Question

Balance the following equations and indicate whether they are combination, decomposition, or combustion reactions: (a) \(\mathrm{PbCO}_{3}(s) \longrightarrow \mathrm{PbO}(s)+\mathrm{CO}_{2}(g)\) (b) \(\mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)\) (c) \(\mathrm{Mg}(s)+\mathrm{N}_{2}(g) \longrightarrow \mathrm{Mg}_{3} \mathrm{~N}_{2}(s)\) (d) \(\mathrm{C}_{7} \mathrm{H}_{8} \mathrm{O}_{2}(l)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)\) (e) \(\mathrm{Al}(s)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{AlCl}_{3}(s)\)

Short answer

(a) The balanced equation is \(\mathrm{PbCO}_{3}(s) \longrightarrow \mathrm{PbO}(s)+\mathrm{CO}_{2}(g)\) and it is a decomposition reaction. (b) The balanced equation is \[\mathrm{C}_{2} \mathrm{H}_{4}(g) + 3\,\mathrm{O}_{2}(g) \longrightarrow 2\,\mathrm{CO}_{2}(g) + 2\,\mathrm{H}_{2}\mathrm{O}(g)\] and it is a combustion reaction. (c) The balanced equation is \[3\,\mathrm{Mg}(s) + \mathrm{N}_{2}(g) \longrightarrow \mathrm{Mg}_{3}\mathrm{N}_{2}(s)\] and it is a combination reaction. (d) The balanced equation is \[\mathrm{C}_{7} \mathrm{H}_{8} \mathrm{O}_{2}(l) + 9\, \mathrm{O}_{2}(g) \longrightarrow 7\, \mathrm{CO}_{2}(g) + 4\, \mathrm{H}_{2} \mathrm{O}(g)\] and it is a combustion reaction. (e) The balanced equation is \[2\,\mathrm{Al}(s) + 3\,\mathrm{Cl}_{2}(g) \longrightarrow 2\,\mathrm{AlCl}_{3}(s)\] and it is a combination reaction.

Step-by-step solution

(a) Balancing the equation and identifying reaction type

In this reaction, we have \(\mathrm{PbCO}_{3}(s) \longrightarrow \mathrm{PbO}(s)+\mathrm{CO}_{2}(g)\). The equation is already balanced, as there is one atom of each element on both the reactant and product sides. Since one compound is breaking down into simpler substances, this is a decomposition reaction.

(b) Balancing the equation and identifying reaction type

We have \(\mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)\). To balance this equation, adjust the number of molecules to match the atoms in both sides: \[\mathrm{C}_{2} \mathrm{H}_{4}(g) + 3\,\mathrm{O}_{2}(g) \longrightarrow 2\,\mathrm{CO}_{2}(g) + 2\,\mathrm{H}_{2}\mathrm{O}(g)\] Since a substance reacts with oxygen gas and produces carbon dioxide and water, this is a combustion reaction.

(c) Balancing the equation and identifying reaction type

In this reaction, we have \(\mathrm{Mg}(s)+\mathrm{N}_{2}(g) \longrightarrow \mathrm{Mg}_{3}\mathrm{N}_{2}(s)\). Balancing the equation gives: \[3\,\mathrm{Mg}(s) + \mathrm{N}_{2}(g) \longrightarrow \mathrm{Mg}_{3}\mathrm{N}_{2}(s)\] This reaction involves two substances combining to form a single product, so it is a combination reaction.

(d) Balancing the equation and identifying reaction type

We have \(\mathrm{C}_{7} \mathrm{H}_{8} \mathrm{O}_{2}(l)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)\). To balance the equation: \[\mathrm{C}_{7} \mathrm{H}_{8} \mathrm{O}_{2}(l) + 9\, \mathrm{O}_{2}(g) \longrightarrow 7\, \mathrm{CO}_{2}(g) + 4\, \mathrm{H}_{2} \mathrm{O}(g)\] As a substance reacts with oxygen gas and produces carbon dioxide and water, this is a combustion reaction.

(e) Balancing the equation and identifying reaction type

In this reaction, we have \(\mathrm{Al}(s)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{AlCl}_{3}(s)\). Balancing the equation gives: \[2\,\mathrm{Al}(s) + 3\,\mathrm{Cl}_{2}(g) \longrightarrow 2\,\mathrm{AlCl}_{3}(s)\] This reaction involves two substances combining to form a single product, so it is a combination reaction.