AP Chemistry
6.9 Hess’s Law
Hydrazine, \(\text{N}_2\text{H}_4\), is an inorganic compound used as a rocket propellant. A student investigates the synthesis of liquid hydrazine from gaseous ammonia and oxygen gas according to the following reaction:
\[ 2\,\text{NH}_3(g) + \frac{1}{2}\,\text{O}_2(g) \rightarrow \text{N}_2\text{H}_4(l) + \text{H}_2\text{O}(l) \]
The student finds the following thermochemical data:
\[ \text{N}_2\text{H}_4(l) + \text{O}_2(g) \rightarrow \text{N}_2(g) + 2\,\text{H}_2\text{O}(l) \quad \Delta H^\circ = -622\text{ kJ/mol}_{\text{rxn}} \]
\[ \text{N}_2(g) + 3\,\text{H}_2(g) \rightarrow 2\,\text{NH}_3(g) \quad \Delta H^\circ = -92\text{ kJ/mol}_{\text{rxn}} \]
\[ 2\,\text{H}_2(g) + \text{O}_2(g) \rightarrow 2\,\text{H}_2\text{O}(l) \quad \Delta H^\circ = -572\text{ kJ/mol}_{\text{rxn}} \]
Based on the data provided, what is the value of \(\Delta H^\circ\) for the synthesis reaction?
\[ 2\,\text{NH}_3(g) + \frac{1}{2}\,\text{O}_2(g) \rightarrow \text{N}_2\text{H}_4(l) + \text{H}_2\text{O}(l) \]
The student finds the following thermochemical data:
\[ \text{N}_2\text{H}_4(l) + \text{O}_2(g) \rightarrow \text{N}_2(g) + 2\,\text{H}_2\text{O}(l) \quad \Delta H^\circ = -622\text{ kJ/mol}_{\text{rxn}} \]
\[ \text{N}_2(g) + 3\,\text{H}_2(g) \rightarrow 2\,\text{NH}_3(g) \quad \Delta H^\circ = -92\text{ kJ/mol}_{\text{rxn}} \]
\[ 2\,\text{H}_2(g) + \text{O}_2(g) \rightarrow 2\,\text{H}_2\text{O}(l) \quad \Delta H^\circ = -572\text{ kJ/mol}_{\text{rxn}} \]
Based on the data provided, what is the value of \(\Delta H^\circ\) for the synthesis reaction?
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