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

Step by step solution

01

(a) Balancing the equation and determining the reaction type

: Given equation: \(PbCO_3(s) \longrightarrow PbO(s) + CO_2(g)\) This equation seems to be properly balanced, so we can directly analyze its reaction type. As a single reactant breaks down into multiple products, it is a decomposition reaction. Balanced equation and type: \(PbCO_3(s) \longrightarrow PbO(s) + CO_2(g)\) (Decomposition Reaction)

02

(b) Balancing the equation and determining the reaction type

: Given equation: \(C_2H_4(g) + O_2(g) \longrightarrow CO_2(g) + H_2O(g)\) To balance this equation, we need to start by adjusting the coefficients of the compounds. Step 1: Balance the carbon atoms. \(C_2H_4(g) + O_2(g) \longrightarrow 2CO_2(g) + H_2O(g)\) Step 2: Balance the hydrogen atoms. \(C_2H_4(g) + O_2(g) \longrightarrow 2CO_2(g) + 2H_2O(g)\) Step 3: Balance the oxygen atoms. \(C_2H_4(g) + 3O_2(g) \longrightarrow 2CO_2(g) + 2H_2O(g)\) The equation is now balanced. As we can observe reactants combining to produce one or more complex products, so this is a combustion reaction. Balanced equation and type: \(C_2H_4(g) + 3O_2(g) \longrightarrow 2CO_2(g) + 2H_2O(g)\) (Combustion Reaction)

03

(c) Balancing the equation and determining the reaction type

: Given equation: \(Mg(s) + N_2(g) \longrightarrow Mg_3N_2(s)\) To balance this equation, we need to adjust the coefficients of the compounds. Step 1: Balance the magnesium atoms. \[ 3Mg(s) + N_2(g) \longrightarrow Mg_3N_2(s) \] Step 2: Balance the nitrogen atoms. \[ 3Mg(s) + 1/2N_2(g) \longrightarrow Mg_3N_2(s) \] To avoid fractions, we can multiply the entire equation by 2, \[ 6Mg(s) + N_2(g) \longrightarrow 2Mg_3N_2(s) \] The equation is now balanced. As two simpler substances combine to form a single, more complex compound, this is a combination reaction. Balanced equation and type: \(6Mg(s) + N_2(g) \longrightarrow 2Mg_3N_2(s)\) (Combination Reaction)

04

(d) Balancing the equation and determining the reaction type

: Given equation: \(C_7H_8O_2(l) + O_2(g) \longrightarrow CO_2(g) + H_2O(g)\) To balance this equation, we need to adjust the coefficients of the compounds. Step 1: Balance the carbon atoms. \(C_7H_8O_2(l) + O_2(g) \longrightarrow 7CO_2(g) + H_2O(g)\) Step 2: Balance the hydrogen atoms. \(C_7H_8O_2(l) + O_2(g) \longrightarrow 7CO_2(g) + 4H_2O(g)\) Step 3: Balance the oxygen atoms. \(C_7H_8O_2(l) + 9O_2(g) \longrightarrow 7CO_2(g) + 4H_2O(g)\) The equation is now balanced. As we can see reactants combining to form one or more complex products, this is a combustion reaction. Balanced equation and type: \(C_7H_8O_2(l) + 9O_2(g) \longrightarrow 7CO_2(g) + 4H_2O(g)\) (Combustion Reaction)

05

(e) Balancing the equation and determining the reaction type

: Given equation: \(Al(s) + Cl_2(g) \longrightarrow AlCl_3(s)\) To balance this equation, we need to adjust the coefficients of the compounds. Step 1: Balance the aluminum atoms. \[ 2Al(s) + Cl_2(g) \longrightarrow 2AlCl_3(s) \] Step 2: Balance the chlorine atoms. \[ 2Al(s) + 3Cl_2(g) \longrightarrow 2AlCl_3(s) \] The equation is now balanced. As two simpler substances combine to form a single, more complex compound, this is a combination reaction. Balanced equation and type: \(2Al(s) + 3Cl_2(g) \longrightarrow 2AlCl_3(s)\) (Combination Reaction)

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