To determine which chemical equation is correctly balanced, we need to ensure that the number of atoms of each element on the reactant side (left side) is equal to the number of atoms of the same element on the product side (right side).
Let's examine each option one by one:
### A. [tex]\( Na_2CO_3 \rightarrow NaCl + 3 O_2 \)[/tex]
- Reactant side:
- [tex]\( Na \)[/tex]: 2 atoms
- [tex]\( C \)[/tex]: 1 atom
- [tex]\( O \)[/tex]: 3 atoms
- Product side:
- [tex]\( Na \)[/tex]: 1 atom
- [tex]\( Cl \)[/tex]: 1 atom
- [tex]\( O \)[/tex]: 6 atoms
This equation is not balanced as the number of atoms of sodium (Na), carbon (C), and oxygen (O) differ on both sides.
### B. [tex]\( 2 HgO \rightarrow 2 Hg + O_2 \)[/tex]
- Reactant side:
- [tex]\( Hg \)[/tex]: 2 atoms
- [tex]\( O \)[/tex]: 2 atoms (from [tex]\( HgO \)[/tex])
- Product side:
- [tex]\( Hg \)[/tex]: 2 atoms
- [tex]\( O \)[/tex]: 2 atoms (from [tex]\( O_2 \)[/tex])
This equation has equal numbers of mercury (Hg) and oxygen (O) atoms on both sides, meaning it is balanced.
### C. [tex]\( 2 ZnS + O_2 \rightarrow 2 ZnO + 2 SO_2 \)[/tex]
- Reactant side:
- [tex]\( Zn \)[/tex]: 2 atoms
- [tex]\( S \)[/tex]: 2 atoms
- [tex]\( O \)[/tex]: 2 atoms
- Product side:
- [tex]\( Zn \)[/tex]: 2 atoms
- [tex]\( S \)[/tex]: 2 atoms
- [tex]\( O \)[/tex]: 6 atoms (2 from ZnO and 4 from 2 [tex]\(SO_2\)[/tex])
This equation is not balanced as the number of oxygen atoms differs on both sides.
### D. [tex]\( 4 CO + Fe_3O_4 \rightarrow 4 CO_2 + Fe \)[/tex]
- Reactant side:
- [tex]\( C \)[/tex]: 4 atoms
- [tex]\( O \)[/tex]: 8 atoms (4 from CO and 4 from [tex]\( Fe_3O_4 \)[/tex])
- [tex]\( Fe \)[/tex]: 3 atoms
- Product side:
- [tex]\( C \)[/tex]: 4 atoms
- [tex]\( O \)[/tex]: 8 atoms (4 from [tex]\( CO_2 \)[/tex])
- [tex]\( Fe \)[/tex]: 1 atom
This equation is not balanced as the number of iron (Fe) atoms differs on both sides.
### E. [tex]\( 2 Fe + 2 Cl_2 \rightarrow 2 FeCl_3 \)[/tex]
- Reactant side:
- [tex]\( Fe \)[/tex]: 2 atoms
- [tex]\( Cl \)[/tex]: 4 atoms
- Product side:
- [tex]\( Fe \)[/tex]: 2 atoms
- [tex]\( Cl \)[/tex]: 6 atoms
This equation is not balanced as the number of chlorine (Cl) atoms differs on both sides.
Reviewing the equations, we can see that option B. [tex]\( 2 HgO \rightarrow 2 Hg + O_2 \)[/tex] is the only correctly balanced equation.
Therefore, the correctly balanced equation is:
[tex]\[ \boxed{2 HgO \rightarrow 2 Hg + O_2} \][/tex]
