5. [tex]FeCl_3(aq)[/tex] undergoes a double displacement reaction with [tex]Ba(OH)_2(aq)[/tex]. If the reaction produces a solid product containing iron and the other product is in an aqueous solution, what is the balanced chemical equation for this reaction? Briefly explain how to arrive at the balanced reaction equation.

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29-07-2024
Chemistry

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5. [tex]FeCl_3(aq)[/tex] undergoes a double displacement reaction with [tex]Ba(OH)_2(aq)[/tex]. If the reaction produces a solid product containing iron and the other product is in an aqueous solution, what is the balanced chemical equation for this reaction? Briefly explain how to arrive at the balanced reaction equation.

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GinnyAnswer GinnyAnswer · Answer 1 · 2024-07-29T15:25:03-04:00

To balance the chemical equation for the reaction between [tex]\( FeCl_3(aq) \)[/tex] and [tex]\( Ba(OH)_2(aq) \)[/tex], we need to follow a systematic approach.

### Step-by-Step Solution:
1. Write down the reactants and products based on the reaction description:

Reactants:
[tex]\[ FeCl_3(aq) \][/tex]
[tex]\[ Ba(OH)_2(aq) \][/tex]

Products (based on double displacement reaction):
[tex]\[ Fe(OH)_3(s) \][/tex] (Solid product containing iron)
[tex]\[ BaCl_2(aq) \][/tex] (Aqueous product)

2. Write the unbalanced chemical equation, showing the double displacement:
[tex]\[ FeCl_3(aq) + Ba(OH)_2(aq) \rightarrow Fe(OH)_3(s) + BaCl_2(aq) \][/tex]

3. Identify the number of each type of atom on both sides of the equation:

- Left Side (Reactants):
- [tex]\( Fe: 1 \)[/tex]
- [tex]\( Cl: 3 \)[/tex]
- [tex]\( Ba: 1 \)[/tex]
- [tex]\( O: 2 \)[/tex]
- [tex]\( H: 2 \)[/tex]

- Right Side (Products):
- [tex]\( Fe: 1 \)[/tex]
- [tex]\( OH: 3 \)[/tex] (or [tex]\( O: 3 \)[/tex] and [tex]\( H: 3 \)[/tex])
- [tex]\( Ba: 1 \)[/tex]
- [tex]\( Cl: 2 \)[/tex]

4. Balance the chlorine atoms (Cl):
Since there are 3 chlorine atoms on the left side and only 2 on the right side, we need to balance the chlorine by increasing the number of [tex]\( BaCl_2 \)[/tex] molecules on the right side. To do this, multiply [tex]\( BaCl_2 \)[/tex] by 3:
[tex]\[ FeCl_3 + Ba(OH)_2 \rightarrow Fe(OH)_3 + 3BaCl_2 \][/tex]

5. Recalculate the number of atoms after increasing [tex]\( BaCl_2 \)[/tex] to 3:

- Left Side (Reactants):
- [tex]\( Fe: 1 \)[/tex]
- [tex]\( Cl: 3 \)[/tex]
- [tex]\( Ba: 1 \)[/tex]
- [tex]\( O: 2 \)[/tex]
- [tex]\( H: 2 \)[/tex]

- Right Side (Products):
- [tex]\( Fe: 1 \)[/tex]
- [tex]\( OH: 3 \)[/tex] (or [tex]\( O: 3 \)[/tex] and [tex]\( H: 3 \)[/tex]
- [tex]\( Ba: 3 \)[/tex]
- [tex]\( Cl: 6 \)[/tex]

6. Balance the barium atoms (Ba):
There are 3 barium atoms on the right side and only 1 on the left side. Balance the barium atoms by multiplying [tex]\( Ba(OH)_2 \)[/tex] by 3:
[tex]\[ FeCl_3 + 3Ba(OH)_2 \rightarrow Fe(OH)_3 + 3BaCl_2 \][/tex]

7. Recheck the number of atoms after making these adjustments:

- Left Side (Reactants):
- [tex]\( Fe: 1 \)[/tex]
- [tex]\( Cl: 3 \)[/tex]
- [tex]\( Ba: 3 \)[/tex]
- [tex]\( O: 6 \)[/tex]
- [tex]\( H: 6 \)[/tex]

- Right Side (Products):
- [tex]\( Fe: 1 \)[/tex]
- [tex]\( OH: 3 \)[/tex] (or [tex]\( O: 3 \)[/tex] and [tex]\( H: 3 \)[/tex]
- [tex]\( Ba: 3 \)[/tex]
- [tex]\( Cl: 6 \)[/tex]

Now, our equation is balanced in terms of all the atoms.

### Balanced Chemical Equation:
[tex]\[ FeCl_3(aq) + 3Ba(OH)_2(aq) \rightarrow Fe(OH)_3(s) + 3BaCl_2(aq) \][/tex]

This is the balanced chemical equation indicating that [tex]\(1\)[/tex] mole of iron(III) chloride reacts with [tex]\(3\)[/tex] moles of barium hydroxide to produce [tex]\(1\)[/tex] mole of iron(III) hydroxide and [tex]\(3\)[/tex] moles of barium chloride.