To solve the problem of determining the formula unit for a compound made from [tex]\( Fe^{3+} \)[/tex] and oxygen, let’s follow these steps:
1. Identify the Charges:
- The iron (Fe) ion has a charge of +3, denoted as [tex]\( Fe^{3+} \)[/tex].
- The oxygen (O) ion typically has a charge of -2, denoted as [tex]\( O^{2-} \)[/tex].
2. Balance the Charges:
- To form a stable ionic compound, the total charge must be zero.
- We need to balance the positive charge from the iron ions with the negative charge from the oxygen ions.
3. Determine the Ratio of Ions:
- Since [tex]\( Fe^{3+} \)[/tex] has a +3 charge and [tex]\( O^{2-} \)[/tex] has a -2 charge, we need to find the smallest ratio of ions that results in a net charge of zero.
- We calculate the least common multiple (LCM) of the charges (3 and 2), which is 6. This means we need 6 positive charges to balance 6 negative charges.
4. Calculate the Number of Ions Needed:
- To get 6 positive charges, we need 2 [tex]\( Fe^{3+} \)[/tex] ions (because [tex]\( 2 \times 3 = 6 \)[/tex]).
- To get 6 negative charges, we need 3 [tex]\( O^{2-} \)[/tex] ions (because [tex]\( 3 \times -2 = -6 \)[/tex]).
5. Formula Unit:
- Combining these ions in the ratio needed to balance the charges, we get [tex]\( Fe_2O_3 \)[/tex].
So, the formula unit for a compound made from [tex]\( Fe^{3+} \)[/tex] and oxygen is:
[tex]\[ Fe_2O_3 \][/tex]
Matching Question:
- A nonmetal that gained two electrons is typically written as [tex]\( D^{2-} \)[/tex].
- Therefore, match: D [tex]$^{2-}$[/tex] - A) A nonmetal that gained two electrons
Summarizing:
- [tex]\( Fe_2O_3 \)[/tex] is the formula unit for the compound formed by [tex]\( Fe^{3+} \)[/tex] and oxygen.
Thus, for the multiple-choice question:
Correct Answer: [tex]\( Fe_2O_3 \)[/tex].
