Calculate Delta G in kj/mol for 2NH3(g) + 5/2 O2(g) = 2NO(g) + 3H20(l)

To calculate the change in Gibbs free energy ($\Delta G$) for the given reaction, we need to use the standard Gibbs free energy of formation ($\Delta G_f^\circ$) for each compound involved in the reaction. The formula to calculate $\Delta G$ for a reaction is:

$\Delta G^\circ = \sum \Delta G_f^\circ (\text{products}) - \sum \Delta G_f^\circ (\text{reactants})$

1. Break Down the Problem

Identify the compounds involved and their respective $\Delta G_f^\circ$ values:

• $\Delta G_f^\circ$ for $\text{NH}_3(g)$
• $\Delta G_f^\circ$ for $\text{O}_2(g)$
• $\Delta G_f^\circ$ for $\text{NO}(g)$
• $\Delta G_f^\circ$ for $\text{H}_2\text{O}(l)$

2. Relevant Concepts

Use the standard Gibbs free energy of formation values:

• $\Delta G_f^\circ$ for $\text{NH}_3(g)$ = -16.45 kJ/mol
• $\Delta G_f^\circ$ for $\text{O}_2(g)$ = 0 kJ/mol (as it is a standard state element)
• $\Delta G_f^\circ$ for $\text{NO}(g)$ = 86.60 kJ/mol
• $\Delta G_f^\circ$ for $\text{H}_2\text{O}(l)$ = -237.13 kJ/mol

3. Analysis and Detail

Calculate the $\Delta G^\circ$ for the reaction:

1. Products: $2 \times \Delta G_f^\circ (\text{NO}) + 3 \times \Delta G_f^\circ (\text{H}_2\text{O})$ $= 2 \times 86.60 + 3 \times (-237.13)$ $= 173.20 - 711.39 = -538.19 \, \text{kJ/mol}$

2. Reactants: $2 \times \Delta G_f^\circ (\text{NH}_3) + \frac{5}{2} \times \Delta G_f^\circ (\text{O}_2)$ $= 2 \times (-16.45) + \frac{5}{2} \times 0$ $= -32.90 \, \text{kJ/mol}$

4. Verify and Summarize

Calculate $\Delta G^\circ$ for the reaction: $\Delta G^\circ = -538.19 - (-32.90) = -538.19 + 32.90 = -505.29 \, \text{kJ/mol}$

Final Answer

The change in Gibbs free energy ($\Delta G$) for the reaction $2\text{NH}_3(g) + \frac{5}{2}\text{O}_2(g) \rightarrow 2\text{NO}(g) + 3\text{H}_2\text{O}(l)$ is $-505.29 \, \text{kJ/mol}$.