Balance the following equations representing combustion reactions: c. $C_{12} \mathrm{H}_{22} \mathrm{O}_{11}(s)+\mathrm{O}_{2}(g) \rightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)$ d. Fe \((s)+\mathrm{O}_{2}(g) \rightarrow \mathrm{Fe}_{2} \mathrm{O}_{3}(s)\) e. $\mathrm{FeO}(s)+\mathrm{O}_{2}(g) \rightarrow \mathrm{Fe}_{2} \mathrm{O}_{3}(s)$

Given the equation: \(C_{12}H_{22}O_{11}(s)+ O_{2}(g) \rightarrow CO_{2}(g)+ H_{2}O(g)\) 1. Count the atoms of each element on both sides of the equation. Left side: 12 C, 22 H, and 12 O atoms Right side: 1 C, 2 H, and 3 O atoms 2. Balance the Carbon atoms by adding a coefficient to the CO₂ term on the right side: \(C_{12}H_{22}O_{11}(s) + O_{2}(g) \rightarrow 12CO_{2}(g) + H_{2}O(g)\) 3. Balance the Hydrogen atoms by adding a coefficient to the H₂O term on the right side: \(C_{12}H_{22}O_{11}(s) + O_{2}(g) \rightarrow 12CO_{2}(g) + 11H_{2}O(g)\) 4. Finally, balance the Oxygen atoms by adding a coefficient to the O₂ term on the left side: \(C_{12}H_{22}O_{11}(s) + 12O_{2}(g) \rightarrow 12CO_{2}(g) + 11H_{2}O(g)\) The balanced equation for (c) is: \(C_{12}H_{22}O_{11}(s) + 12O_{2}(g) \rightarrow 12CO_{2}(g) + 11H_{2}O(g)\)

Given the equation: \(Fe(s) + O_{2}(g) \rightarrow Fe_{2}O_{3}(s)\) 1. Count the atoms of each element on both sides of the equation. Left side: 1 Fe and 2 O atoms Right side: 2 Fe and 3 O atoms 2. Balance the Iron atoms by adding a coefficient to the Fe term on the left side: \(4Fe(s) + O_{2}(g) \rightarrow 2Fe_{2}O_{3}(s)\) 3. Balance the Oxygen atoms by adding a coefficient to the O₂ term on the left side: \(4Fe(s) + 3O_{2}(g) \rightarrow 2Fe_{2}O_{3}(s)\) The balanced equation for (d) is: \(4Fe(s) + 3O_{2}(g) \rightarrow 2Fe_{2}O_{3}(s)\)

Given the equation: \(FeO(s)+ O_{2}(g) \rightarrow Fe_{2}O_{3}(s)\) 1. Count the atoms of each element on both sides of the equation. Left side: 1 Fe, and 3 O atoms Right side: 2 Fe and 3 O atoms 2. Balance the Iron atoms by adding a coefficient to the FeO term on the left side: \(2FeO(s)+ O_{2}(g) \rightarrow Fe_{2}O_{3}(s)\) 3. Balance the Oxygen atoms (already balanced, no need for change): \(2FeO(s)+ O_{2}(g) \rightarrow Fe_{2}O_{3}(s)\) The balanced equation for (e) is: \(2FeO(s)+ O_{2}(g) \rightarrow Fe_{2}O_{3}(s)\)