mathrm{H}\) NMR spectrum of compound A recorded at 300 MHz is shown in Figure 2a (solvent \(\ce{CDCl3}\) (7.27 ppm), reference tetramethylsilane). The signals at 3.9, 6.3 and 9.8 ppm are singlets. Figure 2b is an expansion of the region 6.9 – 7.6 ppm.

    Figure 3

    Figure 2b

    Selected chemical shift and coupling constant values are given in Table 1.

    The signal at 6.3 ppm disappears when a drop of \(\ce{D2O}\) is added.

    4.5 Which of the following does this indicate? Mark with an X.

    • Exchange of carbon-bonded hydrogen □
    • Exchange of oxygen-bonded hydrogen □
    • Dilution effect □
    • Hydrolysis □

    The same signal moves to a lower ppm value upon dilution with \(\ce{CDCl3}\).

    4.6 Which of the following does this indicate?

    Indicate the true statements (more than one).

    • Increased hydrogen bonding □
    • Decrease in hydrogen bonding □
    • Intermolecular hydrogen bonding □
    • Intramolecular hydrogen bonding □
    • No hydrogen bonding □

    4.7 Draw the four possible structural formulas for compound A based on the information given above

    4.8 Give structural formulas for the fragments lost corresponding to the peaks at 137 and 123 mass units in the mass spectrum.

    4.9 Two of the isomers have a lower \(pK_a\) value than the others. Write the formulas for those.

    Table 1. \({}^{1}\mathrm{H}\) Chemical Shift \(\delta\)

    Hydrogens attached to carbon

    Methyl \(\ce{CH3-C-}\)
    \(\ce{CH3-C=O-}\)
    \(\ce{CH3-O-R}\)
    \(\ce{CH3-OCOR}\)    		 0.9 – 1.6 ppm
    2.0 – 2.4 ppm
    3.3 – 3.8 ppm
    3.7 – 4.0 ppm
    Methylene \(\ce{CH2-C-}\)
    \(\ce{CH2-C=O-}\)
    \(\ce{CH2-OR}\)
    \(\ce{CH2-OCOR}\)    		 1.4 – 2.7 ppm
    2.2 – 2.9 ppm
    3.4 – 4.1 ppm
    4.3 – 4.4 ppm
    Methine \(\ce{CH-}\) 1.5 – 5.0 ppm
    depending on the substituents. Generally higher than for methyl and methylene
    Alkene 4.0 – 7.3 ppm
    depending on the substituent
    Aldehyde \(\ce{R-CHO}\) 9.0 – 10.0 ppm

    Table 1 (continued) \({}^{1}\mathrm{H}\) Chemical Shift \(\delta\)

    Hydrogens attached to oxygen

    Alcohols \(\ce{ROH}\) 0.5 – 5.0 ppm
    Phenols \(\ce{ArOH}\) 4.0 – 7.0 ppm
    Carboxylic acids \(\ce{RCOOH}\) 10.0 – 13.0 ppm

    Selected spin-spin coupling constants

    Alkanes
    (free rotation)    		 \(\ce{H-C-C-H}\) vicinal 6 – 8 Hz
    Alkenes trans
    cis
    geminal    		 11 – 18 Hz
    6 – 12 Hz
    0 – 3 Hz
    Aromates ortho
    meta
    para    		 6 – 10 Hz
    1 – 4 Hz
    0 – 2 Hz

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  5. Problem 5: Protein and DNA

    Figure 1

    DNA is composed of 2’-deoxy-nucleotides carrying the bases adenine (A), guanine (G), cytosine (C) and thymine (T). The molar mass of the 2’-deoxy-nucleotide-5’-triphosphates is given in table 2:

    Table 2

    dNTP Molar mass /g mol\(^{-1}\)
    dATP 487
    dGTP 503
    dCTP 464
    dTTP 478

    5.1 Calculate the molar mass of a double stranded DNA fragment consisting of 1000 base pairs with a uniform distribution of the four bases.

    This DNA fragment can be isolated and cloned by using the PCR method (polymerase chain reaction), in which a heat stable DNA polymerase enzyme multiplies the number of molecules of a specific piece of DNA in a cyclic process. Under optimal conditions the number of double-stranded DNA copies doubles in each cycle. Using the PCR method you perform 30 cycles starting from a single double stranded DNA molecule.

    5.2 Calculate the approximate mass of the DNA you obtain from this experiment.

    The bacteria-virus T4 enzyme - polynucleotide kinase (PNK) catalyzes the transfer of the terminal phosphate of ATP (\(\gamma\)-orthophosphate) to the 5'-hydroxyl termini of ribo- and deoxyribonucleotides:

    Figure 2

    PNK is commonly used to label DNA at the 5’-end with the radioactive phosphorus isotope \(\ce{^{32}P}\) using ATP in which the \(\gamma\)-P (the outermost of the phosphorus atoms) is replaced with \(\ce{^{32}P}\). The amount of \(\ce{^{32}P}\) and thus the amount of labeled DNA can be measured.

    A 10 µL solution containing double stranded DNA is labelled 100 % with \([\gamma\text{-}\ce{^{32}P}]\mathrm{ATP}\) by PNK. 37 days ago, the specific activity of \([\gamma\text{-}\ce{^{32}P}]\mathrm{ATP}\) was 10 Ci/mmol or \(370\cdot10^9\) Bq/mmol. \(\ce{^{32}P}\) has a half-life of 14.2 days, and during the decay a \(\beta\)-particle is emitted. Now the labelled DNA emits 40000 \(\beta\)-particles/s.

