Problem: The "free-base" form of cocaine (C17H21NO4) and its protonated hydrochloride form (C17H22ClNO4) are shown below; the free-base form can be converted to the hydrochloride form with one equivalent of HCl. For clarity, not all the carbon and hydrogen atoms are shown; each vertex represents a carbon atom with the appropriate number of hydrogen atoms so that each carbon makes four bonds to other atoms.The hydrochloride form of cocaine has a solubility of 1.00 g in 0.400 mL water. Calculate the molarity of a saturated solution of the hydrochloride form of cocaine in water.

FREE Expert Solution

Recall that molarity is the ratio of the moles of solute and the volume of solution (in liters). In other words:

$\boxed{\mathbf{molarity}\mathbf{ }\mathbf{\left(}\mathbf{M}\mathbf{\right)}\mathbf{=}\frac{\mathbf{moles}\mathbf{ }\mathbf{solute}}{\mathbf{L}\mathbf{ }\mathbf{solution}}}$

The moles of cocaine hydrochloride is:

molar mass C₁₇H₂₂ClNO₄ = 339.806 g/mol

$\mathbf{moles}\mathbf{ }{\mathbf{C}}_{\mathbf{17}}{\mathbf{H}}_{\mathbf{22}}{\mathbf{ClNO}}_{\mathbf{4}}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{00}\mathbf{ }\cancel{\mathbf{g}}\mathbf{\times }\frac{\mathbf{1}\mathbf{ }\mathbf{mol}}{\mathbf{339}\mathbf{.}\mathbf{806}\mathbf{ }\cancel{\mathbf{g}}}$

moles C₁₇H₂₂ClNO₄ = 2.9428x10^-3 mol

Calculate the volume of the solution: 1 mL = 10^-3 L

$\mathbf{volume}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{400}\mathbf{ }\cancel{\mathbf{mL}}\mathbf{\times }\frac{{\mathbf{10}}^{\mathbf{-}\mathbf{3}}\mathbf{ }\mathbf{L}}{\mathbf{1}\mathbf{ }\cancel{\mathbf{mL}}}$

volume = 4.0x10^-4 L

We can now calculate for molarity:

95% (223 ratings)