International Chemistry Olympiad

IChO 1992

Pittsburgh, USA · 9 theory problems with complete solutions

  1. Problem 1: Diatoms, whales and the carbon cycle

    Diatoms, microscopic organisms, are an abundant food source in the oceans producing carbohydrates from carbon dioxide and water by photosynthesis:

    Figure 1

    1.1 During the first five years of life blue whales gain 75 kg of mass per day by feeding on krill. The whale must consume ten times this mass of krill each day. The krill must consume 10.0 kg of diatoms to produce 1.0 kg of krill. Assuming that the mass gain in the first years of a whale's life is due to the consumption of carbohydrates (\(\ce{C6H12O6}\)), calculate the volume of \(\ce{CO2}\) at STP (0 °C, 101 kPa) that must be used by the diatoms to produce the carbohydrates consumed by a blue whale in its first five years of life.

    1.2 There is 0.23 cm³ of dissolved \(\ce{CO2}\) per one litre sea water (at 24 °C and 101 kPa).

    i) If diatoms can completely remove carbon dioxide from the water they process, what volume of water would they process to produce the carbohydrates required by a blue whale during the first five years of life?

    ii) What fraction of the total volume of the oceans will be needed to supply the carbon dioxide for the first five years of growth of 1000 blue whales? The volume of the oceans is \(1.37\times10^{18}\ \mathrm{m^3}\).

    1.3 Three percent of the mass of a \(9.1\times10^4\) kg adult whale is nitrogen. When a \(9.1\times10^4\) kg blue whale dies, what is the maximum mass of \(\ce{NH4+}\) that can become available for other marine organisms?

    1.4 Eighteen percent of a \(9.1\times10^4\) kg whale's mass is carbon. Carbon can be returned to the atmosphere as \(\ce{CO2}\) and then removed from the atmosphere by weathering of rocks containing calcium silicate.

    Figure 2

    What are the maximum number of grams of \(\ce{CaSiO3}\) that can be weathered by the carbon dioxide produced from the decomposition of 1000 blue whales, the number estimated to die annually?

    Official English text of the problem.

  2. Problem 2: Acid mine drainage: oxidation of pyrite

    Many streams drain in areas where coal or metallic ores are mined. These streams have become acidic and contain high concentrations of dissolved iron and sulphate, due to sulphur-containing ores being exposed to the atmosphere or to oxygenated waters. The most common sulphur-containing mineral is pyrite, \(\ce{FeS2}\), in which the oxidation state of iron is +2. As the iron-rich streams mix with other waters, the dissolved iron precipitates as goethite, \(\ce{FeO(OH)}\), which coats the stream bottom while the water remains acidic.

    2.1 Draw the electron dot structure that illustrates the bonding in the ion \(\ce{S2^2-}\), showing all valence electrons.

    2.2 Write a balanced chemical equation to show how hydrogen ions (\(\ce{H+}\)) are generated during the oxidation of pyrite to form a solution of iron(II) and sulphate ions.

    2.3 Write a balanced equation to show how many additional moles of hydrogen are generated when iron(II) ions are oxidized to form the mineral goethite, \(\ce{FeO(OH)}\).

    2.4 Calculate how many moles of pyrite would be required to bring \(1.0\ \mathrm{dm^3}\) of pure water to a pH of 3.0 if the pyrite was completely converted into \(\ce{FeO(OH)}\) and \(\ce{H+}\) ions. Neglect the formation of \(\ce{HSO4-}\).

    2.5 The concentration of iron as \(\ce{Fe(II)}\) in a stream is 0.00835 M. At a very narrow point in the stream it empties into a large pond, with a flow rate of 20.0 l each minute. The water in this stream is sufficiently aerated that 75 % of the \(\ce{Fe(II)}\) is oxidized to \(\ce{Fe(III)}\). The pH of the pond is high enough (> 7) that the iron(III) precipitates immediately as \(\ce{Fe(OH)3}\) which on aging becomes \(\ce{Fe2O3}\). What mass of \(\ce{Fe2O3}\) will be deposited on the bottom of the pond in two years?

