Fluoxymesterone , `C_(20) H_(29)FO_(3)`, is an anabolic steroid . A 500 ml solution is prepared by dissolving 10.0 mg of the steroid in water. 10.0 mL portion of this solution is diluted to final volume of 1.00 L. What is the resulting molarity ?

Options

A. `1.19 xx 10^(-10)`
B. `1.19 xx 10^(-7)`
C. `5.95 xx 10^(-8)`
D. `2.38 xx10^(-11)`

Answer

To find the resulting molarity of the diluted solution of fluoxymesterone, we will follow these steps:

### Step 1: Calculate the number of moles of fluoxymesterone in the initial solution.

1. **Convert the mass of fluoxymesterone from milligrams to grams**:
\[ \text{Mass} = 10.0 \, \text{mg} = 10.0 \times 10^{-3} \, \text{g} = 0.0100 \, \text{g} \]

2. **Determine the molecular weight of fluoxymesterone**:
\[ \text{Molecular weight of } C_{20}H_{29}FO_{3} = 336.4 \, \text{g/mol} \]

3. **Calculate the number of moles**:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molecular weight (g/mol)}} = \frac{0.0100 \, \text{g}}{336.4 \, \text{g/mol}} \approx 2.97 \times 10^{-5} \, \text{mol} \]

### Step 2: Calculate the molarity of the initial solution.

1. **Convert the volume of the solution from milliliters to liters**:
\[ \text{Volume} = 500 \, \text{ml} = 0.500 \, \text{L} \]

2. **Calculate the molarity (M)**:
\[ M = \frac{\text{number of moles}}{\text{volume (L)}} = \frac{2.97 \times 10^{-5} \, \text{mol}}{0.500 \, \text{L}} \approx 5.94 \times 10^{-5} \, \text{M} \]

### Step 3: Calculate the molarity of the diluted solution.

1. **Use the dilution equation \( M_1 V_1 = M_2 V_2 \)**:
- \( M_1 = 5.94 \times 10^{-5} \, \text{M} \)
- \( V_1 = 10 \, \text{ml} = 0.010 \, \text{L} \)
- \( V_2 = 1.00 \, \text{L} \)

2. **Rearranging the equation to find \( M_2 \)**:
\[ M_2 = \frac{M_1 V_1}{V_2} = \frac{(5.94 \times 10^{-5} \, \text{M})(0.010 \, \text{L})}{1.00 \, \text{L}} = 5.94 \times 10^{-7} \, \text{M} \]

### Final Result:
The resulting molarity of the diluted solution is approximately:
\[ \text{Molarity} \approx 5.94 \times 10^{-7} \, \text{M} \]

---