Question

A standard solution is prepared for the analysis of fluoxymesterone \(\left(\mathrm{C}_{20} \mathrm{H}_{29} \mathrm{FO}_{3}\right)\), an anabolic steroid. A stock solution is first prepared by dissolving \(10.0 \mathrm{mg}\) of fluoxymesterone in enough water to give a total volume of \(500.0 \mathrm{~mL}\). A \(100.0-\mu \mathrm{L}\) aliquot (portion) of this solution is diluted to a final volume of \(100.0 \mathrm{~mL}\). Calculate the concentration of the final solution in terms of molarity.

Short answer

The concentration of the final solution of fluoxymesterone is approximately \(5.94 \times 10^{-8} \: \text{mol/L}\).

Step-by-step solution

Determine the number of moles of fluoxymesterone in the stock solution.

First, we need to determine the number of moles of fluoxymesterone present in the 10 mg of fluoxymesterone. To do this, we'll use the molar mass of fluoxymesterone (C20H29FO3). The molar mass can be calculated as follows: Molar mass = 20(12.01) + 29(1.01) + 1(19.00) + 3(16.00) = 240.20 + 29.29 + 19.00 + 48.00 = 336.49 g/mol Now, to find the number of moles, we can use the formula: Number of moles = mass / molar mass We were given that 10 mg of fluoxymesterone was used, so we need to convert this mass to grams. mass (g) = 10 mg × (1 g / 1000 mg) = 0.010 g Now, we can calculate the number of moles: Number of moles = 0.010 g / 336.49 g/mol ≈ 0.0000297 mol

Calculate the concentration of the stock solution.

To find the concentration of the stock solution, we can use the formula: Concentration (mol/L) = number of moles / volume (L) The stock solution has a volume of 500.0 mL, so we need to convert this to liters before using the formula. volume (L) = 500.0 mL × (1 L / 1000 mL) = 0.500 L Now, we can calculate the concentration of the stock solution: Stock concentration (mol/L) = 0.0000297 mol / 0.500 L ≈ 0.0000594 mol/L

Calculate the number of moles in the 100 μL aliquot.

To calculate the number of moles in the 100 μL aliquot, we can use the stock concentration we just found. First, convert the aliquot volume to liters: volume (L) = 100 μL × (1 mL / 1000 μL) × (1 L / 1000 mL) = 0.0001 L Now, we can use the formula: Number of moles = concentration (mol/L) × volume (L) Number of moles in the aliquot = 0.0000594 mol/L × 0.0001 L ≈ 5.94 × 10⁻⁹ mol

Calculate the concentration of the final solution.

Finally, to find the concentration of the final solution (after dilution), we can use the number of moles from the aliquot and the final volume of the solution. The final volume is 100.0 mL, which needs to be converted to liters before using the formula. Final volume (L) = 100.0 mL × (1 L / 1000 mL) = 0.100 L Now, calculate the concentration of the final solution: Final concentration (mol/L) = number of moles / volume (L) Final concentration (mol/L) = 5.94 × 10⁻⁹ mol / 0.100 L = 5.94 × 10⁻⁸ mol/L The concentration of the final solution in terms of molarity is approximately 5.94 × 10⁻⁸ mol/L.

Key concepts

Concentration calculation

Understanding how to calculate concentration is vital in chemistry, especially when preparing solutions. Concentration refers to the amount of solute present in a solution. It is often expressed in terms of molarity, which identifies the number of moles of a solute per liter of solution. To perform a concentration calculation, we need to know the number of moles of the solute and the total volume of the solution in liters.

• Use the formula: \[ ext{Concentration (mol/L)} = \frac{\text{Number of moles}}{\text{Volume (L)}} \]
• Ensure all units are consistent, typically converting volumes to liters and masses to grams before calculation.

Concentration calculation is fundamental for working with solutions in a laboratory, allowing chemists to predict how substances will react when mixed or diluted.

Dilution

Dilution involves adding more solvent to a solution to decrease the concentration of the solute. It's a common laboratory procedure. When you dilute a solution, the number of moles of solute remains unchanged, but the volume increases, thus reducing concentration. The dilution equation is a helpful tool here:

• The equation: \[ C_1V_1 = C_2V_2 \]
• Where \( C_1 \) and \( V_1 \) are the initial concentration and volume, and \( C_2 \) and \( V_2 \) are the final concentration and volume respectively.

In our exercise, we diluted a 100 \(\mu \mathrm{L}\) aliquot to a final volume of 100 \(\mathrm{mL}\), which involved calculating the new concentration based on the initial concentration of the stock solution.

Molar mass

Molar mass is the mass of one mole of a given substance, usually expressed in grams per mole (g/mol). It can be calculated by summing the atomic masses of each element in a chemical formula. For fluoxymesterone, our exercise breaks it down as follows:

• The formula is \( \text{C}_{20}\text{H}_{29}\text{FO}_{3} \)
• Each element contributes to the overall molar mass based on its frequency and atomic mass:
  • Carbon (C): 20 atoms
  • Hydrogen (H): 29 atoms
  • Fluorine (F): 1 atom
  • Oxygen (O): 3 atoms

The calculated molar mass of fluoxymesterone is approximately 336.49 g/mol, essential for converting grams to moles, which subsequently aids in concentration calculations.

Stock solution

A stock solution is a concentrated form of a chemical solution, from which diluted solutions are made. In our example, we prepared a stock solution by dissolving 10.0 mg of fluoxymesterone in enough water to make a 500.0 mL solution. When working with stock solutions, it is critical to understand the initial concentration, as it is used to prepare other solution concentrations via dilution. This procedure is polished with techniques to ensure precision and accuracy, as errors at this stage may distort results in subsequent experiments.

Aliquot

An aliquot refers to a measured sub-volume of a solution. It allows chemists to take a precise amount of a solution for further processing or analysis. In the context of our exercise, a 100 \(\mu \mathrm{L}\) aliquot was extracted from the stock solution for dilution. Aliquots are versatile tools, useful for scaling reactions or analytic tests without needing to handle an entire bulk of solution. This controlled approach helps manage reactants economically and reduces waste in chemical practices.

Fluoxymesterone

Fluoxymesterone, represented by the formula \( \text{C}_{20} \text{H}_{29} \text{FO}_{3}\), is an anabolic steroid. It's used medicinally to treat specific health conditions due to its muscle-building properties. Chemically, fluoxymesterone is studied for its complex structure, comprising carbon, hydrogen, fluorine, and oxygen. Understanding its molecular composition through molar mass calculations assists in creating accurately dosed solutions for research and medical applications. Working with steroids requires careful measurement and dilution to maintain safety and effectiveness across usage scenarios.