Problem 131 - Chemistry An Atoms First Approach

Question

Anabolic steroids are performance enhancement drugs whose use has been banned from most major sporting activities. One anabolic steroid is fluoxymesterone \(\left(\mathrm{C}_{20} \mathrm{H}_{29} \mathrm{FO}_{3}\right) .\) Calculate the percent composition by mass of fluoxymesterone.

Step-by-Step Solution

Answer

The percent composition by mass of fluoxymesterone is approximately 71.41% carbon, 8.70% hydrogen, 5.65% fluorine, and 14.27% oxygen.

Step 1: Determine the molar mass of fluoxymesterone

To find the molar mass of fluoxymesterone, we must first identify the molar mass of each individual element and then multiply each element's molar mass by its stoichiometric coefficient. The molar masses of the given elements are: - Carbon (C): \(12.01 \frac{g}{mol}\) - Hydrogen (H): \(1.01 \frac{g}{mol}\) - Fluorine (F): \(19.00 \frac{g}{mol}\) - Oxygen (O): \(16.00 \frac{g}{mol}\) Now, we can find the molar mass of fluoxymesterone: Molar mass = (Molar mass of C) × (Number of C atoms) + (Molar mass of H) × (Number of H atoms) + (Molar mass of F) × (Number of F atoms) + (Molar mass of O) × (Number of O atoms)

Step 2: Calculate the molar mass of fluoxymesterone

Applying the molar masses and the stoichiometric coefficients to the formula: Molar mass = (20 × 12.01) + (29 × 1.01) + (19.00) + (3 × 16.00) Molar mass = 240.20 + 29.29 + 19.00 + 48.00 Molar mass = 336.49 g/mol We now have the molar mass of fluoxymesterone.

Step 3: Calculate the percentage composition by mass

Now, we need to find the fraction of each element's mass within the molar mass of fluoxymesterone, and then multiply that by 100 to get the percentage composition. Percentage of C = (\(\frac{Mass of C}{Molar mass of fluoxymesterone}\)) × 100 Percentage of H = (\(\frac{Mass of H}{Molar mass of fluoxymesterone}\)) × 100 Percentage of F = (\(\frac{Mass of F}{Molar mass of fluoxymesterone}\)) × 100 Percentage of O = (\(\frac{Mass of O}{Molar mass of fluoxymesterone}\)) × 100 Using these formulas: Percentage of C = (\(\frac{240.20}{336.49}\)) × 100 = 71.41% Percentage of H = (\(\frac{29.29}{336.49}\)) × 100 = 8.70% Percentage of F = (\(\frac{19.00}{336.49}\)) × 100 = 5.65% Percentage of O = (\(\frac{48.00}{336.49}\)) × 100 = 14.27% The percent composition by mass of fluoxymesterone is approximately 71.41% carbon, 8.70% hydrogen, 5.65% fluorine, and 14.27% oxygen.

Key Concepts

Molar Mass Calculation

Understanding how to calculate molar mass is foundational to mastering stoichiometry and percent composition in chemistry. Molar mass is fundamentally the mass of one mole of a substance, measured in grams per mole (g/mol). To calculate the molar mass of a compound like fluoxymesterone (C₂₀H₂₉FO₃), you would need to know the atomic masses of each element involved, typically found on the periodic table.

Here's a simple break down for fluoxymesterone:

• Carbon (C) has an atomic mass of 12.01 g/mol.
• Hydrogen (H) is 1.01 g/mol.
• Fluorine (F) stands at 19.00 g/mol.
• Oxygen (O) is 16.00 g/mol.

By multiplying each atomic mass by the number of atoms in a molecule of the compound and adding the products, we arrive at the compound's molar mass. This calculation method is a critical stepping stone for the subsequent analysis of a substance's composition and reactivity in chemical reactions.

Stoichiometry

Stoichiometry is the section of chemistry that provides tools for calculating relative quantities of reactants and products in chemical reactions. Essential for figuring out how much of each substance is involved in a reaction, stoichiometry is based on the law of conservation of mass, which states that matter cannot be created or destroyed.

In the context of the percent composition calculation, stoichiometry allows us to understand that each atom in the chemical formula contributes a specific part to the overall mass of the compound. Utilizing ratios derived from the balanced reaction or formula unit, chemists can calculate necessary amounts for desired chemical yields, which is handy not only in academic exercises but fundamental in industrial applications for creating everything from pharmaceuticals to plastics.

Chemical Formula

The chemical formula of a substance tells us the specific types and numbers of atoms present in a single unit of that compound. It serves as a type of shorthand that conveys a wealth of information to those with a knowledge of chemistry. For instance, fluoxymesterone's formula, C₂₀H₂₉FO₃, indicates that each molecule consists of 20 carbon atoms, 29 hydrogen atoms, one fluorine atom, and three oxygen atoms. Understanding the chemical formula is key to not only figuring out molar mass but also to determining the percent composition, as shown in the workout problem. It's this formula that allows us to calculate the mass contribution of each element efficiently and can be used to infer properties about the compound, predict how it might react with other substances, and understand its role within a larger chemical process such as drug development.