Let's dive into solving for the heat of the reaction step by step.
1. Understanding the problem:
- We are given a chemical reaction:
[tex]\[
2 \text{HCl} + \text{Mg} \rightarrow \text{MgCl}_2 + \text{H}_2
\][/tex]
- We are provided with the heat of the solution, \( q_{\text{soln}} \), which is \( +9240 \) J.
2. Heat of the solution (\( q_{\text{soln}} \)):
- This value represents the amount of heat absorbed by the solution during the reaction. Since it is positive, it indicates that the solution is absorbing heat.
3. Heat of the reaction (\( q_{\text{rxn}} \)):
- The heat of the reaction (\( q_{\text{rxn}} \)) is the amount of heat released or absorbed by the chemical reaction.
- By convention, the heat of the reaction is the negative of the heat absorbed by the solution. Therefore,
[tex]\[
q_{\text{rxn}} = -q_{\text{soln}}
\][/tex]
4. Applying the given values:
- Given \( q_{\text{soln}} = +9240 \) J.
- Thus,
[tex]\[
q_{\text{rxn}} = - (+9240 \text{ J}) = -9240 \text{ J}
\][/tex]
5. Conclusion:
- The heat of the reaction, \( q_{\text{rxn}} \), is \( -9240 \) J. This indicates that the reaction is exothermic, meaning it releases \( 9240 \) J of heat to the surroundings.
So, the heat of the reaction \( q_{\text{rxn}} \) is:
[tex]\[
q_{\text{rxn}} = -9240 \text{ J}
\][/tex]