    5-3 Calculate the concentration of the DNA solution.

    In an experiment in which PNK is incubated with \([\gamma\text{-}\ce{^{32}P}]\mathrm{ATP}\) and single stranded DNA, the reaction can be monitored by isolating labeled DNA and measuring the \(\beta\)-particle emission. Using this kind of measurements in a 1 cm\(^{3}\) experimental mixture, a labeling of 9 nmol DNA/min was calculated. PNK has a catalytic rate constant (turnover number) of 0.05 s\(^{-1}\) and molar mass of 34620 g mol\(^{-1}\).

    5.4 Calculate the concentration (in mg/cm\(^{3}\)) of PNK in the experimental mixture.

    Aromatic amino acids, tryptophan, tyrosine and phenylalanine absorb UV light of a wavelength between 240 nm and 300 nm. In a protein containing several aromatic amino acids, the sum of the molar absorptivity per amino acid \(\Sigma\varepsilon_{\text{amino acid}}\), is approximately equal to the molar absorptivity, \(\varepsilon_{\text{protein}}\), for the protein. The molar absorptivity, \(\varepsilon_{\text{amino acid}}\), at 280 nm for tyrosine, tryptophan and phenylalanine is 1400 M\(^{-1}\) cm\(^{-1}\), 5600 M\(^{-1}\) cm\(^{-1}\) and 5 M\(^{-1}\) cm\(^{-1}\), respectively. The absorbance of a 10 µM solution of PNK is 0.644 at 280 nm and with 1.00 cm light path. The amino acid sequence of PNK contains 14 tyrosines and 9 phenylalanines.

    \((\mathrm{M}=\mathrm{mol\,dm^{-3}})\)

    5.5 Calculate the number of tryptophan residues in a PNK molecule.

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  6. Problem 6: Hard Water

    In Denmark the subsoil consists mainly of limestone. In contact with ground water containing carbon dioxide some of the calcium carbonate dissolves as calcium hydrogen carbonate. As a result, such ground water is hard, and when used as tap water the high content of calcium hydrogen carbonate causes problems due to precipitation of calcium carbonate in, for example, kitchen and bathroom environments.

    Carbon dioxide, \(\ce{CO2}\), is a diprotic acid in aqueous solution. The \(pK_a\)-values at \(0~^\circ\mathrm{C}\) are:

    Figure 1

    The liquid volume change associated with dissolution of \(\ce{CO2}\) may be neglected for all of the following problems. The temperature is to be taken as being \(0~^\circ\mathrm{C}\).

    6.1 The total concentration of carbon dioxide in water which is saturated with carbon dioxide at a carbon dioxide partial pressure of \(1.00~\mathrm{bar}\) is \(0.0752~\mathrm{mol\,dm^{-3}}\). Calculate the volume of carbon dioxide gas which can be dissolved in one litre of water under these conditions.

    The gas constant \[ R=8.314~\mathrm{J\,mol^{-1}\,K^{-1}} =0.08314~\mathrm{L\,bar\,mol^{-1}\,K^{-1}} \]

    6.2 Calculate the equilibrium concentration of hydrogen ions and the equilibrium concentration of \(\ce{CO2}\) in water saturated with carbon dioxide at a carbon dioxide partial pressure of \(1.00~\mathrm{bar}\).

    6.3 Calculate the equilibrium concentration of hydrogen ions in a \(0.0100~\mathrm{M}\) aqueous solution of sodium hydrogen carbonate saturated with carbon dioxide at a carbon dioxide partial pressure of \(1.00~\mathrm{bar}\).

    6.4 Calculate the equilibrium concentration of hydrogen ions in a \(0.0100~\mathrm{M}\) aqueous solution of sodium carbonate saturated with carbon dioxide at a carbon dioxide partial pressure of \(1.00~\mathrm{bar}\). Ignore water dissociation effects.

    6.5 The solubility of calcium carbonate in water at \(0~^\circ\mathrm{C}\) is \(0.0012~\mathrm{g}\) per \(100~\mathrm{cm^3}\) of water. Calculate the concentration of calcium ions in a saturated solution of calcium carbonate in water.

    The hard groundwater in Denmark is formed via contact of water with limestone in the subsoil which reacts with carbon dioxide dissolved in the groundwater according to the equilibrium equation:

    Figure 2

    The equilibrium constant, \(K\), for this reaction is \(10^{-4.25}\) at \(0~^\circ\mathrm{C}\).

    6.6 Calculate the concentration of calcium ions in water in equilibrium with calcium carbonate in an atmosphere with a partial pressure of carbon dioxide of \(1.00~\mathrm{bar}\).

    6.7 A \(0.0150~\mathrm{M}\) solution of calcium hydroxide is saturated with carbon dioxide gas at a partial pressure of \(1.00~\mathrm{bar}\). Calculate the concentration of calcium ions in the solution by considering the equilibrium equation given above in connection with problem 6.6.

    6.8 The calcium hydroxide solution referred to in problem 6.7 is diluted to twice the volume with water before saturation with carbon dioxide gas at a partial pressure of \(1.00~\mathrm{bar}\). Calculate the concentration of calcium ions in the resulting solution saturated with \(\ce{CO2}\).

    6.9 Calculate the solubility product constant for calcium carbonate from the data given above.

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