International Chemistry Olympiad · 2015

Problems

Problem 1New and well-forgotten old refrigerants. Refrigerants are compared thermodynamically in a model refrigeration cycle: liquid refrigerant boils at constant pressure $p_1$ and temperature $T_1$ (absorbing heat $Q$ ), the vapour is compressed reversibly and adiabatically to $T_2$ (work $W$ ), then cooled at constant pressure $p_2$ and returned to the initial state. For 1 mole of refrigerant with $T_1 = 280$ K and $T_2 = 380$ K, ideal vapour, the data are: $\ce{NH3}$ — $\Delta H_{vap} = 21.3$ kJ mol $^{-1}$ , $C_V(\text{gas}) = 26.7$ J K $^{-1}$ mol $^{-1}$ ; $\ce{CHF2Cl}$ — $20.0$ kJ mol $^{-1}$ and $48.8$ J K $^{-1}$ mol $^{-1}$ ; $\ce{CF3CH2F}$ — $22.1$ kJ mol $^{-1}$ and $79$ J K $^{-1}$ mol $^{-1}$ ; $\ce{CF3CF=CH2}$ — $19.1$ kJ mol $^{-1}$ and $120$ J K $^{-1}$ mol $^{-1}$ . (a) Calculate $Q$ and $W$ for $\ce{NH3}$ and $\ce{CHF2Cl}$ . (b) The coefficient of performance is $COP = Q/W$ ; calculate it for both refrigerants. (c) Calculate the COP for $\ce{CF3CH2F}$ and $\ce{CF3CF=CH2}$ — did efficiency improve relative to $\ce{CHF2Cl}$ ?Solutions: 1
Problem 3Two binding centers — competition or cooperation? A host molecule H has two binding centers $a$ and $b$ with different affinities for a guest molecule G: $\ce{H + G <=> HGa}$ ( $K_a$ ) and $\ce{H + G <=> HGb}$ ( $K_b$ ), where HGa and HGb denote complexes with G bound at center $a$ and $b$ respectively. Attachment of one G can change the second center's affinity, described by the interaction factor $\beta$ : the second binding step $\ce{HGa + G <=> HG2}$ (G now binds center $b$ ) has equilibrium constant $\beta K_b$ (HG2 is the doubly bound complex). (a) Give the range of $\beta$ values corresponding to cooperation, competition, and independence of the centers. (b) Find the equilibrium constant of $\ce{HGb + G <=> HG2}$ in terms of $K_a$ , $K_b$ , $\beta$ . (c) A solution was prepared with $[\ce{H}]_0 = 1$ and $[\ce{G}]_0 = 2$ mol dm $^{-3}$ . At equilibrium $[\ce{H}]$ decreased tenfold and $[\ce{G}]$ fourfold. Given $K_b = 2K_a$ , find the concentrations of all species and the values of $K_a$ and $\beta$ . (d) 1 mol of H and some amount of G were dissolved to give 1 dm $^3$ of solution in which $[\ce{HG2}] = [\ce{HGa}] + [\ce{HGb}]$ . With $K_a$ , $K_b$ and $\beta$ from part (c), find the initial amount of G.Solutions: 1