Question

a standard solution is prepared for the analysis of fluoxymesterone (c₂₀h₂₉fo₃), an anabolic steroid. a stock solution is first prepared by dissolving 10.0 mg of fluoxymesterone in enough water to give a total volume of 500.0 ml. a 100.0 μl aliquot (portion) of this solution is diluted to a final volume of 110.0 ml. calculate the concentration of the final solution in terms of molarity.

Explanation:

Step1: Calculate the molar mass of \(C_{20}H_{29}FO_3\)

The molar mass \(M\) of \(C_{20}H_{29}FO_3\) is calculated as follows:

• For carbon (\(C\)): \(20\times12.01\space g/mol = 240.2\space g/mol\)
• For hydrogen (\(H\)): \(29\times1.008\space g/mol=29.232\space g/mol\)
• For fluorine (\(F\)): \(1\times18.998\space g/mol = 18.998\space g/mol\)
• For oxygen (\(O\)): \(3\times16.00\space g/mol=48.00\space g/mol\)

\(M=(240.2 + 29.232+18.998 + 48.00)\space g/mol=336.43\space g/mol\)

Step2: Calculate the concentration of the stock solution

The mass of fluoxymesterone \(m = 10.0\space mg=10.0\times10^{- 3}\space g\)
The volume of the stock solution \(V_1 = 500.0\space mL = 0.5000\space L\)

The number of moles of fluoxymesterone \(n=\frac{m}{M}=\frac{10.0\times 10^{-3}\space g}{336.43\space g/mol}\approx2.97\times10^{-5}\space mol\)

The concentration of the stock solution \(C_1=\frac{n}{V_1}=\frac{2.97\times 10^{-5}\space mol}{0.5000\space L}=5.94\times10^{-5}\space mol/L\)

Step3: Use the dilution formula \(C_1V_1 = C_2V_2\)

The volume of the aliquot \(V_{1,\text{aliquot}}=100.0\space\mu L = 100.0\times10^{-6}\space L\)
The final volume \(V_2 = 110.0\space mL=0.1100\space L\)

We know \(C_1V_{1,\text{aliquot}}=C_2V_2\), so \(C_2=\frac{C_1V_{1,\text{aliquot}}}{V_2}\)

Substitute \(C_1 = 5.94\times10^{-5}\space mol/L\), \(V_{1,\text{aliquot}}=100.0\times10^{-6}\space L\) and \(V_2 = 0.1100\space L\)

\(C_2=\frac{5.94\times 10^{-5}\space mol/L\times100.0\times10^{-6}\space L}{0.1100\space L}\)

\(C_2=\frac{5.94\times10^{-9}\space mol}{0.1100\space L}=5.4\times10^{-8}\space mol/L\)

Answer:

\(5.4\times 10^{-8}\space M\)