To determine the enthalpy change for the given chemical reaction, we need to follow the enthalpy change equation:
[tex]\[
\Delta H_{\text{reaction}} = \sum (\Delta H_{\text{products}}) - \sum (\Delta H_{\text{reactants}})
\][/tex]
First, let's gather the given data for the enthalpy change of formation ([tex]\( \Delta H \)[/tex]) of each component:
- For [tex]\( NH_3 \)[/tex]: [tex]\( \Delta H_{NH_3} = -45.9 \, \text{kJ} \)[/tex]
- For [tex]\( H_2O \)[/tex]: [tex]\( \Delta H_{H_2O} = -241.8 \, \text{kJ} \)[/tex]
- For [tex]\( NO \)[/tex]: [tex]\( \Delta H_{NO} = 91.3 \, \text{kJ} \)[/tex]
Next, let's identify the coefficients from the balanced chemical reaction:
[tex]\[
4 \, NH_3 (g) + 5 \, O_2 (g) \rightarrow 6 \, H_2O (g) + 4 \, NO (g)
\][/tex]
Given the coefficients:
- 4 for [tex]\( NH_3 \)[/tex]
- 6 for [tex]\( H_2O \)[/tex]
- 4 for [tex]\( NO \)[/tex]
Now, let's calculate the total enthalpy change for the reactants:
[tex]\[
\Delta H_{\text{reactants}} = 4 \times \Delta H_{NH_3}
\][/tex]
[tex]\[
\Delta H_{\text{reactants}} = 4 \times (-45.9 \, \text{kJ}) = -183.6 \, \text{kJ}
\][/tex]
Next, let's calculate the total enthalpy change for the products:
[tex]\[
\Delta H_{\text{products}} = 6 \times \Delta H_{H_2O} + 4 \times \Delta H_{NO}
\][/tex]
[tex]\[
\Delta H_{\text{products}} = 6 \times (-241.8 \, \text{kJ}) + 4 \times (91.3 \, \text{kJ})
\][/tex]
[tex]\[
\Delta H_{\text{products}} = -1450.8 \, \text{kJ} + 365.2 \, \text{kJ}
\][/tex]
[tex]\[
\Delta H_{\text{products}} = -1085.6 \, \text{kJ}
\][/tex]
Finally, we apply the enthalpy change equation to find the enthalpy change for the reaction:
[tex]\[
\Delta H_{\text{reaction}} = \Delta H_{\text{products}} - \Delta H_{\text{reactants}}
\][/tex]
[tex]\[
\Delta H_{\text{reaction}} = -1085.6 \, \text{kJ} - (-183.6 \, \text{kJ})
\][/tex]
[tex]\[
\Delta H_{\text{reaction}} = -1085.6 \, \text{kJ} + 183.6 \, \text{kJ}
\][/tex]
[tex]\[
\Delta H_{\text{reaction}} = -902.0 \, \text{kJ}
\][/tex]
Thus, the enthalpy change for the reaction is [tex]\( -902.0 \, \text{kJ} \)[/tex]. The correct answer is:
[tex]\[
-902 \, \text{kJ}
\][/tex]
