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Ch.10 - Gases: Their Properties & Behavior
All textbooksMcMurry 8th EditionCh.10 - Gases: Their Properties & BehaviorProblem 146a
Chapter 10, Problem 146a

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.

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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.
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).
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.
Step 4: Combining all the information, we can say that the formula for the unknown gas is C2H6O2.
Step 5: The balanced equation for the combustion reaction is: C2H6O2 + 3O2 → 2CO2 + 3H2O.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.
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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.
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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.
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Related Practice
Textbook Question

An empty 4.00-L steel vessel is filled with 1.00 atm of CH4(g) and 4.00 atm of O2(g) at 300 °C. A spark causes the CH4 to burn completely, according to the equation

CH4(g) + 2 O2(g) → CO2(g) + 2 H2O(g) ΔH° = -802 kJ

(b) What is the final temperature inside the vessel after combustion, assuming that the steel vessel has a mass of 14.500 kg, the mixture of gases has an average molar heat capacity of 21 J/(mol·°C), and the heat capacity of steel is 0.449 J/(g·°C)?

Textbook Question

An empty 4.00-L steel vessel is filled with 1.00 atm of CH4(g) and 4.00 atm of O2(g) at 300 °C. A spark causes the CH4 to burn completely, according to the equation

CH4(g) + 2 O2(g) → CO2(g) + 2 H2O(g) ΔH° = -802 kJ

(c) What is the partial pressure of CO2(g) in the vessel after combustion?

Textbook Question

Isooctane, C8H18, is the component of gasoline from which the term octane rating derives. (a) Write a balanced equation for the combustion of isooctane to yield CO2 and H2O.

Textbook Question

Isooctane, C8H18, is the component of gasoline from which the term octane rating derives. (b) Assuming that gasoline is 100% isooctane, that isooctane burns to produce only CO2 and H2O, and that the density of isooctane is 0.792 g/mL, what mass of CO2 in kilograms is produced each year by the annual U.S. gasoline consumption of 4.6⨉1010 L?