Question

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

Short answer

The balanced equations for the combustion reactions are as follows: c. \(12C_{12}H_{22}O_{11}(s) + 12O_{2}(g) \rightarrow 12CO_{2}(g) + 11H_{2}O(g)\) d. \(4Fe(s) + 3O_{2}(g) \rightarrow 2Fe_{2}O_{3}(s)\) e. \(2FeO(s) + O_{2}(g) \rightarrow Fe_{2}O_{3}(s)\)

Step-by-step solution

c. Balancing combustion of \(C_{12} H_{22} O_{11}\){

}Our initial equation is: \[C_{12} H_{22} O_{11}(s)+O_{2}(g) \rightarrow C O_{2}(g)+H_{2} O(g)\] Step 1: Balance carbon atoms: \[12 C_{12} H_{22} O_{11}(s)+O_{2}(g) \rightarrow 12 CO_{2}(g)+H_{2} O(g)\] Step 2: Balance hydrogen atoms: \[12 C_{12} H_{22} O_{11}(s)+O_{2}(g) \rightarrow 12 CO_{2}(g)+11H_{2}O(g)\] Step 3: Balance oxygen atoms: \[12 C_{12} H_{22} O_{11}(s)+12O_{2}(g) \rightarrow 12 CO_{2}(g)+11H_{2}O(g)\] The balanced equation is: \[12C_{12}H_{22}O_{11}(s) + 12O_{2}(g) \rightarrow 12CO_{2}(g) + 11H_{2}O(g)\]

d. Balancing combustion of \(\mathrm{Fe}\) and \(\mathrm{O}_{2}\) to form \(\mathrm{Fe}_{2}\mathrm{O}_{3}\){

}Our initial equation is: \[\mathrm{Fe}(s)+\mathrm{O}_{2}(g) \rightarrow \mathrm{Fe}_{2}\mathrm{O}_{3}(s)\] Step 1: Balance iron atoms: \[4\mathrm{Fe}(s)+\mathrm{O}_{2}(g) \rightarrow 2\mathrm{Fe}_{2}\mathrm{O}_{3}(s)\] Step 2: Balance oxygen atoms: \[4\mathrm{Fe}(s)+3\mathrm{O}_{2}(g) \rightarrow 2\mathrm{Fe}_{2}\mathrm{O}_{3}(s)\] The balanced equation is: \[4Fe(s) + 3O_{2}(g) \rightarrow 2Fe_{2}O_{3}(s)\]

e. Balancing combustion of \(\mathrm{FeO}\) and \(\mathrm{O}_{2}\) to form \(\mathrm{Fe}_{2}\mathrm{O}_{3}\){

}Our initial equation is: \[\operatorname{FeO}(s)+\mathbf{O}_{2}(g) \rightarrow \operatorname{Fe}_{2}\mathbf{O}_{3}(s)\] Step 1: Balance iron atoms: \[2\operatorname{FeO}(s)+\mathbf{O}_{2}(g) \rightarrow \operatorname{Fe}_{2}\mathbf{O}_{3}(s)\] Step 2: Balance oxygen atoms: \[2\operatorname{FeO}(s)\operatorname{+\mathbf{O}_{2}(g)} \rightarrow \operatorname{Fe}_{2}\mathbf{O}_{3}(s)\] The balanced equation is: \[2FeO(s) + O_{2}(g) \rightarrow Fe_{2}O_{3}(s)\]

Key concepts

Combustion Reactions

Combustion reactions are chemical processes in which a substance reacts rapidly with oxygen to produce heat and often light. In a combustion reaction, typically a hydrocarbon (containing carbon and hydrogen) or a metal reacts with oxygen to form oxidation products.
As seen in the above exercise, the sugar molecule sucrose \(C_{12}H_{22}O_{11}\), a common carbohydrate, undergoes combustion to form carbon dioxide (\(CO_2\)) and water vapor (\(H_2O\)). The same concept applies to the combustion of iron (\(Fe\)) in the presence of oxygen (\(O_2\)), forming iron(III) oxide (\(Fe_2O_3\)).

Chemical Stoichiometry

Chemical stoichiometry is the component of chemistry that pertains to the calculation of reactants and products in chemical reactions. It allows chemists to determine the quantities of substances consumed and produced in a given reaction based on the law of conservation of mass — matter is neither created nor destroyed.
Within the solution provided, chemical stoichiometric principles are used to determine the amount of oxygen needed to completely react with sucrose and iron, ensuring all atoms are accounted for and the mass remains constant before and after the reaction.

Chemical Reaction Balancing

The process of balancing chemical reactions is integral to chemistry. It involves adjusting the coefficients of the reactants and products to ensure the same number of each type of atom appears on both sides of the equation. This complies with the law of conservation of mass.
For each of the solutions provided, the process starts by balancing the atoms that appear in the least amount of compounds, typically metals or carbon, followed by hydrogens and finally, oxygen atoms. This systematic approach helps organize the balancing process and leads to the correct stoichiometric coefficients.

Oxygen Atoms Balancing

Oxygen atoms balancing is often the final step in balancing combustion reactions due to oxygen's presence in multiple compounds and its diatomic molecular form. After balancing other atoms, the total number of oxygen atoms from all reactants must equal the total number in the products.
The textbook solutions demonstrate this by adjusting the coefficient of oxygen gas after carbon and hydrogen, or iron atoms, are balanced. For instance, with sucrose, once the carbon and hydrogen atoms have been balanced, the final coefficient for oxygen gas is adjusted to ensure that the number of oxygen atoms on both sides of the equation is equal, finalizing the balanced reaction equation.