    Official English text of the problem.

  3. Problem 3: Coniferyl alcohol: structure and stereoisomers of its dibromide

    Coniferyl alcohol has the molecular formula \(\ce{C10H12O3}\). It is isolated from pine trees. Coniferyl alcohol is not soluble in water or aqueous \(\ce{NaHCO3}\). A solution of \(\ce{Br2}\) in \(\ce{CCl4}\) is decolorized when added to coniferyl alcohol forming A (\(\ce{C10H12O3Br2}\)). Upon reductive ozonolysis coniferyl alcohol produces vanillin (4-hydroxy-3-methoxybenzaldehyd) and B (\(\ce{C2H4O2}\)). Coniferyl alcohol reacts with benzoyl chloride (\(\ce{C6H5COCl}\)) in the presence of a base to form C (\(\ce{C24H20O5}\)). This product rapidly decolorizes \(\ce{KMnO4}\) (aq) and is insoluble in dilute \(\ce{NaOH}\).

    Coniferyl alcohol reacts with cold \(\ce{HBr}\) to form D (\(\ce{C10H11O2Br}\)). Hot \(\ce{HI}\) converts \(\ce{ArOR}\) to \(\ce{ArOH}\) and \(\ce{RI}\). Coniferyl alcohol reacts with excess hot \(\ce{HI}\) to give E (\(\ce{C9H9O2I}\)) and \(\ce{CH3I}\). \(\ce{CH3I}\) in aqueous base reacts with coniferyl alcohol to form F (\(\ce{C11H14O3}\)), which is not soluble in a strong base, but decolorizes \(\ce{Br2}/\ce{CCl4}\)-solution.

    3.1 Draw the structures of coniferyl alcohol and compounds A - F.

    3.2 There are a number of stereoisomers of compound A. Draw structure of compound A. Label each chiral centre in compound A with an asterisk (*). For all stereoisomers draw Fischer projections and label each chiral center with the proper \(R\) or \(S\) designation giving the absolute configuration about the chiral centre.

    Official English text of the problem.

  4. Problem 4: Geraniol from rose oil

    Rose oil is an essential oil obtained from the steam distillation of plant material from roses. It contains a number of terpenes, one of which is geraniol, \(\ce{C10H18O}\) (A). Upon oxidation, geraniol can either give a ten-carbon aldehyde or a ten-carbon carboxylic acid. Reaction with two moles of bromine gives a tetrabromide (\(\ce{C10H18OBr4}\)) (B). Geraniol reacts with \(\ce{HBr}\) to give two bromides of formula \(\ce{C10H17Br}\).

    When geraniol is vigorously oxidized, three products are obtained:

    Figure 1

    4.1 Give the structure of geraniol A.

    4.2 Give the structure of compound B.

    4.3 Give the structures of the two bromides of formula \(\ce{C10H17Br}\).

    4.4 Indicate which of the two bromides is formed in greater proportions.

    Official English text of the problem.

  5. Problem 5: Nitrogen dioxide - dinitrogen tetroxide equilibrium and kinetics

    Nitrogen dioxide \(\ce{NO2}\) is one of a number of oxides of nitrogen found in our atmosphere. It can dimerize to give \(\ce{N2O4(g)}\):

    Figure 1

    5.1 With a diagram, show the bonds present in \(\ce{NO2(g)}\) using the concept of resonance if necessary. Nitrogen dioxide, \(\ce{NO2}\), is paramagnetic.

    5.2 Show, with bonding diagrams, how two molecules of \(\ce{NO2(g)}\) combine to give a molecule of \(\ce{N2O4(g)}\) which is not paramagnetic.

