To determine which reaction is balanced, we need to compare the total charges on the reactants' side and the products' side. Let's examine each option:
Option A:
[tex]\[ Sn ^{2+} + Fe ^{3+} \rightarrow Sn ^{4+} + Fe ^{2+} \][/tex]
- Reactants:
- [tex]\( Sn ^{2+} \)[/tex] has a charge of [tex]\( +2 \)[/tex].
- [tex]\( Fe ^{3+} \)[/tex] has a charge of [tex]\( +3 \)[/tex].
- Total charge on reactants' side: [tex]\( 2 + 3 = +5 \)[/tex].
- Products:
- [tex]\( Sn ^{4+} \)[/tex] has a charge of [tex]\( +4 \)[/tex].
- [tex]\( Fe ^{2+} \)[/tex] has a charge of [tex]\( +2 \)[/tex].
- Total charge on products' side: [tex]\( 4 + 2 = +6 \)[/tex].
The charges are not balanced. This option is not correct.
Option B:
[tex]\[ 2 Sn ^{2+} + Fe ^{3+} \rightarrow 2 Sn ^{4+} + Fe ^{2+} \][/tex]
- Reactants:
- [tex]\( 2 Sn ^{2+} \)[/tex] each with a charge of [tex]\( +2 \)[/tex]: [tex]\( 2 \times +2 = +4 \)[/tex].
- [tex]\( Fe ^{3+} \)[/tex] has a charge of [tex]\( +3 \)[/tex].
- Total charge on reactants' side: [tex]\( 4 + 3 = +7 \)[/tex].
- Products:
- [tex]\( 2 Sn ^{4+} \)[/tex] each with a charge of [tex]\( +4 \)[/tex]: [tex]\( 2 \times +4 = +8 \)[/tex].
- [tex]\( Fe ^{2+} \)[/tex] has a charge of [tex]\( +2 \)[/tex].
- Total charge on products' side: [tex]\( 8 + 2 = +10 \)[/tex].
The charges are not balanced. This option is not correct.
Option C:
[tex]\[ Sn ^{2+} + 2 Fe ^{3+} \rightarrow Sn ^{4+} + Fe ^{2+} \][/tex]
- Reactants:
- [tex]\( Sn ^{2+} \)[/tex] has a charge of [tex]\( +2 \)[/tex].
- [tex]\( 2 Fe ^{3+} \)[/tex] each with a charge of [tex]\( +3 \)[/tex]: [tex]\( 2 \times +3 = +6 \)[/tex].
- Total charge on reactants' side: [tex]\( 2 + 6 = +8 \)[/tex].
- Products:
- [tex]\( Sn ^{4+} \)[/tex] has a charge of [tex]\( +4 \)[/tex].
- [tex]\( Fe ^{2+} \)[/tex] has a charge of [tex]\( +2 \)[/tex].
- Total charge on products' side: [tex]\( 4 + 2 = +6 \)[/tex].
The charges are not balanced. This option is not correct.
Option D:
[tex]\[ Sn ^{2+} + 2 Fe ^{3+} \rightarrow Sn ^{4+} + 2 Fe ^{2+} \][/tex]
- Reactants:
- [tex]\( Sn ^{2+} \)[/tex] has a charge of [tex]\( +2 \)[/tex].
- [tex]\( 2 Fe ^{3+} \)[/tex] each with a charge of [tex]\( +3 \)[/tex]: [tex]\( 2 \times +3 = +6 \)[/tex].
- Total charge on reactants' side: [tex]\( 2 + 6 = +8 \)[/tex].
- Products:
- [tex]\( Sn ^{4+} \)[/tex] has a charge of [tex]\( +4 \)[/tex].
- [tex]\( 2 Fe ^{2+} \)[/tex] each with a charge of [tex]\( +2 \)[/tex]: [tex]\( 2 \times +2 = +4 \)[/tex].
- Total charge on products' side: [tex]\( 4 + 4 = +8 \)[/tex].
The charges are balanced. Therefore, option D is correct.
Thus, the balanced reaction is:
[tex]\[ \boxed{D) \: Sn ^{2+} + 2 Fe ^{3+} \rightarrow Sn ^{4+} + 2 Fe ^{2+}} \][/tex]
