International Chemistry Olympiad · 2017

Problems

Problem 1Production of propene using heterogeneous catalysts. Propene is one of the most valuable chemicals for the petrochemical industry. It can be synthesized by direct dehydrogenation of propane over a heterogeneous catalyst, $\ce{C3H8(g) <=> C3H6(g) + H2(g)}$ , but the reaction is not economically feasible. Use the following average bond enthalpy relations: $H_{\text{bond}}(\ce{C=C}) = 1.77\,H_{\text{bond}}(\ce{C-C})$ , $H_{\text{bond}}(\ce{H-H}) = 1.05\,H_{\text{bond}}(\ce{C-H})$ , and $H_{\text{bond}}(\ce{C-H}) = 1.19\,H_{\text{bond}}(\ce{C-C})$ . (a) What is the enthalpy change of the direct dehydrogenation of propane? Express the answer in terms of $H_{\text{bond}}(\ce{C-C})$ . (b) It is difficult to increase the amount of propene by raising the pressure at constant temperature — which law or principle best explains this? (c) For this reaction at equilibrium, what are the correct signs of $\Delta H$ , $\Delta S$ , and the change of $\Delta G$ when the temperature is raised to a higher value $T^*$ relative to the initial temperature?Solutions: 1
Problem 2Kinetic isotope effect (KIE) and zero-point vibrational energy (ZPE). The harmonic oscillator model gives the vibrational frequency $\nu = \dfrac{1}{2\pi}\sqrt{\dfrac{k}{\mu}}$ , where $k$ is the force constant and $\mu = \dfrac{m_1 m_2}{m_1 + m_2}$ is the reduced mass. Vibrational energies are $E_n = (n + \tfrac{1}{2})h\nu$ ( $n = 0, 1, 2, \dots$ ), and the zero-point energy is $\text{ZPE} = \tfrac{1}{2}h\nu$ . (a) Calculate the reduced masses $\mu_{\ce{CH}}$ and $\mu_{\ce{CD}}$ in atomic mass units (u), taking $m(\ce{C}) = 12.00$ u, $m(\ce{H}) = 1.008$ u, and $m(\ce{D}) = 2.014$ u. (b) Given $k_{\ce{CH}} = k_{\ce{CD}}$ and the $\ce{C-H}$ stretching wavenumber $\tilde{\nu}_{\ce{CH}} = 2900\ \text{cm}^{-1}$ , calculate the $\ce{C-D}$ stretching wavenumber $\tilde{\nu}_{\ce{CD}}$ (cm $^{-1}$ ). (c) Calculate $\text{ZPE}_{\ce{CH}}$ and $\text{ZPE}_{\ce{CD}}$ in kJ mol $^{-1}$ . (d) Calculate the difference in bond dissociation energies $\Delta \text{BDE} = \text{BDE}_{\ce{CD}} - \text{BDE}_{\ce{CH}}$ (kJ mol $^{-1}$ ). (e) Assuming $E_a \approx \text{BDE}$ and identical Arrhenius pre-exponential factors, calculate the theoretical primary KIE $k_{\ce{CH}}/k_{\ce{CD}}$ at $25\ ^{\circ}\text{C}$ . (f) In the chromic acid oxidation of diphenylmethanol, measured first-order rate constants are $k_{\ce{CH}} = 0.012\ \text{min}^{-1}$ and $k_{\ce{CD}} = 0.0018\ \text{min}^{-1}$ . Compare this experimental ratio with the theoretical value and determine whether $\ce{C-H}$ bond cleavage is rate-determining.Solutions: 1