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Ch.3 - Chemical Reactions and Reaction Stoichiometry
Chapter 3, Problem 54b

Determine the empirical and molecular formulas of each of the following substances: (b) Cadaverine, a foul-smelling substance produced by the action of bacteria on meat, contains 58.55% C, 13.81% H, and 27.40% N by mass; its molar mass is 102.2 g/mol.

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Assume a 100 g sample of cadaverine. This assumption simplifies the calculation as the percentages can be directly converted to grams. Thus, you have 58.55 g of carbon (C), 13.81 g of hydrogen (H), and 27.40 g of nitrogen (N).
Convert the mass of each element to moles by using the atomic masses (C = 12.01 g/mol, H = 1.008 g/mol, N = 14.01 g/mol). Calculate the moles of each element by dividing the mass of each element by its atomic mass.
Determine the simplest whole number ratio of the moles of each element. Divide the number of moles of each element by the smallest number of moles calculated in the previous step.
Write the empirical formula by using the whole number ratios as subscripts for each element. If any of the subscripts are not whole numbers, multiply all subscripts by the smallest factor that converts all subscripts to whole numbers.
Calculate the molecular formula using the empirical formula and the given molar mass of cadaverine (102.2 g/mol). First, calculate the molar mass of the empirical formula. Then, divide the molar mass of cadaverine by the molar mass of the empirical formula to find the factor by which to multiply the subscripts in the empirical formula.

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Key Concepts

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

Empirical Formula

The empirical formula represents the simplest whole-number ratio of the elements in a compound. To determine it, the percentage composition of each element is converted to moles, and then the mole ratios are simplified to the smallest integers. This formula provides insight into the basic composition of the substance without indicating the actual number of atoms in a molecule.
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Molecular Formula

The molecular formula indicates the actual number of atoms of each element in a molecule of the compound. It can be derived from the empirical formula by multiplying the subscripts by a whole number, which is determined by dividing the compound's molar mass by the empirical formula mass. This formula gives a complete picture of the molecular structure and composition.
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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 based on its molecular formula. Knowing the molar mass is essential for converting between grams and moles, which is crucial for determining both empirical and molecular formulas.
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Related Practice
Textbook Question

Determine the empirical and molecular formulas of each of the following substances: (b) Caffeine, a stimulant found in coffee, contains 49.5% C, 5.15% H, 28.9% N, and 16.5% O by mass and has a molar mass of 195 g/mol.

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Textbook Question

Determine the empirical and molecular formulas of each of the following substances: (c) Monosodium glutamate (MSG), a flavor enhancer in certain foods, contains 35.51% C, 4.77% H, 37.85% O, 8.29% N, and 13.60% Na, and has a molar mass of 169 g/mol.

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Textbook Question

Determine the empirical and molecular formulas of each of the following substances: (a) Ibuprofen, a headache remedy, contains 75.69% C, 8.80% H, and 15.51% O by mass and has a molar mass of 206 g/mol.

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Textbook Question

Determine the empirical and molecular formulas of each of the following substances: (c) Epinephrine (adrenaline), a hormone secreted into the bloodstream in times of danger or stress, contains 59.0% C, 7.1% H, 26.2% O, and 7.7% N by mass; its molar mass is about 180 u.

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Textbook Question

(a) Combustion analysis of toluene, a common organic solvent, gives 5.86 mg of CO2 and 1.37 mg of H2O. If the compound contains only carbon and hydrogen, what is its empirical formula?

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Textbook Question

(b) Menthol, the substance we can smell in mentholated cough drops, is composed of C, H, and O. A 0.1005-g sample of menthol is combusted, producing 0.2829 g of CO2 and 0.1159 g of H2O. What is the empirical formula for menthol? If menthol has a molar mass of 156 g/mol, what is its molecular formula?

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