Final answer:
The initial rate of the appearance of water to the initial rate of disappearance of oxygen, based on the balanced chemical equation 2H₂ + O₂ → 2H₂O, is 2:1. This is derived from the stoichiometric ratio of the reactants and products in the equation.
Step-by-step explanation:
When considering the balanced chemical equation 2H₂ + O₂ → 2H₂O, we look at the stoichiometry to determine the relationships between the reactants and products. The coefficients indicate that two moles of hydrogen gas react with one mole of oxygen gas to produce two moles of water. Therefore, the stoichiometric ratio for the appearance of water (H₂O) to the disappearance of oxygen (O₂) is 2:1.
However, the question asks for the initial rate of appearance and disappearance, which is influenced by the stoichiometry of the reaction but expressed differently considering rate depends on time. Rates of reactions are directly proportional to the stoichiometric coefficients. So, when considering initial rates, the ratio for the appearance of water to the disappearance of oxygen is 2:1, following the coefficients from the balanced equation.
Thus, for every single oxygen molecule that reacts, two water molecules are produced. Consequently, if the initial rate of disappearance of oxygen is x, the initial rate of appearance of water would be 2x, giving us a rate ratio of 2:1.