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.

Short answer

The percent composition by mass of fluoxymesterone is approximately 71.31% carbon, 8.69% hydrogen, 5.65% fluorine, and 14.35% oxygen.

Step-by-step solution

Determine the molar mass of each element

Using the periodic table, we can find the molar mass of each element: Molar mass of carbon (C): 12.01 g/mol Molar mass of hydrogen (H): 1.01 g/mol Molar mass of fluorine (F): 19.00 g/mol Molar mass of oxygen (O): 16.00 g/mol

Calculate the molar mass of fluoxymesterone

To calculate the molar mass of fluoxymesterone, we multiply the molar mass of each element by the number of its atoms in the molecule and add them up. Molar mass of fluoxymesterone = (20 × molar mass of C) + (29 × molar mass of H) + (1 × molar mass of F) + (3 × molar mass of O) Molar mass of fluoxymesterone = (20 × 12.01) + (29 × 1.01) + (1 × 19.00) + (3 × 16.00) Molar mass of fluoxymesterone = 240.2 + 29.29 + 19.00 + 48.00 Molar mass of fluoxymesterone = 336.49 g/mol

Calculate the percent composition by mass of each element

To calculate the percent composition of each element in fluoxymesterone, we divide the molar mass of the element (multiplied by its number of atoms) by the total molar mass of the compound, and then multiply by 100. Percent of Carbon (C) = \(\frac{20 \times 12.01}{336.49}\) × 100 = 71.31% Percent of Hydrogen (H) = \(\frac{29 \times 1.01}{336.49}\) × 100 = 8.69% Percent of Fluorine (F) = \(\frac{1 \times 19.00}{336.49}\) × 100 = 5.65% Percent of Oxygen (O) = \(\frac{3 \times 16.00}{336.49}\) × 100 = 14.35% The percent composition by mass of fluoxymesterone is approximately 71.31% carbon, 8.69% hydrogen, 5.65% fluorine, and 14.35% oxygen.

Key concepts

Molar Mass

The concept of molar mass is a fundamental aspect of chemistry and is crucial for understanding the composition of compounds. Molar mass is essentially the weight of one mole of a substance, measured in grams per mole (g/mol). It is calculated by summing up the atomic masses of all the elements present in a compound based on their proportions.
Each element has a specific molar mass. For example, carbon (C) has a molar mass of 12.01 g/mol, hydrogen (H) 1.01 g/mol, fluorine (F) 19.00 g/mol, and oxygen (O) 16.00 g/mol.
When calculating the molar mass of a compound, such as fluoxymesterone, you multiply the molar mass of each element by the number of atoms of that element in the compound, and then sum these values.

• For fluoxymesterone (C₂₀H₂₉FO₃), the molar mass is found by adding:
  • 20 times the molar mass of carbon,
  • 29 times the molar mass of hydrogen,
  • 1 time the molar mass of fluorine,
  • and 3 times the molar mass of oxygen.
• The total molar mass sums up to approximately 336.49 g/mol.

Molar mass helps in calculating other important chemical properties, such as the percent composition, which determines the proportionate amounts of different elements within a compound.

Elemental Composition

Elemental composition refers to the relative abundance of each element within a compound. It's generally expressed as a percentage and conveys how much mass each element contributes to the overall compound.
By knowing the molar mass of the entire compound and the molar masses of the individual elements, you can determine the elemental composition of a compound. Here's how you can calculate it:

• First, calculate the total molar mass of the compound.
• For each element, multiply the number of atoms by its molar mass to get the total mass of that element in the compound.
• To find the percent composition by mass of the element, divide the element's total mass by the compound's molar mass and multiply by 100.

For example, in fluoxymesterone:

• Percent carbon is calculated as \(\frac{20 \times 12.01}{336.49} \times 100\) which equals about 71.31%.
• Percent hydrogen as \(\frac{29 \times 1.01}{336.49} \times 100\) resulting in 8.69%.
• Percent fluorine and oxygen are calculated similarly, yielding 5.65% and 14.35% respectively.

Understanding elemental composition is key in many fields, such as biochemistry and materials science, as it provides insights into the properties and behaviors of substances.

Chemical Formula

A chemical formula is a shorthand representation of a chemical compound that indicates the types and numbers of atoms involved. Each element is represented by its chemical symbol from the periodic table, and the numbers denote how many atoms of each are present in one molecule of the compound.
For example, the chemical formula of fluoxymesterone is C₂₀H₂₉FO₃. Here's what the formula tells us:

• C₂₀: There are 20 carbon atoms.
• H₂₉: There are 29 hydrogen atoms.
• F: There is 1 fluorine atom.
• O₃: There are 3 oxygen atoms.

The chemical formula is crucial in determining both the molar mass and the elemental composition.
By understanding the arrangement and quantity of atoms, you gain better insight into the molecular structure and reactivity of the compound. Chemical formulas are foundational in fields spanning from pharmacology to industrial chemistry and beyond, where precise information dictates how substances react and interact.