Question

Complete and balance each combustion reaction. (a) \(\mathrm{S}(s)+\mathrm{O}_{2}(g) \longrightarrow\) (b) \(\mathrm{C}_{7} \mathrm{H}_{16}(l)+\mathrm{O}_{2}(g)\) (c) \(\mathrm{C}_{4} \mathrm{H}_{10} \mathrm{O}(l)+\mathrm{O}_{2}(g) \longrightarrow\) (d) \(\mathrm{CS}_{2}(l)+\mathrm{O}_{2}(g)\)

Short answer

(a) \(\mathrm{S}(s) + \frac{1}{2}\mathrm{O}_2(g) \longrightarrow \mathrm{SO}_2(g)\). (b) \(\mathrm{C}_7\mathrm{H}_{16}(l) + 11\mathrm{O}_2(g) \longrightarrow 7\mathrm{CO}_2(g) + 8\mathrm{H}_2\mathrm{O}(l)\). (c) \(\mathrm{C}_4\mathrm{H}_{10}\mathrm{O}(l) + \frac{13}{2}\mathrm{O}_2(g) \longrightarrow 4\mathrm{CO}_2(g) + 5\mathrm{H}_2\mathrm{O}(l)\). (d) \(\mathrm{CS}_2(l) + 3\mathrm{O}_2(g) \longrightarrow 1\mathrm{CO}_2(g) + 2\mathrm{SO}_2(g)\).

Step-by-step solution

Identify the products of combustion

In a combustion reaction, a substance reacts with oxygen to produce energy, usually in the form of heat and light. Typically, the products include carbon dioxide (CO2) and water (H2O) when the substance contains carbon and hydrogen, and sulfur dioxide (SO2) when the substance contains sulfur.

Balance the combustion of sulfur (S)

The combustion reaction for sulfur is \(\mathrm{S}(s) + \mathrm{O}_2(g) \longrightarrow \mathrm{SO}_2(g)\). To balance it, place a coefficient of 1 in front of the sulfur and sulfur dioxide. Since the oxygen molecule (\(\mathrm{O}_2\)) has two oxygen atoms, and we have one sulfur dioxide (\(\mathrm{SO}_2\)) on the product side, we will need to balance the oxygen atoms by placing a coefficient of \(\frac{1}{2}\) in front of \(\mathrm{O}_2\). The balanced equation is \(\mathrm{S}(s) + \frac{1}{2}\mathrm{O}_2(g) \longrightarrow \mathrm{SO}_2(g)\).

Balance the combustion of heptane (C7H16)

The combustion reaction for heptane is \(\mathrm{C}_7\mathrm{H}_{16}(l) + \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_2(g) + \mathrm{H}_2\mathrm{O}(l)\). Each mole of heptane produces 7 moles of CO2 and 8 moles of H2O. To completely oxidize heptane, we need \(7 \times 2 + 8 = 22\) atoms of oxygen, or 11 \(\mathrm{O}_2\) molecules. The balanced equation is \(\mathrm{C}_7\mathrm{H}_{16}(l) + 11\mathrm{O}_2(g) \longrightarrow 7\mathrm{CO}_2(g) + 8\mathrm{H}_2\mathrm{O}(l)\).

Balance the combustion of butanol (C4H10O)

The combustion reaction for butanol is \(\mathrm{C}_4\mathrm{H}_{10}\mathrm{O}(l) + \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_2(g) + \mathrm{H}_2\mathrm{O}(l)\). Each mole of butanol produces 4 moles of CO2 and 5 moles of H2O. To completely oxidize butanol, we need \(4 \times 2 + 5 = 13\) atoms of oxygen, or \(\frac{13}{2}\) \(\mathrm{O}_2\) molecules. The balanced equation is \(\mathrm{C}_4\mathrm{H}_{10}\mathrm{O}(l) + \frac{13}{2}\mathrm{O}_2(g) \longrightarrow 4\mathrm{CO}_2(g) + 5\mathrm{H}_2\mathrm{O}(l)\).

