International Chemistry Olympiad · 2013

Problems

Problem 1The “clathrate gun” scenario: ocean-floor methane hydrates could decompose explosively as oceans warm. Upon decomposition of 1.00 g of a methane hydrate of fixed composition at 25 °C and 101.3 kPa, 205 cm $^3$ of methane is released. (a) Determine $n$ in $\ce{CH4 \cdot n H2O}$ . (b) Real hydrate is close to $\ce{CH4 \cdot 6 H2O}$ , stable at 1 atm down to its decomposition at $-81$ °C; write its decomposition to methane and ice, $\Delta H = +17.47$ kJ mol $^{-1}$ . Assuming $\Delta H$ is T- and p-independent, that the volume change equals the released methane volume, and that methane is ideal, find the external pressure at which decomposition occurs at $-5$ °C. (c) What is the minimum possible depth of pure liquid water at which methane hydrates are stable? First choose the minimum temperature at which the hydrate can coexist with liquid water: 272.9 K, 273.15 K, or 273.4 K. (d) In Lake Baikal, hydrate samples raised from 1400 m began to decompose at 372 m depth ( $\Delta_{fus}H$ (ice) = 6.01 kJ mol $^{-1}$ ); find the water temperature at 372 m. (e) Total methane in hydrates is $\geq 5 \times 10^{11}$ t; by how many degrees would Earth's atmosphere heat if it all burned ( $\Delta_c H(\ce{CH4}) = -889$ kJ mol $^{-1}$ , atmospheric heat capacity $4 \times 10^{21}$ J K $^{-1}$ )?Solutions: 1
Problem 2The Hill reaction dissects photosynthesis. (a) Write the overall equation of plant photosynthesis, reducing $\ce{CO2}$ to $\{\ce{CH2O}\}$ . (b) Hill found that isolated chloroplasts do not evolve $\ce{O2}$ in light even with $\ce{CO2}$ , but do so upon adding potassium ferrioxalate $\ce{K3[Fe(C2O4)3]}$ (with excess oxalate) without $\ce{CO2}$ . Give the oxidant and reducing agent in natural photosynthesis and in the Hill reaction. (c) Hill measured evolved $\ce{O2}$ with haemoglobin (Hb binds $\ce{O2}$ 1:1, initial $[\text{Hb}] = 0.6 \times 10^{-4}$ mol dm $^{-3}$ ); at $[\ce{Fe^{III}}] = 2.0 \times 10^{-4}$ mol dm $^{-3}$ the HbO $_2$ fraction saturates at about 75 %. Estimate the Fe/ $\ce{O2}$ ratio, write the Hill reaction equation, and calculate its $\Delta G$ at $T = 298$ K, $p(\ce{O2}) = 1$ mmHg, pH = 8, standard concentrations of other species ( $E^{\circ}$ : $\ce{O2 + 4H+ + 4e- -> 2H2O}$ +1.23 V; $\ce{[Fe(C2O4)3]^{3-} + e- -> [Fe(C2O4)3]^{4-}}$ +0.05 V). Is it spontaneous? (d) Isolated chloroplasts were irradiated 2 h with 672 nm light of 0.503 mJ s $^{-1}$ , producing 47.6 mm $^3$ $\ce{O2}$ (10 °C, 740 mmHg). Calculate the quantum requirement (photons per electron transferred). (e) Conclusions: are water oxidation and $\ce{CO2}$ reduction spatially separated? Is $\ce{O2}$ produced from $\ce{CO2}$ ? Does water oxidation require light? Do most chlorophylls participate directly? Does each photon transfer one electron?Solutions: 1