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Chapter 4: Problem 91

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

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

Step by step solution

01

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
02

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
03

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
04

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.

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