International Chemistry Olympiad · 1997

Problems

Problem 2Professor Molina (MIT, Nobel Prize 1995) studied the acid-rain reaction producing $\ce{H2SO4}$ in the atmosphere and proposed two stoichiometries: Proposal A: $\ce{H2O(g) + SO3(g) -> H2SO4(g)}$ ; Proposal B: $\ce{2H2O(g) + SO3(g) -> H2SO4(g) + H2O(g)}$ . (2.1) Using simple collision theory, what reaction orders are expected for A and B? Proposal B is thought to proceed via $\ce{SO3 + 2H2O <=>[k_1][k_{-1}] SO3.2H2O}$ (fast) and $\ce{SO3.2H2O ->[k_2] H2SO4 + H2O}$ (slow, $k_2 \ll k_1, k_{-1}$ ). (2.2) Apply the steady-state principle to derive the rate law and order of this mechanism. (2.3) Quantum calculations give overall activation energies $E_A = +80$ kJ mol⁻¹ (A) and $E_B = -20$ kJ mol⁻¹ (B). Write the Arrhenius temperature dependence for each and predict how each rate constant varies with T. (2.4) $\ce{H2SO4}$ formation is faster in the upper atmosphere (175 K) than at the surface (300 K): which pathway dominates in the upper atmosphere?Solutions: 1