Math

QuestionBalancing chemical equations with interfering coemicents
Balance the chemical equation below using the smallest possible whole number stoichiometric coefficients. Fe(s)+O2(g)+H2O(l)Fe(OH)2(aq)\mathrm{Fe}(s)+\mathrm{O}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) \rightarrow \mathrm{Fe}(\mathrm{OH})_{2}(a q)

Studdy Solution

STEP 1

1. The chemical equation involves iron (Fe), oxygen (O2 \mathrm{O}_2 ), and water (H2O \mathrm{H}_2\mathrm{O} ) as reactants, and iron(II) hydroxide (Fe(OH)2 \mathrm{Fe(OH)}_2 ) as the product.
2. The goal is to balance the equation by ensuring the same number of each type of atom on both sides of the equation.

STEP 2

1. Identify the number of atoms for each element in the unbalanced equation.
2. Balance the equation by adjusting coefficients, starting with the most complex molecule.
3. Verify that all elements are balanced.

STEP 3

Identify the number of atoms for each element in the unbalanced equation:
- Reactants: - Fe \mathrm{Fe} : 1 atom - O2 \mathrm{O}_2 : 2 atoms of O - H2O \mathrm{H}_2\mathrm{O} : 2 atoms of H, 1 atom of O
- Products: - Fe(OH)2 \mathrm{Fe(OH)}_2 : 1 atom of Fe, 2 atoms of O, 2 atoms of H

STEP 4

Balance the equation by adjusting coefficients. Start with the most complex molecule, Fe(OH)2 \mathrm{Fe(OH)}_2 .
- Balance Fe: - There is 1 Fe atom on both sides, so Fe is already balanced.
- Balance O and H: - In Fe(OH)2 \mathrm{Fe(OH)}_2 , there are 2 O atoms and 2 H atoms. - We need 1 molecule of O2 \mathrm{O}_2 and 2 molecules of H2O \mathrm{H}_2\mathrm{O} to provide the necessary O and H atoms.
Adjust coefficients: Fe(s)+12O2(g)+H2O(l)Fe(OH)2(aq) \mathrm{Fe}(s) + \frac{1}{2}\mathrm{O}_2(g) + \mathrm{H}_2\mathrm{O}(l) \rightarrow \mathrm{Fe(OH)}_2(aq)

STEP 5

To eliminate fractional coefficients, multiply all coefficients by 2 to obtain whole numbers:
2Fe(s)+O2(g)+2H2O(l)2Fe(OH)2(aq) 2\mathrm{Fe}(s) + \mathrm{O}_2(g) + 2\mathrm{H}_2\mathrm{O}(l) \rightarrow 2\mathrm{Fe(OH)}_2(aq)

STEP 6

Verify that all elements are balanced:
- Fe: 2 atoms on both sides - O: 4 atoms on both sides (2 from O2 \mathrm{O}_2 and 2 from H2O \mathrm{H}_2\mathrm{O} ) - H: 4 atoms on both sides (from 2 H2O \mathrm{H}_2\mathrm{O} )
All elements are balanced.
The balanced chemical equation is:
2Fe(s)+O2(g)+2H2O(l)2Fe(OH)2(aq) 2\mathrm{Fe}(s) + \mathrm{O}_2(g) + 2\mathrm{H}_2\mathrm{O}(l) \rightarrow 2\mathrm{Fe(OH)}_2(aq)

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