To balance the chemical equation [tex]\( \text{FeCl}_3 + \text{NaOH} \rightarrow \text{Fe(OH)}_3 + \text{NaCl} \)[/tex], we need to ensure that the number of atoms of each element on the reactants side is equal to the number on the products side. Here is the step-by-step solution:
1. Write the unbalanced equation:
[tex]\[
\text{FeCl}_3 + \text{NaOH} \rightarrow \text{Fe(OH)}_3 + \text{NaCl}
\][/tex]
2. Identify the number of atoms of each element in the reactants and products:
- Reactants:
- Fe: 1
- Cl: 3
- Na: 1
- O: 1
- H: 1
- Products:
- Fe: 1
- Cl: 1
- Na: 1
- O: 3
- H: 3
3. Balance the elements one by one, starting with the metal (Fe):
- Fe: 1 Fe atom on both sides (already balanced)
4. Balance the chlorine (Cl) atoms:
- Reactants: 3 Cl atoms in [tex]\(\text{FeCl}_3\)[/tex]
- Products: 1 Cl atom in [tex]\(\text{NaCl}\)[/tex]
- To balance Cl, we need 3 [tex]\(\text{NaCl}\)[/tex] on the products side:
[tex]\[
\text{FeCl}_3 + \text{NaOH} \rightarrow \text{Fe(OH)}_3 + 3\text{NaCl}
\][/tex]
5. Next, balance the sodium (Na) atoms:
- Reactants: 1 Na atom in [tex]\(\text{NaOH}\)[/tex]
- Products: 3 Na atoms in [tex]\(3\text{NaCl}\)[/tex]
- To balance Na, we need 3 [tex]\(\text{NaOH}\)[/tex] on the reactants side:
[tex]\[
\text{FeCl}_3 + 3\text{NaOH} \rightarrow \text{Fe(OH)}_3 + 3\text{NaCl}
\][/tex]
6. Balance the oxygen (O) and hydrogen (H) atoms:
- Reactants: [tex]\(3 \text{NaOH}\)[/tex] provides 3 O atoms and 3 H atoms
- Products: [tex]\(\text{Fe(OH)}_3\)[/tex] has 3 O atoms and 3 H atoms
- With 3 [tex]\(\text{NaOH}\)[/tex], both O and H are balanced
Thus, the balanced chemical equation is:
[tex]\[
\text{FeCl}_3 + 3\text{NaOH} \rightarrow \text{Fe(OH)}_3 + 3\text{NaCl}
\][/tex]
Summary:
- Reactants: 1 [tex]\(\text{FeCl}_3\)[/tex], 3 [tex]\(\text{NaOH}\)[/tex]
- Products: 1 [tex]\(\text{Fe(OH)}_3\)[/tex], 3 [tex]\(\text{NaCl}\)[/tex]
We have ensured that the equation is balanced with 1 molecule of [tex]\(\text{FeCl}_3\)[/tex] and 3 molecules of [tex]\(\text{NaOH}\)[/tex] reacting to produce 1 molecule of [tex]\(\text{Fe(OH)}_3\)[/tex] and 3 molecules of [tex]\(\text{NaCl}\)[/tex].
