Ch.3 - Molecules and Compounds

Tro - Chemistry: A Molecular Approach 6th Edition

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Tro 6th Edition

Ch.3 - Molecules and Compounds

Problem 133

Chapter 3, Problem 133

A compound of molar mass 177 g/mol contains only carbon, hydrogen, bromine, and oxygen. Analysis reveals that the compound contains eight times as much carbon as hydrogen by mass. Find the molecular formula.

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Identify the elements present in the compound: carbon (C), hydrogen (H), bromine (Br), and oxygen (O).

Let the mass of hydrogen be x grams. According to the problem, the mass of carbon is 8x grams.

Express the mass of each element in terms of moles: \( \text{moles of C} = \frac{8x}{12.01} \), \( \text{moles of H} = \frac{x}{1.008} \).

Assume the remaining mass is due to bromine and oxygen. Let the mass of bromine be y grams and the mass of oxygen be z grams. The total mass is 177 grams, so \( 8x + x + y + z = 177 \).

Use the molar masses to express the moles of bromine and oxygen: \( \text{moles of Br} = \frac{y}{79.90} \), \( \text{moles of O} = \frac{z}{16.00} \).

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Key Concepts

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

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is calculated by summing the atomic masses of all the atoms in a molecule. Understanding molar mass is crucial for determining the number of moles in a given mass of a compound, which is essential for stoichiometric calculations in chemistry.

Mass Ratio

The mass ratio is a comparison of the mass of one element to the mass of another element in a compound. In this question, the mass ratio indicates that the mass of carbon is eight times that of hydrogen. This relationship allows us to set up equations to find the relative amounts of each element in the compound, which is vital for deriving the molecular formula.

Empirical and Molecular Formulas

The empirical formula represents the simplest whole-number ratio of the elements in a compound, while the molecular formula shows the actual number of atoms of each element in a molecule. To find the molecular formula, one often starts with the empirical formula and uses the molar mass to determine the actual number of atoms. This distinction is important for accurately describing the composition of the compound in question.

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Empirical vs Molecular Formula

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Textbook Question

Epsom salts is a hydrated ionic compound with the following formula: MgSO₄ • x H₂O. A 4.93-g sample of Epsom salts is heated to drive off the water of hydration. The mass of the sample after complete dehydration is 2.41 g. Find the number of waters of hydration (x) in Epsom salts.

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Textbook Question

A hydrate of copper(II) chloride has the following formula: CuCl₂ • x H₂O. The water in a 3.41-g sample of the hydrate is driven off by heating. The remaining sample has a mass of 2.69 g. Find the number of waters of hydration (x) in the hydrate.

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Textbook Question

Find the total number of atoms in a sample of cocaine hydrochloride, C₁₇H₂₂ClNO₄, of mass 23.5 mg.

The chloride of an unknown metal is believed to have the formula MCl₃. A 2.395-g sample of the compound contains 3.606×10^-2 mol Cl. Find the atomic mass of M.

Estrone, which contains only carbon, hydrogen, and oxygen, is a female sexual hormone in the urine of pregnant women. Combustion analysis of a 1.893-g sample of estrone produces 5.545 g of CO₂ and 1.388 g H₂O. The molar mass of estrone is 270.36 g/mol. Find its molecular formula.

Researchers obtained the following data from experiments to find the molecular formula of benzocaine, a local anesthetic, which contains only carbon, hydrogen, nitrogen, and oxygen. Complete combustion of a 3.54-g sample of benzocaine with excess O₂ forms 8.49 g of CO₂ and 2.14 g H₂O. Another 2.35-g sample contains 0.199 g of N. The molar mass of benzocaine is 165 g/mol. Find the molar formula of benzocaine.

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