International Chemistry Olympiad · 2010

Problems

Problem 1In 1894 Lord Rayleigh found that nitrogen prepared chemically (mean mass in a fixed vessel: 2.2990 g) was lighter than \“atmospheric nitrogen\” freed of $\ce{O2}$ (2.3102 g), at 15.0 \°C and $1.013 \times 10^{5}$ Pa; the difference was later attributed to argon. (a) Calculate the vessel volume and the mole fraction of Ar in atmospheric nitrogen. (b) Ramsay isolated helium from cleveite; it emits the D $_3$ line at 587.7 nm. Calculate the photon energy and identify the corresponding transition in the He orbital diagram (answer: the highest-energy allowed transition, 3d \→ 2p) and the nuclear process that produces He in uranium minerals ( $\alpha$ -decay) and Ar in rocks (electron capture/positron decay of $\ce{^{40}K}$ ). (c) An unknown gas at 15.0 \°C and atmospheric pressure has density $0.850 \pm 0.005\ \text{kg m}^{-3}$ ; sound in it has $\lambda = 0.116$ m at $f = 3520$ Hz, with $v_s = f\lambda = \sqrt{\gamma RT/M}$ . Find $M$ and $\gamma$ and identify the gas among HCl, HF, Ne, Ar.Solutions: 1
Problem 2(a) In the NaCl crystal, $\ce{Na+}$ and $\ce{Cl-}$ each form a face-centred cubic lattice; the ionic radii are $r(\ce{Na+}) = 0.102$ nm and $r(\ce{Cl-}) = 0.181$ nm. Give the numbers of $\ce{Na+}$ and $\ce{Cl-}$ per unit cell, their coordination numbers, and calculate the crystal density. (b) From the Born\–Haber data \— $\Delta_fH(\ce{NaCl(s)}) = -411$ , $\Delta_{sub}H(\ce{Na}) = +109$ , $IE(\ce{Na}) = +496$ , $D(\ce{Cl2}) = +242$ , $EA(\ce{Cl}) = -349$ kJ mol $^{-1}$ \— write the equations for the formation step and the direct dissociation $\ce{NaCl(s) -> Na+(g) + Cl-(g)}$ , and calculate the lattice formation enthalpy. (c) The Solvay process achieves $\ce{2NaCl + CaCO3 -> Na2CO3 + CaCl2}$ through the cycle: $\ce{CaCO3 ->[\Delta] A + B}$ ; $\ce{NaCl + NH3 + B + H2O -> C + D}$ ; $\ce{2C ->[\Delta] Na2CO3 + H2O + B}$ ; $\ce{A + H2O -> E}$ ; $\ce{E + 2D -> CaCl2 + 2H2O + 2NH3}$ . Identify compounds A\–E.Solutions: 1