Balance the combustion of carbon disulfide (CS2)

The combustion reaction for carbon disulfide is \(\mathrm{CS}_2(l) + \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_2(g) + \mathrm{SO}_2(g)\). Each mole of carbon disulfide produces 1 mole of CO2 and 2 moles of SO2. We need 3 moles of \(\mathrm{O}_2\) to provide the 6 atoms of oxygen required for complete combustion. The balanced equation is \(\mathrm{CS}_2(l) + 3\mathrm{O}_2(g) \longrightarrow 1\mathrm{CO}_2(g) + 2\mathrm{SO}_2(g)\).

Key concepts

Chemical Equation Balancing

Understanding how to balance chemical equations is essential for anyone studying chemistry. When we balance an equation, we ensure the conservation of mass by making the number of atoms for each element equal on both sides of the reaction. This is based on the law of conservation of mass, which states that matter cannot be created or destroyed in a chemical reaction.

For example, in a combustion reaction such as \( \mathrm{S}(s) + \mathrm{O}_2(g) \longrightarrow \mathrm{SO}_2(g) \), sulfur (S) is combusting in the presence of oxygen (\(\mathrm{O}_2\)) to produce sulfur dioxide (\(\mathrm{SO}_2\)). The equation must be balanced so that the atoms of sulfur and oxygen are equal on both sides. Initially, we have 1 sulfur atom and 2 oxygen atoms on the reactant side, but on the product side, there is 1 sulfur atom and only 1 oxygen atom in \(\mathrm{SO}_2\). To balance it, we adjust the coefficient of \(\mathrm{O}_2\) to \(\frac{1}{2}\), making the oxygen atom count equal to 1 on both sides, thus achieving a balanced equation.

Through this process, we learn to apply math to chemical formulas, which helps us understand the exact proportions in which substances react.

Stoichiometry

Stoichiometry is the study of the quantitative relationships or ratios between reactants and products in chemical reactions. It allows chemists to predict the amounts of substances consumed and produced in a given reaction. The term 'mole' plays a crucial role in stoichiometry, as it is a standard scientific unit for measuring large quantities of very small entities such as atoms, molecules, or other specified particles.

When examining the combustion of heptane (\(\mathrm{C}_7\mathrm{H}_{16}\)), stoichiometry informs us that the burning of 1 mole of heptane will produce 7 moles of carbon dioxide (\(\mathrm{CO}_2\)) and 8 moles of water (\(\mathrm{H}_2O\)), assuming complete combustion. To find out how much oxygen is necessary for this reaction, we calculate the oxygen requirement by summing the oxygen atoms needed for both products, resulting in 22 atoms of oxygen, or equivalently, 11 moles of oxygen molecules (\(\mathrm{O}_2\)). Stoichiometry helps us understand these proportions and to scale reactions appropriately for practical applications.

Oxidation-Reduction Reactions

Oxidation-reduction reactions, often called redox reactions, are processes where electrons are transferred between substances. In a typical redox reaction, the substance that donates electrons is oxidized, and the one that accepts electrons is reduced. Combustion reactions are a common type of redox reaction where a substance combines with oxygen, resulting in the oxidation of the substance.

For instance, when carbon disulfide (\(\mathrm{CS}_2\)) undergoes combustion, it is oxidized to form carbon dioxide (\(\mathrm{CO}_2\)) and sulfur dioxide (\(\mathrm{SO}_2\)). This process involves the transfer of electrons from \(\mathrm{CS}_2\) to the oxygen molecules, \(\mathrm{O}_2\). In this redox reaction, \(\mathrm{CS}_2\) loses electrons (oxidation), and the oxygen gains electrons (reduction). Understanding these electron transfer processes enhances our understanding of chemical reactivity and the changes in energy that accompany these reactions.