Question

Question #29519

Answer 1

`"5.33 mM"`

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, `"mg/dL"`. As you know, molarity is defined as moles of solute per 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.