To determine the correct formula for a compound formed by the ions [tex]\( \text{Al}^{+3} \)[/tex] (aluminum ion) and [tex]\( \text{CO}_3^{-2} \)[/tex] (carbonate ion), we need to balance the charges of the cations and anions. Here's a step-by-step explanation of how to do this:
1. Identify the charges on the ions:
- Aluminum ion ([tex]\( \text{Al}^{+3} \)[/tex]) has a charge of +3.
- Carbonate ion ([tex]\( \text{CO}_3^{-2} \)[/tex]) has a charge of -2.
2. Determine the total charge balance needed:
- We need to combine the ions in such a way that the overall charge of the compound is neutral (net charge = 0).
3. Find the smallest common multiple of the charges:
- The charges are +3 for [tex]\( \text{Al}^{+3} \)[/tex] and -2 for [tex]\( \text{CO}_3^{-2} \)[/tex]. To balance these charges, we need to find the least common multiple of 3 and 2, which is 6.
4. Calculate the number of each ion required to achieve charge neutrality:
- To get a total positive charge of +6, we need 2 aluminum ions: [tex]\( 2 \times (\text{Al}^{+3}) = 2 \times 3 = +6 \)[/tex].
- To get a total negative charge of -6, we need 3 carbonate ions: [tex]\( 3 \times (\text{CO}_3^{-2}) = 3 \times (-2) = -6 \)[/tex].
5. Combine the ions in the correct ratio:
- Combine 2 aluminum ions ([tex]\( \text{Al}^{+3} \)[/tex]) with 3 carbonate ions ([tex]\( \text{CO}_3^{-2} \)[/tex]) to create a neutral compound.
6. Write the chemical formula:
- Since we have 2 [tex]\( \text{Al}^{+3} \)[/tex] ions and 3 [tex]\( \text{CO}_3^{-2} \)[/tex] ions, the formula of the compound is [tex]\( \text{Al}_2(\text{CO}_3)_3 \)[/tex].
Thus, the correct formula for the compound formed by the ionic species [tex]\( \text{Al}^{+3} \)[/tex] and [tex]\( \text{CO}_3^{-2} \)[/tex] is:
[tex]\[ \boxed{\text{Al}_2(\text{CO}_3)_3} \][/tex]
