Let's analyze the chemical equation given:
[tex]\[ 3 Cu + 8 HNO_3 \rightarrow 3 Cu(NO_3)_2 + 2 NO + 4 H_2O \][/tex]
We need to determine the number of nitrate ions (\(\text{NO}_3\)) on the products side of the reaction.
First, we focus on the product \( \text{Cu(NO}_3\text{)}_2 \):
- Each molecule of \( \text{Cu(NO}_3\text{)}_2 \) contains 2 nitrate ions (\(\text{NO}_3\)).
Given in the equation, there are 3 molecules of \( \text{Cu(NO}_3\text{)}_2 \):
- So, each of these 3 molecules has 2 \(\text{NO}_3\) ions.
To find the total number of nitrate ions on the products side, multiply the number of \(\text{NO}_3\) ions in one molecule by the number of these molecules:
[tex]\[
3 \text{ molecules} \times 2 \text{ NO}_3 \text{ per molecule} = 6 \text{ NO}_3
\][/tex]
Thus, the total number of [tex]\(\text{NO}_3\)[/tex] ions on the products side is [tex]\(\boxed{6}\)[/tex].
