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

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. Is the formula you calculated an empirical formula or a molecular formula? Explain.

Verified step by step guidance
1
Start by understanding the problem: A gaseous compound X containing carbon (C), hydrogen (H), and oxygen (O) is burned in oxygen (O2). The reaction involves 1 volume of compound X reacting with 3 volumes of O2 to produce 2 volumes of CO2 and 3 volumes of H2O.
Use the concept of stoichiometry and the ideal gas law, which states that equal volumes of gases at the same temperature and pressure contain the same number of molecules. This means the volume ratios can be directly translated into mole ratios.
Write the balanced chemical equation for the combustion reaction. Let the formula of compound X be CxHyOz. The reaction can be represented as: CxHyOz + O2 → CO2 + H2O. Use the given volume ratios to balance the equation.
From the balanced equation, determine the number of carbon, hydrogen, and oxygen atoms in the compound X. The production of 2 volumes of CO2 indicates 2 moles of carbon atoms, and 3 volumes of H2O indicate 6 moles of hydrogen atoms. Use these to deduce the formula of X.
Finally, determine whether the formula calculated is an empirical formula or a molecular formula. An empirical formula represents the simplest whole-number ratio of atoms in a compound, while a molecular formula represents the actual number of atoms in a molecule. Since the problem involves direct volume ratios, the formula derived is likely the molecular formula.

Key Concepts

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

Empirical Formula

The empirical formula of a compound represents the simplest whole-number ratio of the elements present in that compound. It does not provide information about the actual number of atoms in a molecule, but rather the relative proportions of each element. For example, the empirical formula for glucose (C6H12O6) is CH2O, indicating a 1:2:1 ratio of carbon, hydrogen, and oxygen.
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Molecular Formula

The molecular formula of a compound indicates the actual number of atoms of each element in a molecule. It can be the same as the empirical formula or a multiple of it. For instance, while the empirical formula for glucose is CH2O, its molecular formula is C6H12O6, showing that it contains six carbon atoms, twelve hydrogen atoms, and six oxygen atoms.
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Stoichiometry of Gaseous Reactions

Stoichiometry in gaseous reactions involves the relationships between the volumes of gases involved, based on the ideal gas law and Avogadro's principle. In this case, the reaction shows that 1 volume of compound X reacts with 3 volumes of O2 to produce 2 volumes of CO2 and 3 volumes of H2O, allowing for the determination of the mole ratios of the reactants and products, which is essential for deriving the empirical and molecular formulas.
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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

(a) What mass of CO2(g) is produced in the reaction?

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

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.

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.