The industrial production of ammonia is commonly performed near

CHEMISTRY · Multi-part · A Level · Chemistry · Energetics · Energetics

Problem

The industrial production of ammonia is commonly performed near 700 K700\,\text{K}, whereas many data tables report ΔH∘\Delta H^\circ values at 298 K298\,\text{K}. Consider the overall synthesis reaction N2(g)+3 H2(g)→2 NH3(g)N_2(g) + 3\,H_2(g) \to 2\,NH_3(g) Selected data are provided below. 1. Standard molar heat capacities (assumed temperature-independent over the interval 298 K298\,\text{K}–700 K700\,\text{K}): Cp,m[N2(g)]=29.1 J mol−1 K−1C_{p,m}[\text{N}_2(g)] = 29.1\,\text{J}\,\text{mol}^{-1}\,\text{K}^{-1} Cp,m[H2(g)]=28.8 J mol−1 K−1C_{p,m}[\text{H}_2(g)] = 28.8\,\text{J}\,\text{mol}^{-1}\,\text{K}^{-1} Cp,m[NH3(g)]=35.1 J mol−1 K−1C_{p,m}[\text{NH}_3(g)] = 35.1\,\text{J}\,\text{mol}^{-1}\,\text{K}^{-1} 2. Standard enthalpies of formation at 298 K298\,\text{K}: ΔHf∘[N2(g)]=0\Delta H_f^\circ[\text{N}_2(g)] = 0 ΔHf∘[H2(g)]=0\Delta H_f^\circ[\text{H}_2(g)] = 0 ΔHf∘[NH3(g)]=−46.1 kJ mol−1\Delta H_f^\circ[\text{NH}_3(g)] = -46.1\,\text{kJ}\,\text{mol}^{-1} 3. An experimental calorimetric study at 700 K700\,\text{K} reports ΔH∘=−93 kJ\Delta H^\circ = -93\,\text{kJ} for the reaction as written. Answer the questions that follow. (a) Calculate the standard molar enthalpy change for the synthesis reaction at 298 K298\,\text{K} using the formation-enthalpy data. (b) Using the heat-capacity data, estimate the standard molar enthalpy change for the reaction at 700 K700\,\text{K}. Assume ideal-gas behavior and that Cp,mC_{p,m} values remain constant over the temperature range. (c) Compare your calculated value in part (b) with the reported experimental value at 700 K700\,\text{K}. Discuss whether the experimental result appears thermodynamically consistent with the tabulated data, providing quantitative justification. (d) Explain how the temperature dependence of heat capacities influences the enthalpy change of the reaction, and comment on the practical implications for designing an efficient ammonia synthesis process.

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