Answered

Balance the following chemical equations or determine if they are already balanced:



1) $1 N_2 + 3 H_2 \longrightarrow 2 NH_3$

2) $2 Na + 2 H_2 O \longrightarrow 2 NaOH + 1 H_2$

3) $2 KClO_3 \longrightarrow 2 KCl + 3 O_2$

4) $2 NaCl + 1 F_2 \longrightarrow 2 NaF + 1 Cl_2$

5) $2 H_2 + 1 O_2 \longrightarrow 2 H_2 O$

6) $\_ Pb(OH)_2 + \_ HCl \longrightarrow \_ H_2 O + \_ PbCl_2$

7) $\_ AlBr_3 + \_ K_2 SO_4 \longrightarrow \_ KBr + \_ Al_2(SO_4)_3$

8) $\_ C_3 H_8 + \_ O_2 \longrightarrow \_ CO_2 + \_ H_2 O$

9) $\_ FeCl_3 + \_ NaOH \longrightarrow \_ Fe(OH)_3 + \_ NaCl$

Verified Answer :

  • Equation 6: \(1Pb(OH)_2 + 2HCl \longrightarrow 2H_2O + 1PbCl_2\)
  • Equation 7: \(2AlBr_3 + 3K_2SO_4 \longrightarrow 6KBr + 1Al_2(SO_4)_3\)
  • Equation 8: \(1C_3H_8 + 5O_2 \longrightarrow 3CO_2 + 4H_2O\)
  • Equation 9: \(1FeCl_3 + 3NaOH \longrightarrow 1Fe(OH)_3 + 3NaCl\)
  • All equations are balanced by equating the number of atoms of each element on both sides of the reaction. The coefficients are \(\boxed{1,2,2,1; 2,3,6,1; 1,5,3,4; 1,3,1,3}\).

Explanation

  1. Analysis and Methodology

To balance a chemical equation, we must ensure that the law of conservation of mass is satisfied, meaning the number of atoms for each element must be equal on both the reactant and product sides. We will determine the smallest integer coefficients for equations 6 through 9 by treating them as systems of linear equations based on atom counts. Equations 1 through 5 are already given as balanced.

  1. Balancing Equation 6

For equation (6) \(Pb(OH)_2 + HCl \longrightarrow H_2O + PbCl_2\):

  • Lead (Pb): \(1 \text{ atom on left} = 1 \text{ on right}\)
  • Oxygen (O): \(2 \text{ atoms on left} = 1 \text{ on right} \rightarrow\) balance with \(2 H_2O\)
  • Hydrogen (H): \(2 + 1 = 3 \text{ on left} = 4 \text{ on right} \rightarrow\) adjust \(HCl\) to \(2 HCl\), making H count \(2+2=4\) on left and \(4\) on right.
  • Chlorine (Cl): \(2 \text{ atoms on left} = 2 \text{ on right}\)

The balanced equation is: \(1Pb(OH)_2 + 2HCl \longrightarrow 2H_2O + 1PbCl_2\)

  1. Balancing Equation 7

For equation (7) \(AlBr_3 + K_2SO_4 \longrightarrow KBr + Al_2(SO_4)_3\):

  • Aluminum (Al): \(1 \text{ on left} = 2 \text{ on right} \rightarrow\) adjust \(AlBr_3\) to \(2AlBr_3\)
  • Bromine (Br): \(2 \times 3 = 6 \text{ on left} = 1 \text{ on right} \rightarrow\) adjust \(KBr\) to \(6KBr\)
  • Sulfate (\(SO_4\)): \(1 \text{ on left} = 3 \text{ on right} \rightarrow\) adjust \(K_2SO_4\) to \(3K_2SO_4\)
  • Potassium (K): \(3 \times 2 = 6 \text{ on left} = 6 \text{ on right}\)

The balanced equation is: \(2AlBr_3 + 3K_2SO_4 \longrightarrow 6KBr + 1Al_2(SO_4)_3\)

  1. Balancing Equation 8

For equation (8) \(C_3H_8 + O_2 \longrightarrow CO_2 + H_2O\):

  • Carbon (C): \(3 \text{ on left} = 1 \text{ on right} \rightarrow\) adjust \(CO_2\) to \(3CO_2\)
  • Hydrogen (H): \(8 \text{ on left} = 2 \text{ on right} \rightarrow\) adjust \(H_2O\) to \(4H_2O\)
  • Oxygen (O): \(2 \text{ on left} = (3 \times 2) + 4 = 10 \text{ on right} \rightarrow\) adjust \(O_2\) to \(5O_2\)

The balanced equation is: \(1C_3H_8 + 5O_2 \longrightarrow 3CO_2 + 4H_2O\)

  1. Balancing Equation 9

For equation (9) \(FeCl_3 + NaOH \longrightarrow Fe(OH)_3 + NaCl\):

  • Iron (Fe): \(1 \text{ on left} = 1 \text{ on right}\)
  • Chlorine (Cl): \(3 \text{ on left} = 1 \text{ on right} \rightarrow\) adjust \(NaCl\) to \(3NaCl\)
  • Sodium (Na): \(1 \text{ on left} = 3 \text{ on right} \rightarrow\) adjust \(NaOH\) to \(3NaOH\)
  • Hydroxide (OH): \(3 \text{ on left} = 3 \text{ on right}\)

The balanced equation is: \(1FeCl_3 + 3NaOH \longrightarrow 1Fe(OH)_3 + 3NaCl\)

Examples

Chemical balancing is essential in industrial processes, such as the production of pharmaceuticals or fuels, where precise quantities of reactants must be used to ensure efficiency and minimize waste. For example, by balancing the combustion equation for propane (\(C_3H_8 + 5O_2 \longrightarrow 3CO_2 + 4H_2O\)), an engineer knows exactly how much oxygen is required for complete combustion, preventing the formation of carbon monoxide and ensuring optimal energy release. Understanding these proportions is fundamental for any chemical or environmental calculation involving reaction stoichiometry.