Final answer:
Chemical equations are balanced when the number of atoms of each element is the same on both the reactant and product sides. The equations provided are all correctly balanced, as they conserve the respective number of atoms for each involved element.
Step-by-step explanation:
To determine if each chemical equation is balanced, we must ensure that the number of atoms of each element on the reactant side is equal to the number on the product side. Starting with the first equation, 2H₂ + O₂ → 2H₂O is already balanced with 4 hydrogen atoms and 2 oxygen atoms on each side. The second equation, CH₄ + 2O₂ → CO₂ + 2H₂O, is also balanced with 1 carbon atom, 4 hydrogen atoms, and 4 oxygen atoms on both sides.
Moving to the next equation, 2K + 2H₂O → 2KOH + H₂↑ is also correctly balanced with 2 potassium, 2 oxygen, and 4 hydrogen atoms being conserved in the reaction. Lastly, the fermentation equation C₆H₁₂O₆ → 2C₂H₅OH + 2CO₂ correctly balances with 6 carbons, 12 hydrogens, and 6 oxygens on each side of the equation.
If we consider the additionally provided equations for analysis, we must perform different checks to confirm their balance. For example, the equation for the combustion of ethylene is represented as C₂H₄(g) + 3O₂(g) → 2CO₂(g) + 2H₂O(l), which balances with 2 carbons, 4 hydrogens, and 6 oxygens on both sides.