Here's how to determine the balanced equation for the reaction between silver (Ag) and mercurous nitrate (Hg₂(NO₃)₂):

1. Identify the Reactants and Products

* Reactants: Silver (Ag) and Mercurous Nitrate (Hg₂(NO₃)₂)

* Products: Silver Nitrate (AgNO₃) and Mercury (Hg)

2. Write the Unbalanced Equation

Ag + Hg₂(NO₃)₂ → AgNO₃ + Hg

3. Balance the Equation

* Balance the Mercury (Hg) atoms: There are 2 Hg atoms on the left and 1 on the right. Place a coefficient of 2 in front of Hg on the right side.

* Balance the Silver (Ag) atoms: There is 1 Ag atom on the left and 1 on the right.

* Balance the Nitrate (NO₃) ions: There are 2 NO₃ ions on the left and 1 on the right. Place a coefficient of 2 in front of AgNO₃ on the right side.

The Balanced Equation:

2 Ag + Hg₂(NO₃)₂ → 2 AgNO₃ + 2 Hg