To determine the correct formula unit for a compound made from [tex]\( Pb^{4+} \)[/tex] and oxygen, follow these steps:
1. Identify the ions involved:
- Lead ion: [tex]\( Pb^{4+} \)[/tex]
- Oxygen ion: [tex]\( O^{2-} \)[/tex]
2. Determine the charges on the ions:
- A lead ion has a charge of [tex]\( +4 \)[/tex].
- An oxygen ion has a charge of [tex]\( -2 \)[/tex].
3. Balance the charges:
- To balance the charges in the formula unit, the total positive charge must equal the total negative charge.
- For [tex]\( Pb^{4+} \)[/tex], we have a charge of [tex]\( +4 \)[/tex].
- For [tex]\( O^{2-} \)[/tex], we need enough oxygen ions to match the [tex]\( +4 \)[/tex] charge of the lead ion.
- Since each [tex]\( O^{2-} \)[/tex] ion has a [tex]\( -2 \)[/tex] charge, and [tex]\( Pb^{4+} \)[/tex] needs to balance a [tex]\( +4 \)[/tex] charge, we need 2 oxygen ions.
[tex]\[
2 \times (-2) = -4
\][/tex]
- The two [tex]\( O^{2-} \)[/tex] ions will provide a total charge of [tex]\( -4 \)[/tex], which balances the [tex]\( +4 \)[/tex] charge of one [tex]\( Pb^{4+} \)[/tex] ion.
4. Write the formula unit:
- Combining the balanced charges, one [tex]\( Pb^{4+} \)[/tex] ion pairs with two [tex]\( O^{2-} \)[/tex] ions.
- The resulting formula unit is [tex]\( PbO_2 \)[/tex].
5. Verify with the provided options:
- The correct formula unit is [tex]\( PbO_2 \)[/tex], which corresponds to option 1.
Thus, the formula unit for a compound made from [tex]\( Pb^{4+} \)[/tex] and oxygen is:
[tex]\[
\boxed{PbO_2}
\][/tex]
