To determine which of the given equations is correctly balanced, we need to count and verify the number of atoms of each element on both sides of the chemical equation:
(a) [tex]\( Fe + 2 O_2 + H_2O \rightarrow Fe_2O_3 \)[/tex]
- Reactants:
- [tex]\( Fe: 1 \)[/tex]
- [tex]\( O: 2 \times 2 + 1 = 5 \)[/tex]
- [tex]\( H: 2 \)[/tex]
- Products:
- [tex]\( Fe: 2 \)[/tex]
- [tex]\( O: 3 \)[/tex]
Clearly, this equation is not balanced because the number of atoms for iron (Fe), oxygen (O), and hydrogen (H) are not equal on both sides.
(b) [tex]\( CO_2 + Ca(OH)_2 \rightarrow CaCO_3 + H_2O \)[/tex]
- Reactants:
- [tex]\( C: 1 \)[/tex]
- [tex]\( O: 2 + 2 = 4 \)[/tex]
- [tex]\( H: 2 \)[/tex]
- [tex]\( Ca: 1 \)[/tex]
- Products:
- [tex]\( C: 1 \)[/tex]
- [tex]\( O: 3 + 1 = 4 \)[/tex]
- [tex]\( H: 2 \)[/tex]
- [tex]\( Ca: 1 \)[/tex]
This equation is balanced because each element has the same number of atoms on both sides.
(c) [tex]\( Mg + O_2 \rightarrow MgO + H_2O \)[/tex]
- Reactants:
- [tex]\( Mg: 1 \)[/tex]
- [tex]\( O: 2 \)[/tex]
- Products:
- [tex]\( Mg: 1 \)[/tex]
- [tex]\( O: 1 + 1 = 2 \)[/tex]
- [tex]\( H: 2 \)[/tex]
This equation is not correct because it has hydrogen atoms on the product side that are not balanced with any hydrogen atoms on the reactant side.
(d) [tex]\( 2 CuSO_4 + Fe \rightarrow Fe(SO_4)_2 + 2 Cu \)[/tex]
- Reactants:
- [tex]\( Cu: 2 \)[/tex]
- [tex]\( S: 2 \)[/tex]
- [tex]\( O: 8 \)[/tex]
- [tex]\( Fe: 1 \)[/tex]
- Products:
- [tex]\( Cu: 2 \)[/tex]
- [tex]\( S: 2 \)[/tex]
- [tex]\( O: 8 \)[/tex]
- [tex]\( Fe: 1 \)[/tex]
This equation is also not balanced as it misrepresents how iron sulfate should form and should not be written as [tex]\( Fe(SO_4)_2 \)[/tex].
After analyzing all the options, we find that the only correctly balanced equation is:
(b) [tex]\( CO_2 + Ca(OH)_2 \rightarrow CaCO_3 + H_2O \)[/tex]
Thus, the correct and balanced equation is option (b).
