Ch.10 - Gases

Brown - Chemistry: The Central Science 14th Edition

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Brown 14th Edition

Ch.10 - Gases

Problem 118a

Chapter 10, Problem 118a

Cyclopropane, a gas used with oxygen as a general anesthetic, is composed of 85.7% C and 14.3% H by mass. (a) If 1.56 g of cyclopropane has a volume of 1.00 L at 99.7 kPa and 50.0 °C, what is the molecular formula of cyclopropane?

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Calculate the molar mass of cyclopropane using the ideal gas law: PV = nRT. Convert the given pressure to atm and temperature to Kelvin, then solve for n (moles of gas).

Determine the empirical formula of cyclopropane. Assume 100 g of the compound, which gives 85.7 g of C and 14.3 g of H. Convert these masses to moles using the atomic masses of C and H.

Find the simplest whole number ratio of moles of C to H to determine the empirical formula.

Calculate the empirical formula mass and compare it to the molar mass obtained from the ideal gas law to find the ratio between the molecular and empirical formulas.

Multiply the subscripts in the empirical formula by this ratio to obtain the molecular formula of cyclopropane.

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Key Concepts

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

Empirical and Molecular Formulas

The empirical formula represents the simplest whole-number ratio of elements in a compound, while the molecular formula indicates the actual number of atoms of each element in a molecule. To determine the molecular formula, one often starts with the empirical formula and uses molar mass data to find the actual composition.

Ideal Gas Law

The Ideal Gas Law, expressed as PV = nRT, relates the pressure (P), volume (V), number of moles (n), gas constant (R), and temperature (T) of a gas. This law is essential for calculating the number of moles of cyclopropane in the given conditions, which is necessary for determining its molecular formula.

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions based on the conservation of mass. In this context, it helps in determining the mass of carbon and hydrogen in cyclopropane from its percentage composition, which is crucial for deriving the empirical formula and subsequently the molecular formula.

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Stoichiometry Concept

Related Practice

Textbook Question

It turns out that the van der Waals constant b equals four times the total volume actually occupied by the molecules of a mole of gas. Using this figure, calculate the fraction of the volume in a container actually occupied by Ar atoms (b) at 20.27 MPa pressure and 0 °C. (Assume for simplicity that the ideal-gas equation still holds.)

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Textbook Question

An herbicide is found to contain only C, H, N, and Cl. The complete combustion of a 100.0-mg sample of the herbicide in excess oxygen produces 83.16 mL of CO₂ and 73.30 mL of H₂O vapor expressed at STP. A separate analysis shows that the sample also contains 16.44 mg of Cl. (c) What other information would you need to know about this compound to calculate its true molecular formula?

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Textbook Question

Consider the following gases, all at STP: Ne, SF₆, N₂, CH₄. (g) Which one would have the largest van der Waals b parameter?

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Textbook Question

An herbicide is found to contain only C, H, N, and Cl. The complete combustion of a 100.0-mg sample of the herbicide in excess oxygen produces 83.16 mL of CO2 and 73.30 mL of H2O vapor expressed at STP. A separate analysis shows that the sample also contains 16.44 mg of Cl. (b) Calculate its empirical formula.

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