In the contact process, sulfur dioxide and oxygen gas react to form sulfur trioxide as follows: 2 SO2(g) + O2(g) → 2 SO3(g). At a certain temperature and pressure, 50 L of SO2 reacts with 25 L of O2. If all the SO2 and O2 are consumed, what volume of SO3, at the same temperature and pressure, will be produced?

Verified step by step guidance

1. Step 1: Identify the balanced chemical equation for the reaction: 2 SO_2(g) + O_2(g) \rightarrow 2 SO_3(g).
2. Step 2: Use the stoichiometry of the balanced equation to determine the mole ratio between the reactants and the product. The ratio is 2:1:2 for SO_2:O_2:SO_3.
3. Step 3: Apply Avogadro's Law, which states that equal volumes of gases at the same temperature and pressure contain equal numbers of moles. Therefore, the volume ratios are the same as the mole ratios.
4. Step 4: Determine the limiting reactant by comparing the given volumes of SO_2 and O_2 to their stoichiometric ratios. Here, 50 L of SO_2 and 25 L of O_2 are provided.
5. Step 5: Calculate the volume of SO_3 produced using the stoichiometric ratio from the balanced equation, considering the limiting reactant.

Key Concepts

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions based on the balanced chemical equation. It allows us to determine the proportions of substances involved in a reaction. In this case, the balanced equation shows that 2 volumes of SO2 react with 1 volume of O2 to produce 2 volumes of SO3, which is essential for calculating the volumes of gases involved.

Gas Laws

Gas laws describe the behavior of gases under various conditions of temperature and pressure. According to Avogadro's law, equal volumes of gases, at the same temperature and pressure, contain an equal number of molecules. This principle is crucial for understanding how the volumes of SO2, O2, and SO3 relate to each other in the reaction, allowing us to predict the volume of SO3 produced.

Conservation of Mass

The conservation of mass principle states that mass is neither created nor destroyed in a chemical reaction. This means that the total volume of reactants must equal the total volume of products when measured under the same conditions. In this problem, applying this principle helps us ensure that the volumes of SO2 and O2 consumed will yield a corresponding volume of SO3, maintaining the balance of the reaction.