To determine the correct statement about the enthalpy of the reaction, we need to follow these steps:
1. Identify the Given Data:
- The enthalpy of formation of [tex]\( HCl \)[/tex] is given as [tex]\( \Delta H_{f, HCl} = -92.3 \text{ kJ/mol} \)[/tex].
- The balanced reaction is:
[tex]\[
H_2(g) + Cl_2(g) \rightarrow 2 HCl(g)
\][/tex]
2. Determine the Enthalpy of Formation for Reactants:
- For elements in their standard states (such as [tex]\( H_2 \)[/tex] and [tex]\( Cl_2 \)[/tex] in this case), the enthalpy of formation is zero.
[tex]\[
\Delta H_{f, H_2} = 0 \text{ kJ/mol}
\][/tex]
[tex]\[
\Delta H_{f, Cl_2} = 0 \text{ kJ/mol}
\][/tex]
3. Calculate the Total Enthalpy of Formation of Products:
- Since the equation produces 2 moles of [tex]\( HCl \)[/tex], we use the enthalpy of formation of [tex]\( HCl \)[/tex]:
[tex]\[
\Delta H_{f, \text{products}} = 2 \times (-92.3 \text{ kJ/mol}) = -184.6 \text{ kJ}
\][/tex]
4. Calculate the Total Enthalpy of Formation of Reactants:
- The reactants are [tex]\( H_2 \)[/tex] and [tex]\( Cl_2 \)[/tex], both having enthalpy of formation of zero:
[tex]\[
\Delta H_{f, \text{reactants}} = 0 + 0 = 0 \text{ kJ}
\][/tex]
5. Determine the Enthalpy Change (ΔH) of the Reaction:
- Using the equation for enthalpy change:
[tex]\[
\Delta H_{\text{reaction}} = \sum \Delta H_{f, \text{products}} - \sum \Delta H_{f, \text{reactants}}
\][/tex]
[tex]\[
\Delta H_{\text{reaction}} = -184.6 \text{ kJ} - 0 \text{ kJ}
\][/tex]
[tex]\[
\Delta H_{\text{reaction}} = -184.6 \text{ kJ}
\][/tex]
6. Determine Whether the Reaction is Exothermic or Endothermic:
- If [tex]\( \Delta H_{\text{reaction}} \)[/tex] is negative, the reaction is exothermic because it releases heat.
- In this case, [tex]\( \Delta H_{\text{reaction}} = -184.6 \text{ kJ} \)[/tex], so the reaction is exothermic.
Conclusion:
The correct statement is: "The enthalpy of the reaction is -184.6 kJ, and the reaction is exothermic."