    5.3 At 298 K, the \(\Delta G^\circ\) of formation for \(\ce{N2O4(g)}\) is 98.28 kJ, whereas for \(\ce{NO2(g)}\) is 51.84 kJ. Starting with one mole of \(\ce{N2O4(g)}\) at 1.0 atm and 298 K, calculate what fraction will be decomposed if the total pressure is kept constant at 1.0 atm and the temperature is maintained at 298 K.

    5.4 If \(\Delta H^\circ\) for the reaction

    Figure 2

    is 58.03 kJ, at what temperature would the fraction of \(\ce{N2O4}\) decomposed be double that calculated in part 5.3?

    5.5 The dissociation of \(\ce{N2O4(g)}\) to give \(\ce{NO2(g)}\) is a first order process with a specific rate constant of \(5.3\times10^4\ \mathrm{s^{-1}}\) at 298 K. Starting with an initial concentration of 0.10 M, how many seconds would it take for 20 % of the original \(\ce{N2O4}\) to decompose?

    5.6 The association of \(\ce{NO2(g)}\) to give \(\ce{N2O4(g)}\) is a second-order process with a specific rate constant of \(9.8\times10^6\ \mathrm{dm^3\,mol^{-1}\,s^{-1}}\) at 298 K. Calculate the concentration equilibrium constant, \(K_c\), at 298 K for the reaction

    Figure 3

    Official English text of the problem.

  6. Problem 6: Carbon dioxide in the atmosphere and in water

    The concentration of carbon dioxide in the atmosphere has increased substantially during this century and is predicted to continue to increase. The \([\ce{CO2}]\) is expected to be about 440 ppm (\(440\times10^{-6}\ \mathrm{atm}\)) in the year 2020.

    6.1 Calculate the concentration (in \(\mathrm{mol\,dm^{-3}}\)) of \(\ce{CO2}\) dissolved in distilled water equilibrated with the atmosphere in the year 2020.

    6.2 Calculate the \(pH\)-value of the solution in 6.1.

    6.3 Calculate the enthalpy of reaction between \(\ce{CO2(aq)}\) and \(\ce{H2O}\).

    6.4 If the temperature of an equilibrated solution of \(\ce{CO2}\) is increased and the concentration of dissolved carbon dioxide is maintained constant, the \(pH\) of the solution may change. Predict whether the \(pH\) will increase or decrease.

    Data:

    Henry's Law constant for \(\ce{CO2}\) at 298 K: \(0.0343\ \mathrm{dm^3\,mol^{-1}\,atm^{-1}}\)

    Thermodynamic values, in kJ/mol at 298 K are:

    \(\Delta_{\mathrm f}G^0\) \(\Delta_{\mathrm f}H^0\)
    \(\ce{CO2(aq)}\) −386.2 −412.9
    \(\ce{H2O(l)}\) −237.2 −285.8
    \(\ce{HCO3^-(aq)}\) −587.1 −691.2
    \(\ce{H+(aq)}\) 0.00 0.00

    Official English text of the problem.

  7. Problem 7: Determination of chloride in Chesapeake Bay water

    When the fresh-water rivers that run into the Chesapeake Bay flood after heavy rains in the spring, the increase in fresh water in the Bay causes a decrease in the salinity in the areas where oysters grow. The minimum concentration of chloride ions needed in oyster beds for normal growth is 8 ppm (\(8\ \mathrm{mg\,dm^{-3}}\)).

    After one week of heavy rain, the following analysis is done on water from the bay. To a \(50.00\ \mathrm{cm^3}\) sample of bay water a few drops of a \(\ce{K2CrO4}\) solution are added. The sample is then titrated with \(16.16\ \mathrm{cm^3}\) of a 0.00164 M \(\ce{AgNO3}\) solution. After \(\ce{AgNO3}\) solution has been added to the sample a bright red-orange precipitate forms.

    7.1 What is the molar concentration of chloride in the sample?

    7.2 Does the water contain sufficient chloride for the normal growth of oysters? Show your calculation.

    7.3 Write a balanced equation for the reaction of the analyte with the titrant.

    7.4 Write a balanced net-ionic equation that describes the reaction responsible for the colour change at the endpoint of the titration. Which compound produces the brick-red colour?

