To determine the correct formula for the compound formed by a metal ion [tex]\( X \)[/tex] with a charge of [tex]\( +3 \)[/tex] and a nonmetal ion [tex]\( Z \)[/tex] with a charge of [tex]\( -4 \)[/tex], we need to balance the total positive and negative charges so that the net charge of the compound is zero. Here are the detailed steps:
1. Identify the charges:
- Metal ion [tex]\( X \)[/tex] has a charge of [tex]\( +3 \)[/tex].
- Nonmetal ion [tex]\( Z \)[/tex] has a charge of [tex]\( -4 \)[/tex].
2. Find the least common multiple (LCM) of the charges:
- The least common multiple of 3 and 4 is 12. This means we need to balance the positive and negative charges to both equal 12.
3. Determine the number of ions needed to balance the charges:
- To get a total positive charge of 12:
- We need 4 [tex]\( X \)[/tex] ions because [tex]\( 4 \times 3 = 12 \)[/tex].
- To get a total negative charge of 12:
- We need 3 [tex]\( Z \)[/tex] ions because [tex]\( 3 \times 4 = 12 \)[/tex].
4. Combine the ions to form a neutral compound:
- Therefore, the correct formula will have 4 [tex]\( X \)[/tex] ions and 3 [tex]\( Z \)[/tex] ions.
The resulting formula that keeps the compound electrically neutral is [tex]\( X_4 Z_3 \)[/tex].
So, the correct answer is:
B. [tex]\( X_4 Z_3 \)[/tex]
