Sure, let's discuss the sulfate ion [tex]\( \text{SO}_4^{2-} \)[/tex] in detail, focusing on the valence electrons and formal charges.
### Step-by-Step Solution:
1. Identify the Valence Electrons:
- Sulfur (S) is in Group 16 of the periodic table, which means it has 6 valence electrons.
- Oxygen (O) is also in Group 16, so each oxygen atom has 6 valence electrons.
2. Total Valence Electrons Calculation:
- Sulfur contributes 6 valence electrons.
- Each of the 4 oxygen atoms contributes 6 valence electrons, totaling [tex]\( 4 \times 6 = 24 \)[/tex] valence electrons.
- The sulfate ion carries a [tex]\( 2- \)[/tex] charge, meaning it has 2 additional electrons.
- Summing these contributions results in:
[tex]\[
6 (\text{from S}) + 24 (\text{from O}) + 2 (\text{extra electrons}) = 32 \text{ total valence electrons}
\][/tex]
3. Structure of Sulfate Ion:
- Sulfate ion [tex]\( \text{SO}_4^{2-} \)[/tex] is typically represented with sulfur at the center and four oxygen atoms surrounding it.
- Two of the oxygen atoms are double-bonded to sulfur, while the other two oxygen atoms are single-bonded to sulfur.
4. Formal Charges:
- Formal charge is calculated using the formula:
[tex]\[
\text{Formal charge} = \text{Valence electrons} - (\text{Non-bonding electrons} + \frac{1}{2} \times \text{Bonding electrons})
\][/tex]
- Sulfur:
- Sulfur forms four bonds: two double bonds (counting 4 electrons each) and two single bonds (counting 2 electrons each).
- Total electrons for sulfur: 0 non-bonding, 12 bonding.
- Formal charge: [tex]\( 6 - (0 + \frac{1}{2} \times 12) = 6 - 6 = 0 \)[/tex].
- Double-bonded Oxygens:
- Each oxygen has 4 non-bonding electrons and shares 4 electrons in the double bond.
- Formal charge: [tex]\( 6 - (4 + \frac{1}{2} \times 4) = 6 - 6 = 0 \)[/tex].
- Single-bonded Oxygens:
- Each oxygen has 6 non-bonding electrons and shares 2 electrons in the single bond.
- Formal charge: [tex]\( 6 - (6 + \frac{1}{2} \times 2) = 6 - 7 = -1 \)[/tex].
5. Summary of Formal Charges:
- Sulfur: 0
- Double-bonded oxygens (2): 0 each
- Single-bonded oxygens (2): -1 each
### Conclusion:
- The overall structure of the sulfate ion [tex]\( \text{SO}_4^{2-} \)[/tex]:
- Total valence electrons: 32
- Formal charges: Sulfur: 0, Oxygen (double-bonded): 0 each, Oxygen (single-bonded): -1 each
These results ensure the sulfate ion is stable with minimized formal charges distributed accordingly.