    7.5 The concentration of chromate at the endpoint is 0.020 M. Calculate the concentration of chloride ions in the solution when the red precipitate forms.

    7.6 For this titration to work most effectively, the solution being titrated must be neutral or slightly basic. Write a balanced equation for the competing reaction that would occur in acidic medium that would influence the observed endpoint of this titration.

    Typically, a buffer is added to the solution being titrated to control the pH if the initial sample is acidic. Suppose the pH of the sample of bay water was 5.10, thus too acidic to perform the analysis accurately.

    7.7 Select a buffer from the list that would enable you to establish and maintain a pH of 7.20 in aqueous medium. Show the calculations which lead to your choice.

    Buffer systems \(K_\mathrm{a}\) of weak acid
    1. 0.10 M lactic acid / 0.10 M sodium lactate \(1.4\times10^{-4}\)
    2. 0.10 M acetic acid / 0.10 M sodium acetate \(1.8\times10^{-5}\)
    3. 0.10 M sodium dihydrogen phosphate /
    / 0.10 M sodium hydrogen phosphate
    \(6.2\times10^{-8}\)
    4. 0.10 M ammonium chloride / 0.10 M ammonia \(5.6\times10^{-10}\)

    7.8 Using the selected buffer system, calculate the mass (in g) of weak acid and of conjugated base you would need to dissolve in distilled water to prepare \(500\ \mathrm{cm^3}\) of a stock solution buffered at a pH of 7.2.

    7.9 The chloride concentration in another \(50.00\ \mathrm{cm^3}\) sample of bay water was determined by the Volhard method. In this method an excess of \(\ce{AgNO3}\) is added to the sample. The excess \(\ce{Ag+}\) is titrated with standardized \(\ce{KSCN}\), forming a precipitate of \(\ce{AgSCN}\). The endpoint is signalled by the formation of the reddish-brown \(\ce{FeSCN^2+}\) complex that forms when \(\ce{Ag+}\) is depleted. If the excess \(\ce{Ag+}\) from the addition of \(50.00\ \mathrm{cm^3}\) of 0.00129 M \(\ce{AgNO3}\) to the water sample required \(27.46\ \mathrm{cm^3}\) of \(1.41\,10^{-3}\) M \(\ce{KSCN}\) for titration, calculate the concentration of chloride in the bay water sample.

    In natural waters with much higher concentration of \(\ce{Cl-}\), the \(\ce{Cl-}\) can be determined gravimetrically by precipitating the \(\ce{Cl-}\) as \(\ce{AgCl}\). A complicating feature of this method is the fact that \(\ce{AgCl}\) is susceptible to photodecomposition as shown by the reaction:

    Figure 1

    Furthermore, if this photodecomposition occurs in the presence of excess \(\ce{Ag+}\), the following additional reaction occurs:

    Figure 2

    If 0.010 g of a 3.000 g sample of \(\ce{AgCl}\) contaminated with excess \(\ce{Ag+}\) undergoes photodecomposition by the above equations

    7.10 Will the apparent weight of \(\ce{AgCl}\) be too high or too low? Explain your answer showing by how many grams the two values will differ.

    Data:

    \[ K_{\mathrm{sp}}(\ce{AgCl})=1.78\times10^{-10} \]

    \[ K_{\mathrm{sp}}(\ce{Ag2CrO4})=1.00\times10^{-12} \]

    Official English text of the problem.

  8. Problem 8: Pourbaix diagrams of water, nitrogen and manganese

    The Pourbaix diagrams for water, nitrogen and manganese are depicted in Fig. 1.

    8.1 Write the formula of the species of nitrogen that is predominant

    i) in \(\ce{O2}\)-rich lakes of \(\mathrm{pH}\approx 6\),

    ii) in highly \(\ce{O2}\)-depleted lakes that are strongly contaminated with acid rain (\(\mathrm{pH}\approx 3\)),

    8.2 Which species of manganese is predominant

    i) in \(\ce{O2}\)-rich lakes of \(\mathrm{pH}\approx 6\),

    ii) in highly \(\ce{O2}\)-depleted lakes that are strongly contaminated with bases (\(\mathrm{pH}\approx 12\))?

