The balanced chemical equation for the fermentation of sucrose by yeast is:

C₁₂H₂₂O₁₁ (aq) + H₂O (l) → 4 C₂H₅OH (aq) + 4 CO₂ (g)

Here's a breakdown:

* C₁₂H₂₂O₁₁ (aq): This represents sucrose (table sugar) dissolved in water (aqueous solution).

* H₂O (l): This represents liquid water.

* C₂H₅OH (aq): This represents ethyl alcohol (ethanol) dissolved in water.

* CO₂ (g): This represents carbon dioxide gas.

Explanation:

In fermentation, yeast enzymes break down sucrose into simpler sugars (glucose and fructose) and then further break down these sugars into ethanol and carbon dioxide. The water molecule plays a role in the enzymatic reactions, but it's not directly consumed.

Note: The fermentation process is a bit more complex than this simplified equation suggests. It involves multiple steps and intermediate products. However, this equation captures the overall reaction and the main products.