To balance the chemical equation \( \text{Al}_2(\text{CO}_3)_3 \rightarrow \text{Al}_2\text{O}_3 + \ldots \text{CO}_2 \), follow these steps:
First, count the number of aluminum, carbon, and oxygen atoms on both sides of the equation. On the left, we have 2 aluminum (Al), 3 carbonate groups (CO\(_3\)) which consist of 3 carbon (C) and 9 oxygen (O) atoms. On the right, we see 2 aluminum (Al) in Al\(_2\)O\(_3\), and we need to determine the coefficients for the products to balance the atoms.
To balance, start with aluminum; it is already balanced with 2 atoms on each side. Next, balance carbon by using the coefficient 3 for CO\(_2\) on the product side, since there are 3 carbons from the carbonate groups originally. This gives us 3 CO\(_2\), which also balances the 9 oxygen atoms on the product side, as \(\text{Al}_2\text{O}_3\) contains 3 oxygens and 3 CO\(_2\) contains 6 oxygens, summing to 9.
The balanced chemical equation is:
[tex]\[ \text{Al}_2(\text{CO}_3)_3 \rightarrow \text{Al}_2\text{O}_3 + 3 \text{CO}_2 \][/tex]
This equation represents a decomposition reaction, where a single compound breaks down into two or more simpler substances.
