The following standard Gibbs energy changes are given for \(25^{\circ} \mathrm{C}\) (1) \(\mathrm{N}_{2}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{NH}_{3}(\mathrm{g})\) \(\Delta G^{\circ}=-33.0 \mathrm{kJ}\) (2) \(4 \mathrm{NH}_{3}(\mathrm{g})+5 \mathrm{O}_{2}(\mathrm{g}) \longrightarrow 4 \mathrm{NO}(\mathrm{g})+6 \mathrm{H}_{2} \mathrm{O}(1)\) \(\Delta G^{\circ}=-1010.5 \mathrm{kJ}\) (3) \(\mathrm{N}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{NO}(\mathrm{g})\) \(\Delta G^{\circ}=+173.1 \mathrm{kJ}\) (4) \(\mathrm{N}_{2}(\mathrm{g})+2 \mathrm{O}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{NO}_{2}(\mathrm{g})\) \(\Delta G^{\circ}=+102.6 \mathrm{kJ}\) (5) \(2 \mathrm{N}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{N}_{2} \mathrm{O}(\mathrm{g})\) \(\Delta G^{\circ}=+208.4 \mathrm{kJ}\) Combine the preceding equations, as necessary, to obtain \(\Delta G^{\circ}\) values for each of the following reactions. (a) \(\mathrm{N}_{2} \mathrm{O}(\mathrm{g})+\frac{3}{2} \mathrm{O}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{NO}_{2}(\mathrm{g}) \quad \Delta G^{\circ}=?\) (b) \(2 \mathrm{H}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(1) \quad \Delta G^{\circ}=?\) (c) \(2 \mathrm{NH}_{3}(\mathrm{g})+2 \mathrm{O}_{2}(\mathrm{g}) \longrightarrow \mathrm{N}_{2} \mathrm{O}(\mathrm{g})+3 \mathrm{H}_{2} \mathrm{O}(1)\) \(\Delta G^{\circ}=?\) Of reactions (a), (b), and (c), which would tend to go to completion at \(25^{\circ} \mathrm{C}\), and which would reach an equilibrium condition with significant amounts of all reactants and products present?

Step by step solution

01

Combine reactions to form the desired reaction (a)

The aim is to form the reaction \(N_{2}O(g) + 1.5 O_{2}(g) \rightarrow 2 NO_{2}(g)\). This can be achieved by reversing reaction (5) and adding it to reaction (4). The combined reaction is: \(2 N_{2}(g) + O_{2}(g) + N_{2}(g) + 2 O_{2}(g) \rightarrow 2 N_{2}O(g) + 2 NO_{2}(g)\). Simplifying gives the desired reaction: \(N_{2}O(g) + 1.5 O_{2}(g) \rightarrow 2 NO_{2}(g)\).

02

Calculate ∆G° for reaction (a)

The ∆G° for the combined reaction is the sum of the ∆G° values of the involved reactions, i.e., -∆G° of reaction (5) + ∆G° of reaction (4). Substitute the respective values: −(208.4 kJ) + 102.6 kJ = -105.8 kJ.

03

Repeat steps 1 and 2 for reactions (b) and (c)

For reaction (b), multiply reaction (2) by half: ∆G° is half of -1010.5 kJ, which equals -505.25 kJ. For reaction (c), subtract reaction (1) once from reaction (2) twice: calculating ∆G° gives -673.5 kJ.

04

Determine completion and equilibrium of reactions

From the final Gibbs energies of the reactions, if ∆G° < 0, the reaction will tend to go to completion. If ∆G° > 0, the reaction will reach equilibrium with significant quantities of both reactants and products. Since all ∆G° values calculated are < 0, all reactions (a), (b) and (c) will tend to go to completion at 25 ⁰C.

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