Question

A patient has a "cholesterol count" of 214. Like many blood-chemistry measurements, this result is measured in units of milligrams per deciliter $\mathbf{(}{\mathrm{mgdL}}^{-1})$

(a) Determine the molar concentration of cholesterol in this patient's blood, taking the molar mass of cholesterol to be $\mathbf{386}\mathbf{.}\mathbf{64}\mathbf{}\mathbf{g}\mathbf{}{\mathbf{mol}}^{\mathbf{-}\mathbf{1}}$.

(b) Estimate the molality of cholesterol in the patient's blood.

(c) If 214 is a typical cholesterol reading among men in the United States, determine the volume of such blood required to furnish 8.10kg of cholesterol.

Short answer

a) The molar concentration of cholesterol in the patient’s blood is $5.53\times {10}^{-3}\mathrm{M}$.

b) The molality of cholesterol in the patient's blood is $5.53\times {10}^{-3}\mathrm{M}$.

c) The volume of blood required to furnish of cholesterol is 3.79L.

Step-by-step solution

Define molar concentration and molality of a solution

Molar concentration (Molarity) is described as the total number of moles of solute dissolved in per liter of solution, i.e. $\mathbf{M}\mathbf{=}\mathbf{mol}\mathbf{/}\mathbf{L}$.

The molar concentration formula is: Molar concentration.$\mathbf{=}\frac{\mathbf{Amountinmoles}}{\mathbf{VolumeofSolution}}$

Molality is defined as the total moles of a solute contained in a kilogram of a solvent.

Thus, the molality of a solution is given by the following formula:

$\begin{array}{l}\mathbf{m}\mathbf{=}\frac{\mathbf{Numberofmolesofsolute}}{\mathbf{Massofsolventinkgs}}\\ \mathbf{m}\mathbf{=}\frac{\mathbf{g}\mathbf{\times }\mathbf{1000}}{\mathbf{W}\mathbf{\times }\mathbf{m}}\end{array}$

Calculate the number of moles of cholesterol 

Calculate the molar concentration of cholesterol in the patient’s blood

Calculate the molality of cholesterol in the patient's blood

Calculate the volume of blood required to furnish of cholesterol