    8.3 People often find that clear, slightly acidic (\(\mathrm{pH}\approx 5\)) water drawn from wells deposits a black manganese-containing solid on standing in toilet bowls.

    i) Write the chemical formula of the black solid?

    ii) Write the formula for the species of manganese found in well water while it is still underground ?

    8.4 According to Pourbaix diagrams two species of nitrogen should oxidize \(\ce{Mn(s)}\) to \(\ce{Mn^2+(aq)}\).

    i) Write the formulas of these two nitrogen species.

    ii) Which of the two species of nitrogen does not oxidize \(\ce{Mn(s)}\) (in practice) at room temperature ?

    8.5 According to the Poubaix diagrams, some of the chemical forms of manganese should oxidize \(\ce{NH3(aq)}\) or \(\ce{NH4+(aq)}\) to \(\ce{N2(g)}\).

    Choose in the following list the forms of Mn that should do it:

    \[ \ce{Mn},\ \ce{Mn(OH)2},\ \ce{Mn^2+},\ \ce{Mn3O4},\ \ce{Mn2O3},\ \ce{MnO2},\ \ce{MnO4^2-},\ \ce{MnO4^-} \]

    8.6 Ammonium permanganate, \(\ce{NH4MnO4}\), is a well-known salt, but ammonium manganate, \(\ce{(NH4)2MnO4}\), is a rarely known salt.

    i) Is \(\ce{NH4MnO4}\) expected to be thermodynamically stable? (YES or NO)

    ii) Is \(\ce{(NH4)2MnO4}\) expected to be thermodynamically stable? (YES or NO)

    iii) Write and balance an equation for the decomposition of \(\ce{NH4MnO4}\) to give \(\ce{MnO2}\) a \(\ce{N2}\).

    iv) Write and balance an equation for the decomposition of \(\ce{(NH4)2MnO4}\) to give \(\ce{Mn}\) a \(\ce{N2}\).

    8.7 According to the Pourbaix diagrams, is it dangerous to grind together in a mortar and pestle

    i potassium nitrate and manganese metal,

    ii) potassium nitrate and manganese dioxide?

    8.8 The standard reduction potential, \(E^0\), for the reduction of \(\ce{MnO4^-}\) to \(\ce{MnO2}\) is \(1.692\ \mathrm{V}\). Applying the Nernst equation calculate the reduction potential, \(E\), for the reduction of \(0.00100\ \mathrm{M}\) \(\ce{MnO4^-}\) solution at a \(\mathrm{pH}=4.0\).

    Figure 1

    Figure 1

    Official English text of the problem.

  9. Problem 9: Reactions of insect pheromones

    Pheromones are chemicals or mixtures of certain chemicals secreted by insects and some animals for communication. They bring about certain responses in another individual of the same species. In the problem below you will find a number of pheromones undergoing reactions which were used in determining their structures. In each case give the structure or structures of the products produced. Show geometric (cis/trans) isomers where appropriate (in part (9.5). You may ignore other forms of stereoisomerism.

    9.1

    Figure 1

    isoamyl acetate,
    bee alarm pheromene

    9.2

    i)

    Figure 2

    2-heptanone
    ant alarm pheromone

    ii)

    Figure 3

    iii)

    Figure 4

    9.3

    i)

    Figure 5

    green peach -
    aphid pheromone

    ii)

    Figure 6

    9.4

    (i)

    Figure 7

    (ii)

    Figure 8

    (iii)

    Figure 9

    9.5

    i)

    Figure 10

    ii)

    Figure 11

    iii)

    Figure 12

    iv)

    Figure 13

    v)

    Figure 14

    vi)

    Figure 15

    Official English text of the problem.