When a gaseous compound X containing only C, H, and O is burned in O₂, 1 volume of the unknown gas reacts with 3 volumes of O₂ to give 2 volumes of CO₂ and 3 volumes of gaseous H₂O. Assume all volumes are measured at the same temperature and pressure. (a) Calculate a formula for the unknown gas, and write a balanced equation for the combustion reaction.

Verified step by step guidance

1. Step 1: From the problem, we know that 1 volume of the unknown gas reacts with 3 volumes of O₂ to give 2 volumes of CO₂ and 3 volumes of H₂O. According to Avogadro's law, equal volumes of gases at the same temperature and pressure contain equal numbers of molecules. Therefore, we can say that 1 molecule of the unknown gas reacts with 3 molecules of O₂ to give 2 molecules of CO₂ and 3 molecules of H₂O.
2. Step 2: From the balanced chemical equation, we can see that each molecule of CO₂ contains 1 atom of carbon (C) and each molecule of H₂O contains 2 atoms of hydrogen (H). Therefore, the unknown gas must contain 2 atoms of carbon (since there are 2 molecules of CO₂) and 6 atoms of hydrogen (since there are 3 molecules of H₂O).
3. Step 3: We also know that the unknown gas reacts with 3 molecules of O₂. Each molecule of O₂ contains 2 atoms of oxygen (O). However, 4 of these oxygen atoms are used to form the 2 molecules of CO₂ and the remaining 2 oxygen atoms are used to form the 3 molecules of H₂O. Therefore, the unknown gas must also contain 2 atoms of oxygen.
4. Step 4: Combining all the information, we can say that the formula for the unknown gas is C₂H₆O₂.
5. Step 5: The balanced equation for the combustion reaction is: C₂H₆O₂ + 3O₂ → 2CO₂ + 3H₂O.

Key Concepts

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It allows chemists to predict the amounts of substances consumed and produced in a reaction based on balanced chemical equations. In this question, stoichiometry is essential for determining the ratios of the gaseous compound X, O2, CO2, and H2O involved in the combustion process.

Combustion Reactions

Combustion reactions are exothermic reactions that occur when a substance reacts with oxygen, typically producing heat and light. In the case of hydrocarbons, combustion results in the formation of carbon dioxide (CO2) and water (H2O). Understanding the general form of combustion reactions is crucial for writing the balanced equation for the combustion of the unknown gas X.

Gas Laws and Volume Relationships

Gas laws describe the behavior of gases in relation to pressure, volume, and temperature. In this question, the volume ratios of the gases involved in the reaction are given, which can be interpreted using Avogadro's law, stating that equal volumes of gases at the same temperature and pressure contain an equal number of molecules. This principle is key to determining the molecular formula of the unknown gas X based on the provided volume ratios.