International Chemistry Olympiad · 2023

Problems

Problem 1Molecular imaging is a powerful tool in medical diagnostics. The nuclear isomer $^{99m}\ce{Tc}$ (m = metastable) is an excellent γ-emitter ( $t_{1/2} = 6.015$ h) obtained by β− decay of a mother nuclide in a technetium generator as $[^{99m}\ce{TcO4}]^-$ . (a) Identify the mother nuclide A and the emitted particle B in $\ce{A -> ^{99m}Tc + B}$ . (b) An eluate from a $^{99m}\ce{Tc}$ generator has an activity of 12.5 GBq (1 GBq = $10^{9}$ decays per second). Calculate how many moles of $^{99m}\ce{Tc}$ are present. (c) For standard imaging about 200 MBq are administered to a patient. Assuming no activity is lost through excretion, calculate how many hours the patient has to wait until the injected activity decreases to under 1% of the starting activity.Solutions: 1
Problem 5To remove sulfur from fuels, hydrogen-assisted hydrodesulfurization is used at refineries, typically over $\ce{MoS2}$ supported on $\ce{SiO2}$ . Isotope exchange at the gas–solid interface exchanges only the surface atoms. An experiment studies the exchange between an $\ce{MoS2/SiO2}$ catalyst ( $m_{\text{cat}} = 1.2350$ g, Mo mass fraction $w_{\ce{Mo}} = 4.280\%$ , initially containing only $^{32}$ S) and gaseous $\ce{H2^{34}S}$ in a flow reactor ( $p = 1.00$ bar, flow $v = 20.0$ mL min $^{-1}$ , $T = 23.0$ °C, $\varphi(\ce{H2^{34}S}) = 1.00\%$ , isotopic purity $\alpha = 99.95$ mol%). After $t = 10.0$ min, the fraction of $^{34}$ S among sulfur atoms in the collected gas was $\gamma = 87.3$ mol%. (a) Calculate the amount of exchanged (surface) sulfur atoms $n(\mathrm{S})_{\text{surface}}$ in mol. (b) Assuming uniform spherical $\ce{MoS2}$ particles of density $\rho = 5.06$ g cm $^{-3}$ , surface areas per atom $A_S = 3.00\times 10^{-19}$ m² (S) and $A_{\ce{Mo}} = 5.00\times 10^{-19}$ m² (Mo), and that only half of each $\ce{MoS2}$ unit is exposed at the surface, calculate the particle radius $R$ in nm ( $M(\ce{MoS2}) = 160.07$ , $M(\ce{Mo}) = 95.95$ g mol $^{-1}$ ).Solutions: 1