Ch.3 - Chemical Reactions and Reaction Stoichiometry

Brown - Chemistry: The Central Science 15th Edition

Brown15th EditionChemistry: The Central ScienceISBN: 9780137542970Not the one you use?Change textbook

Brown 15th Edition

Ch.3 - Chemical Reactions and Reaction Stoichiometry

Problem 26f

Chapter 3, Problem 26f

Calculate the percentage by mass of the indicated element in the following compounds: f. carbon in capsaicin, C18H27NO3, the compound that gives the hot taste to chili peppers.

Verified step by step guidance

Step 1: First, we need to calculate the molar mass of capsaicin, C18H27NO3. The molar mass of an element is the mass of one mole of that element. It is calculated by adding up the atomic masses of all the atoms in the compound. The atomic masses of carbon (C), hydrogen (H), nitrogen (N), and oxygen (O) are approximately 12.01 g/mol, 1.01 g/mol, 14.01 g/mol, and 16.00 g/mol, respectively.

Step 2: Multiply the atomic mass of each element by the number of atoms of that element in the compound. For capsaicin, this would be (18 atoms C * 12.01 g/mol C) + (27 atoms H * 1.01 g/mol H) + (1 atom N * 14.01 g/mol N) + (3 atoms O * 16.00 g/mol O).

Step 3: Add up all the values obtained in step 2 to get the molar mass of capsaicin.

Step 4: To find the percentage by mass of carbon in capsaicin, divide the total mass of carbon in one mole of capsaicin by the molar mass of capsaicin. This would be (18 atoms C * 12.01 g/mol C) / molar mass of capsaicin.

Step 5: Multiply the result from step 4 by 100% to get the percentage by mass of carbon in capsaicin.

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Key Concepts

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

Molar Mass Calculation

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). To calculate the molar mass of a compound, sum the molar masses of all the atoms in its chemical formula. For capsaicin (C18H27NO3), this involves calculating the contributions from carbon, hydrogen, nitrogen, and oxygen based on their respective atomic masses.

Percentage by Mass

Percentage by mass is a way to express the concentration of an element within a compound. It is calculated by dividing the total mass of the element in the compound by the molar mass of the compound, then multiplying by 100. This provides a clear understanding of how much of the compound's mass is due to a specific element, such as carbon in capsaicin.

Empirical and Molecular Formulas

The empirical formula represents the simplest whole-number ratio of elements in a compound, while the molecular formula shows the actual number of each type of atom in a molecule. Capsaicin's molecular formula (C18H27NO3) indicates the exact number of carbon, hydrogen, nitrogen, and oxygen atoms, which is essential for calculating the mass percentage of carbon accurately.

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