Answer :

Let's fill in the blanks given the charge of copper and the type of reaction involved.

First, understand that this is a single displacement reaction, where copper (Cu) displaces silver (Ag) from silver nitrate (AgNO[tex]\(_3\)[/tex]). We need to identify the products of this reaction and ensure the equation is balanced.

1. Identify the reactants and the type of reaction:
- Reactants: [tex]\( Cu \)[/tex] and [tex]\( AgNO_3 \)[/tex]
- Reaction Type: Single displacement

2. Determine the products:
- Copper (Cu) displaces silver (Ag), so silver (Ag) will be produced as a product.
- The remaining part of the silver nitrate (NO[tex]\(_3\)[/tex]) will combine with copper (Cu).

3. Copper nitrate formation:
- Copper has a charge of [tex]\( 2+ \)[/tex].
- Nitrate (NO[tex]\(_3\)[/tex]) has a charge of [tex]\( 1- \)[/tex].
- To balance the charges, one copper ion will combine with two nitrate ions to form copper(II) nitrate, which is [tex]\( Cu(NO_3)_2 \)[/tex].

4. Write the unbalanced equation:
[tex]\[ Cu + AgNO_3 \rightarrow Ag + Cu(NO_3)_2 \][/tex]

5. Balance the chemical equation:
- Check the number of atoms of each element on both sides of the equation.
- Here, there are two nitrate ions on the product side because of [tex]\( Cu(NO_3)_2 \)[/tex]. But there is only one nitrate ion on the reactant side as [tex]\( AgNO_3 \)[/tex].
- To balance the nitride (NO[tex]\(_3\)[/tex]), we place a coefficient of 2 in front of [tex]\( AgNO_3 \)[/tex].

The balanced equation is:
[tex]\[ Cu + 2AgNO_3 \rightarrow 2Ag + Cu(NO_3)_2 \][/tex]

So, the completed and balanced reaction is:

[tex]\[ Cu + 2AgNO_3 \rightarrow 2Ag + Cu(NO_3)_2 \][/tex]

Hence, the final filled-in result is:

[tex]\[ Cu + 2AgNO_3 \rightarrow 2Ag + Cu(NO_3)_2 \][/tex]