To balance the chemical equation \( \text{Cu} + \text{Hg(NO}_3\text{)}_2 \rightarrow \text{Cu(NO}_3\text{)}_2 + \text{Hg} \), we first write out the unbalanced equation:
\[ \text{Cu} + \text{Hg(NO}_3\text{)}_2 \rightarrow \text{Cu(NO}_3\text{)}_2 + \text{Hg} \]
Next, identify the number of atoms of each element on both sides:
Reactants:
- Cu: 1
- Hg: 1
- N: 2 (from 2 \( \text{NO}_3 \))
- O: 6 (from 2 \( \text{NO}_3 \))
Products:
- Cu: 1 (from \( \text{Cu(NO}_3\text{)}_2 \))
- Hg: 1
- N: 2 (from \( \text{Cu(NO}_3\text{)}_2 \))
- O: 6 (from \( \text{Cu(NO}_3\text{)}_2 \))
Now, let's check for balance:
- Copper (Cu): 1 on both sides
- Mercury (Hg): 1 on both sides
- Nitrogen (N): 2 on both sides
- Oxygen (O): 6 on both sides
Since both sides have equal amounts of each element, the equation is already balanced.
Thus, the balanced equation is:
\[ \text{Cu} + \text{Hg(NO}_3\text{)}_2 \rightarrow \text{Cu(NO}_3\text{)}_2 + \text{Hg} \]