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A certain reaction occurs as follows:

Hydrogen reacts with chlorine to form hydrogen chloride:

[tex]\[ H_2(g) + Cl_2(g) \rightarrow 2HCl(g) \][/tex]

Given:
[tex]\[ \Delta H_f(HCl(g)) = -92.3 \, \text{kJ/mol} \][/tex]

Which statement is correct?

[tex]\[
\begin{array}{l}
\text{A. The enthalpy of the reaction is } -184.6 \, \text{kJ}, \text{ and the reaction is exothermic.} \\
\text{B. The enthalpy of the reaction is } -184.6 \, \text{kJ}, \text{ and the reaction is endothermic.} \\
\text{C. The enthalpy of the reaction is } 184.6 \, \text{kJ}, \text{ and the reaction is endothermic.} \\
\text{D. The enthalpy of the reaction is } 184.6 \, \text{kJ}, \text{ and the reaction is exothermic.}
\end{array}
\][/tex]



Answer :

GinnyAnswer
Certainly! Let's analyze the given reaction and determine the enthalpy change and whether the reaction is exothermic or endothermic.

The balanced chemical reaction is:
[tex]\[ \text{H}_2(g) + \text{Cl}_2(g) \rightarrow 2 \text{HCl}(g) \][/tex]

1. Enthalpy Change for the Products:
- Given: The enthalpy change of formation ([tex]\(\Delta H_f\)[/tex]) for HCl is [tex]\(-92.3 \text{ kJ/mol}\)[/tex].
- Since 2 moles of HCl are produced, the total enthalpy change for the products will be:
[tex]\[ \Delta H_{\text{products}} = 2 \times (-92.3 \text{ kJ/mol}) = -184.6 \text{ kJ} \][/tex]

2. Enthalpy Change for the Reactants:
- Both [tex]\(\text{H}_2(g)\)[/tex] and [tex]\(\text{Cl}_2(g)\)[/tex] are in their standard states, so their enthalpy of formation ([tex]\(\Delta H_f\)[/tex]) is 0.
- Therefore, the total enthalpy change for the reactants is:
[tex]\[ \Delta H_{\text{reactants}} = 0 \text{ kJ} \][/tex]

3. Calculating the Enthalpy of the Reaction:
- According to the equation for the enthalpy change of the reaction:
[tex]\[ \Delta H_{\text{reaction}} = \sum \left( \Delta H_{\text{f,products}} \right) - \sum \left( \Delta H_{\text{f,reactants}} \right) \][/tex]
- Substituting in the values we have:
[tex]\[ \Delta H_{\text{reaction}} = -184.6 \text{ kJ} - 0 \text{ kJ} = -184.6 \text{ kJ} \][/tex]

4. Determining if the Reaction is Exothermic or Endothermic:
- A reaction is exothermic if [tex]\(\Delta H_{\text{reaction}}\)[/tex] is negative.
- A reaction is endothermic if [tex]\(\Delta H_{\text{reaction}}\)[/tex] is positive.
- In this case, [tex]\(\Delta H_{\text{reaction}} = -184.6 \text{ kJ}\)[/tex] which is negative.

Therefore, the enthalpy of the reaction is [tex]\(-184.6 \text{ kJ}\)[/tex], and the reaction is exothermic.

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