Here's how to balance the chemical equation for the reaction between sodium carbonate (Na₂CO₃) and silicon dioxide (SiO₂) to produce sodium silicate (Na₂SiO₃) and carbon dioxide (CO₂):

Unbalanced Equation:

Na₂CO₃ + SiO₂ → Na₂SiO₃ + CO₂

Balancing Steps:

1. Count the atoms on each side:

* Left side: 2 Na, 1 C, 3 O, 1 Si

* Right side: 2 Na, 1 Si, 4 O, 1 C

2. Balance the sodium (Na) atoms: They are already balanced.

3. Balance the carbon (C) atoms: They are already balanced.

4. Balance the silicon (Si) atoms: They are already balanced.

5. Balance the oxygen (O) atoms: The left side has 3 oxygen atoms, while the right side has 4. To balance, place a coefficient of 2 in front of Na₂CO₃:

2 Na₂CO₃ + SiO₂ → Na₂SiO₃ + CO₂

6. Recount the atoms on each side to confirm the balance:

* Left side: 4 Na, 2 C, 6 O, 1 Si

* Right side: 4 Na, 2 C, 6 O, 1 Si

Balanced Equation:

2 Na₂CO₃ + SiO₂ → Na₂SiO₃ + 2 CO₂