Question

A standard solution is prepared for the analysis of fluoxymesterone ( $C_{20}{H}_{29}F{O}_3$), 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 $100.0\mu L$aliquot (portion) of this solution is diluted to a final volume of 100.0 mL. Calculate the concentration of the final solution in terms of molarity.

Short answer

Answer

Theconcentration of the final solution in terms of molarity is$5.95\times {10}^{-8}M$

Step-by-step solution

Definition

A solution's molarity is a concept that refers to the amount of solute contained in one litre of the solution. It may be stated mathematically as follows:

$Molarity=\frac{molesofsolute}{volumeofsolutoninliter}$

Determination of initial molarity of C20H29FO3.

Let’s calculate theinitial molarity of the fluoxymesterone,

$$\begin{gathered} Molesof{C}_{20}{H}_{29}F{O}_3=\frac{Massoffluoxymesterone}{MoralMassoffluoxymesterone} \\ =\frac{10.0mg\times {\displaystyle \frac{1.0mg}{1000mg}}}{\left(20\left(12.01\right)+29\left(1.008\right)+1\left(19.00\right)+3\left(16.00\right)\right){\displaystyle \raisebox{1ex}{$g$}\!\left/ \!\raisebox{-1ex}{$mol$}\right.}} \\ =2.97\times {10}^{-5}mol \end{gathered}$$

Let’s calculate the molarity of the fluoxymesterone,

$$\begin{gathered} Molesof{C}_{29}{H}_{20}F{O}_3=\frac{2.97\times {10}^{-5}mol}{5000mL}\times \frac{1000mL}{1.00L} \\ =5.94\times {10}^{-5}M \end{gathered}$$

$$\begin{gathered} Molesof{C}_{29}H20FO3=\frac{2.97\times {10}^{-5}mol}{5000mL}\times \frac{1000mL}{1.00L} \\ =5.94\times {10}^{-5}M \end{gathered}$$

Determination of final concentration of fluoxymesterone

The next step is tocompute the oxymesterone final concentration after dilution. The following equation may be written if $M_i$ is the initial molar concentration of the solution, $V_i$ is theinitial volume of the solution, is the final molar concentration, and $V_f$ is thefinal volume of the solution.

$M_i{V}_i=M_f{V}_f$

Let’s find the following values for the fluoxymesterone solution,

$$\begin{gathered} M_i=5.94\times {10}^{-5}M \\ {V}_i=100.0\mu L \\ =100.0\mu L\times \frac{1.0mL}{1000\mu L} \\ =0.100mL \\ {M}_f=? \\ {V}_f=100.00mL \\ {M}_f=\frac{5.94\times {10}^{-5}M\times 0.100mL}{100.00mL} \\ {M}_f=5.95\times {10}^{-8}M \end{gathered}$$

Therefore the final concentrationis $5.95\times {10}^{-8}M$