# Question #29519

##### 1 Answer

#### Explanation:

You need to pay close attention to the *units* given to you for the patient's cholesterol.

Notice that the cholesterol count is given in *miligrams per deciliter*, **liters of solution**.

This means that you're going to have to convert the mass from *miligrams* to *grams*, since this will allow you to use the molar mass of cholesterol, and the volume from *deciliters* to *liters*, using these conversion factors

#"1 g" = 10^(3)"mg" " "# and#" " "1 L " = " 10 dL"#

The cholesterol count in *grams per liter* will thus be

#206color(red)(cancel(color(black)("mg")))/color(red)(cancel(color(black)("dL"))) * (10color(red)(cancel(color(black)("dL"))))/"1 L" * "1 g"/(10^3color(red)(cancel(color(black)("mg")))) = "2.06 g/L"#

The molarity of cholesterol will thus be

#2.06color(red)(cancel(color(black)("g")))/"L" * "1 mole cholesterol"/(386.64color(red)(cancel(color(black)("g")))) = 0.00533"moles"/"L" = "0.00533 M"#

Alternatively, you can express this value in *milimolar*, which is equivalent to *milimoles per liter*.

#0.00533color(red)(cancel(color(black)("moles")))/"L" * (10^3"mmoles")/(1color(red)(cancel(color(black)("mole")))) = "5.33 mM"#

The answer is rounded to three sig figs, the number of sig figs you have for the cholesterol count.