To determine how many milliliters (mL) of a concentrated 11.5 M HCl aqueous solution are required to convert 1.00 kilogram of the free-base form of cocaine into its hydrochloride form, let's take the following steps:
1. Determine Moles of Cocaine:
- The molar mass of cocaine free-base is 303.353 grams per mole (g/mol).
- Given mass of cocaine: 1.00 kilograms = 1000 grams (g).
- Calculate moles of cocaine:
[tex]\[
\text{Moles of cocaine} = \frac{\text{mass}}{\text{molar mass}} = \frac{1000 \text{ g}}{303.353 \text{ g/mol}} \approx 3.295 \text{ moles}
\][/tex]
2. Determine Volume of HCl Solution Needed:
- The concentration of HCl is given as 11.5 M (Molar), which means 11.5 moles of HCl per liter of solution.
- Use the formula, [tex]\( \text{Volume (L)} = \frac{\text{Moles}}{\text{Concentration (M)}} \)[/tex], to find the volume of HCl solution needed.
[tex]\[
\text{Volume of HCl (L)} = \frac{3.295 \text{ moles}}{11.5 \text{ M}} \approx 0.287 \text{ liters}
\][/tex]
3. Convert Volume to Milliliters:
- There are 1000 milliliters (mL) in a liter.
- Convert the volume from liters to milliliters:
[tex]\[
\text{Volume of HCl (mL)} = 0.287 \text{ L} \times 1000 \text{ mL/L} = 287 \text{ mL}
\][/tex]
Therefore, to convert 1.00 kilogram of the free-base form of cocaine into its hydrochloride form, you would need approximately 287 mL of a concentrated 11.5 M HCl aqueous solution.
