Here's how to balance the equation for the reaction between magnesium (Mg) and silver nitrate (AgNO₃):

Unbalanced Equation:

Mg + AgNO₃ → Mg(NO₃)₂ + Ag

Balancing Steps:

1. Balance the nitrate (NO₃) ions: There are two nitrate ions on the product side (Mg(NO₃)₂) and only one on the reactant side (AgNO₃). Add a coefficient of 2 in front of AgNO₃:

Mg + 2AgNO₃ → Mg(NO₃)₂ + Ag

2. Balance the silver (Ag) atoms: There are now two silver atoms on the reactant side and only one on the product side. Add a coefficient of 2 in front of Ag:

Mg + 2AgNO₃ → Mg(NO₃)₂ + 2Ag

Balanced Equation:

Mg + 2AgNO₃ → Mg(NO₃)₂ + 2Ag