IDNLearn.com: Your one-stop platform for getting reliable answers to any question. Find reliable solutions to your questions quickly and accurately with help from our dedicated community of experts.
Sagot :
To find the standard enthalpy change [tex]\(\Delta H^{\circ}_{\text{rxn}}\)[/tex] for the given reaction:
[tex]\[ 6 \text{Cl}_2(g) + 2 \text{Fe}_2\text{O}_3(s) \rightarrow 4 \text{FeCl}_3(s) + 3 \text{O}_2(g), \][/tex]
we need to use the provided standard enthalpy of formation ([tex]\(\Delta H_{f}^{\circ}\)[/tex]) values for each substance involved.
### Step-by-Step Solution:
1. Identify the enthalpy of formation ([tex]\(\Delta H_{f}^{\circ}\)[/tex]) for each substance:
[tex]\[ \begin{aligned} &\text{Cl}_2(g) & : &\quad 0.0 \, \text{kJ/mol} \\ &\text{Fe}_2\text{O}_3(s) & : &\quad -824.2 \, \text{kJ/mol} \\ &\text{FeCl}_3(s) & : &\quad -399.5 \, \text{kJ/mol} \\ &\text{O}_2(g) & : &\quad 0.0 \, \text{kJ/mol} \\ \end{aligned} \][/tex]
2. Use the stoichiometric coefficients from the balanced chemical equation:
[tex]\[ \begin{aligned} &\text{Cl}_2(g) & : &\quad 6 \\ &\text{Fe}_2\text{O}_3(s) & : &\quad 2 \\ &\text{FeCl}_3(s) & : &\quad 4 \\ &\text{O}_2(g) & : &\quad 3 \\ \end{aligned} \][/tex]
3. Calculate the total enthalpy of the reactants:
[tex]\[ \Delta H_{\text{reactants}} = (6 \times 0.0) + (2 \times -824.2) \][/tex]
[tex]\[ \Delta H_{\text{reactants}} = 0 + (-1648.4) = -1648.4 \, \text{kJ} \][/tex]
4. Calculate the total enthalpy of the products:
[tex]\[ \Delta H_{\text{products}} = (4 \times -399.5) + (3 \times 0.0) \][/tex]
[tex]\[ \Delta H_{\text{products}} = -1598.0 + 0 = -1598.0 \, \text{kJ} \][/tex]
5. Calculate the standard enthalpy change of the reaction ([tex]\(\Delta H^{\circ}_{\text{rxn}}\)[/tex]):
[tex]\[ \Delta H^{\circ}_{\text{rxn}} = \Delta H_{\text{products}} - \Delta H_{\text{reactants}} \][/tex]
[tex]\[ \Delta H^{\circ}_{\text{rxn}} = -1598.0 - (-1648.4) \][/tex]
[tex]\[ \Delta H^{\circ}_{\text{rxn}} = -1598.0 + 1648.4 = 50.4 \, \text{kJ} \][/tex]
Thus, the standard enthalpy change for the reaction, [tex]\(\Delta H^{\circ}_{\text{rxn}}\)[/tex], is [tex]\(50.4 \, \text{kJ}\)[/tex].
[tex]\[ 6 \text{Cl}_2(g) + 2 \text{Fe}_2\text{O}_3(s) \rightarrow 4 \text{FeCl}_3(s) + 3 \text{O}_2(g), \][/tex]
we need to use the provided standard enthalpy of formation ([tex]\(\Delta H_{f}^{\circ}\)[/tex]) values for each substance involved.
### Step-by-Step Solution:
1. Identify the enthalpy of formation ([tex]\(\Delta H_{f}^{\circ}\)[/tex]) for each substance:
[tex]\[ \begin{aligned} &\text{Cl}_2(g) & : &\quad 0.0 \, \text{kJ/mol} \\ &\text{Fe}_2\text{O}_3(s) & : &\quad -824.2 \, \text{kJ/mol} \\ &\text{FeCl}_3(s) & : &\quad -399.5 \, \text{kJ/mol} \\ &\text{O}_2(g) & : &\quad 0.0 \, \text{kJ/mol} \\ \end{aligned} \][/tex]
2. Use the stoichiometric coefficients from the balanced chemical equation:
[tex]\[ \begin{aligned} &\text{Cl}_2(g) & : &\quad 6 \\ &\text{Fe}_2\text{O}_3(s) & : &\quad 2 \\ &\text{FeCl}_3(s) & : &\quad 4 \\ &\text{O}_2(g) & : &\quad 3 \\ \end{aligned} \][/tex]
3. Calculate the total enthalpy of the reactants:
[tex]\[ \Delta H_{\text{reactants}} = (6 \times 0.0) + (2 \times -824.2) \][/tex]
[tex]\[ \Delta H_{\text{reactants}} = 0 + (-1648.4) = -1648.4 \, \text{kJ} \][/tex]
4. Calculate the total enthalpy of the products:
[tex]\[ \Delta H_{\text{products}} = (4 \times -399.5) + (3 \times 0.0) \][/tex]
[tex]\[ \Delta H_{\text{products}} = -1598.0 + 0 = -1598.0 \, \text{kJ} \][/tex]
5. Calculate the standard enthalpy change of the reaction ([tex]\(\Delta H^{\circ}_{\text{rxn}}\)[/tex]):
[tex]\[ \Delta H^{\circ}_{\text{rxn}} = \Delta H_{\text{products}} - \Delta H_{\text{reactants}} \][/tex]
[tex]\[ \Delta H^{\circ}_{\text{rxn}} = -1598.0 - (-1648.4) \][/tex]
[tex]\[ \Delta H^{\circ}_{\text{rxn}} = -1598.0 + 1648.4 = 50.4 \, \text{kJ} \][/tex]
Thus, the standard enthalpy change for the reaction, [tex]\(\Delta H^{\circ}_{\text{rxn}}\)[/tex], is [tex]\(50.4 \, \text{kJ}\)[/tex].
Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. Your questions deserve accurate answers. Thank you for visiting IDNLearn.com, and see you again for more solutions.