Fe_2O_{3(s)} + frac{3}{2} C_{(s)} to frac{3}{ | vedclass

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(A) Let the given equations be:$(1) Fe_2O_{3(s)} + \frac{3}{2} C_{(s)} 	o \frac{3}{2} CO_{2(g)} + 2Fe_{(s)} \quad \Delta H_1^o = +234.1 \ kJ$$(2) C_{

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$ -1648.7 $

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(A) Let the given equations be:$(1) Fe_2O_{3(s)} + \frac{3}{2} C_{(s)} 	o \frac{3}{2} CO_{2(g)} + 2Fe_{(s)} \quad \Delta H_1^o = +234.1 \ kJ$$(2) C_{(s)} + O_{2(g)} 	o CO_{2(g)} \quad \Delta H_2^o = -393.5 \ kJ$We need to find $\Delta H^o$ for:$(3) 4Fe_{(s)} + 3O_{2(g)} 	o 2Fe_2O_{3(s)}$Reverse equation $(1)$ and multiply by $2$:$4Fe_{(s)} + 3CO_{2(g)} 	o 2Fe_2O_{3(s)} + 3C_{(s)} \quad \Delta H_3^o = -2 	imes 234.1 = -468.2 \ kJ$Multiply equation $(2)$ by $3$:$3C_{(s)} + 3O_{2(g)} 	o 3CO_{2(g)} \quad \Delta H_4^o = 3 	imes (-393.5) = -1180.5 \ kJ$Adding the two modified equations:$(4Fe_{(s)} + 3CO_{2(g)}) + (3C_{(s)} + 3O_{2(g)}) 	o (2Fe_2O_{3(s)} + 3C_{(s)}) + 3CO_{2(g)}$Canceling common terms ($3CO_{2(g)}$ and $3C_{(s)}$) gives:$4Fe_{(s)} + 3O_{2(g)} 	o 2Fe_2O_{3(s)}$$\Delta H^o = \Delta H_3^o + \Delta H_4^o = -468.2 + (-1180.5) = -1648.7 \ kJ$

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$Fe_2O_{3(s)} + \frac{3}{2} C_{(s)} \to \frac{3}{2} CO_{2(g)} + 2Fe_{(s)}$$\Delta H^o = +234.1 \ kJ$$C_{(s)} + O_{2(g)} \to CO_{2(g)}$$\Delta H^o = -393.5 \ kJ$Use these equations and $\Delta H^o$ values to calculate $\Delta H^o$ for this reaction:$4Fe_{(s)} + 3O_{2(g)} \to 2Fe_2O_{3(s)}$..... $kJ$