Chemistry

Chemistry

Problem

A chemist investigates the oxidation of nitrogen monoxide according to the overall equation 2 NO(g)+O2(g)⟶2 NO2(g)2\,\text{NO}(g)+\text{O}_2(g)\longrightarrow 2\,\text{NO}_2(g) The following reactions and molar enthalpy changes are available at the same temperature and pressure. 1. N2(g)+12 O2(g)⟶N2O(g)ΔH1∘=+82.1 kJ mol−1\text{N}_2(g)+\tfrac{1}{2}\,\text{O}_2(g)\longrightarrow \text{N}_2\text{O}(g)\qquad \Delta H_1^{\circ}=+82.1\,\text{kJ}\,\text{mol}^{-1} 2. N2O(g)+12 O2(g)⟶2 NO(g)ΔH2∘=+41.2 kJ mol−1\text{N}_2\text{O}(g)+\tfrac{1}{2}\,\text{O}_2(g)\longrightarrow 2\,\text{NO}(g)\qquad \Delta H_2^{\circ}=+41.2\,\text{kJ}\,\text{mol}^{-1} 3. N2(g)+2 O2(g)⟶2 NO2(g)ΔH3∘=+66.4 kJ mol−1\text{N}_2(g)+2\,\text{O}_2(g)\longrightarrow 2\,\text{NO}_2(g)\qquad \Delta H_3^{\circ}=+66.4\,\text{kJ}\,\text{mol}^{-1} All gases behave ideally and all reactions occur at constant pressure. (a) Show, using algebraic manipulation of Reactions 1–3, how to obtain the target equation for the oxidation of nitrogen monoxide. (b) Determine the standard molar enthalpy change, ΔHrxn∘\Delta H_{\text{rxn}}^{\circ}, for the target reaction. Report the value in kJ mol−1\text{kJ}\,\text{mol}^{-1} using the correct sign. (c) Justify why the numerical value obtained in part (b) is independent of the specific reaction pathway that actually occurs in the laboratory.

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