The Haber–Bosch process synthesizes ammonia according to the balanced equation at…

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

Problem

The Haber–Bosch process synthesizes ammonia according to the balanced equation N2(g)+3 H2(g)→2 NH3(g)N_2(g) + 3\,H_2(g) \rightarrow 2\,NH_3(g) at temperatures up to 773 K773\,\text{K}. Selected standard molar entropies at 298 K298\,\text{K} are listed. Species S∘S^\circ (J mol−1 K−1\text{J}\,\text{mol}^{-1}\,\text{K}^{-1}) N2(g)N_2(g) 191.5 H2(g)H_2(g) 130.7 NH3(g)NH_3(g) 192.5 For the purposes of this question, assume that the molar entropies are independent of temperature over the range considered. (1) Part 1: Calculate the standard entropy change ΔS∘\Delta S^\circ for the synthesis of ammonia at 298 K298\,\text{K}. (2) Part 2: Using the assumption stated, estimate the entropy change ΔS\Delta S (in J mol−1 K−1\text{J}\,\text{mol}^{-1}\,\text{K}^{-1}) at 773 K773\,\text{K} for the reaction, and comment briefly on the validity of treating the entropy as temperature-independent over this range. (3) Part 3: The standard enthalpy change ΔH∘\Delta H^\circ for the reaction is −92.4 kJ mol−1-92.4\,\text{kJ}\,\text{mol}^{-1} at 298 K298\,\text{K} and is similarly assumed to be temperature-independent. Using your value of ΔS∘\Delta S^\circ from part (a), calculate the standard Gibbs free-energy change ΔG∘\Delta G^\circ at 298 K298\,\text{K} and state whether the reaction is spontaneous under standard conditions at this temperature. (4) Part 4: Industrial reactors operate at high pressure to shift the equilibrium toward ammonia. Using your thermodynamic results, explain why increasing pressure is particularly important at the elevated temperatures employed in industry.

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