International Chemistry Olympiad · 2004

Problems

Problem 4Determining atomic masses. (4.1) The reaction of element X with hydrogen gives compounds analogous to hydrocarbons. 5.000 g of X form 5.628 g of a molar 2:1 mixture of the stoichiometric X-analogues of methane and ethane. Determine the molar mass of X, give its symbol and the 3D structures of the two products. (4.2) The mineral argyrodite is a stoichiometric compound containing silver (oxidation state +1), sulfur (−2) and an unknown element Y (+4). The mass ratio is $m(\ce{Ag}):m(\ce{Y}) = 11.88:1$ . Y forms a reddish-brown lower sulfide (Y in +2) and a white higher sulfide (Y in +4). When argyrodite is heated in a stream of hydrogen, the coloured lower sulfide sublimes; the residues are $\ce{Ag2S}$ and $\ce{H2S}$ . Complete conversion of 10.0 g of argyrodite needs 0.295 dm $^3$ of $\ce{H2}$ at 400 K and 100 kPa. Determine the molar mass of Y, its symbol, and the empirical formula of argyrodite. (4.3) IR frequencies (wavenumbers) follow Hooke's law $\tilde{\nu} = \frac{1}{2\pi c}\sqrt{k/\mu}$ where, for a tetrahedral $\ce{AB4}$ molecule, $\mu = \frac{3m(A)m(B)}{3m(A)+4m(B)}$ . The C–H vibration of methane is 3030.00 cm $^{-1}$ and that of the Z-analogue of methane is 2938.45 cm $^{-1}$ ; the bond enthalpies are 438.4 and 450.2 kJ mol $^{-1}$ . Determine the force constant $k$ of a C–H bond, estimate $k$ of the Z–H bond assuming proportionality to bond enthalpy, and find the atomic mass and symbol of Z.Solutions: 1