Chemistry

Chemistry

Problem

A multistep thermochemical cycle for the thermal decomposition of solid ammonium nitrate, NH4NO3(s)\mathrm{NH_4NO_3(s)}, is described textually below. Energies are expressed relative to the reactants, whose reference enthalpy is set to 0 kJ0\,\text{kJ}. • Point R (0 kJ0\,\text{kJ}) represents NH4NO3(s)\mathrm{NH_4NO_3(s)} in its standard state. • Point A lies +180 kJ+180\,\text{kJ} above R and corresponds to the solvated ions NH4+(aq)+NO3−(aq)\mathrm{NH_4^+(aq) + NO_3^-(aq)}. • Point B lies a further +340 kJ+340\,\text{kJ} above A and corresponds to the gaseous ions NH4+(g)+NO3−(g)\mathrm{NH_4^+(g) + NO_3^-(g)}. • Point P lies −300 kJ-300\,\text{kJ} below R and represents the final gaseous products N2O(g)+2 H2O(g)+12 O2(g)\mathrm{N_2O(g) + 2\,H_2O(g) + \tfrac12\,O_2(g)}. The cycle contains the following individual steps (arrows): 1. R →\to A ΔH1=+180 kJ\Delta H_1 = +180\,\text{kJ} 2. A →\to B ΔH2=+340 kJ\Delta H_2 = +340\,\text{kJ} 3. B →\to P ΔH3=unknown\Delta H_3 = \text{unknown} 4. Direct path R →\to P ΔHoverall=−300 kJ\Delta H_{\text{overall}} = -300\,\text{kJ} Assume the only energy changes involved are those explicitly listed. (a) Without performing a numerical calculation, state whether ΔH3\Delta H_3 is expected to be exothermic or endothermic and justify your answer qualitatively. (b) Determine the numerical value of ΔH3\Delta H_3 in kJ\text{kJ}. Show your reasoning clearly. (c) Rank the three individual steps (1, 2, and 3) in order of increasing magnitude of enthalpy change (smallest to largest). Support your ranking with appropriate numerical or conceptual justification. (d) Explain briefly how the result obtained in part (b) illustrates the principle of conservation of energy for this process.

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