Question

The concentration of cholesterol (C27H46O) in normal blood is approximately 0.005 M.How many grams of cholesterol are in 610 mL of blood?Express your answer to one significant figure and include the appropriate units

Answer 1

The grams of cholesterol in 610 mL of blood to one significant figure = 1.0 g

Step-by-step explanation

Given:

The concentration of cholesterol (C27H46O) in normal blood = 0.005 M

The volume of blood = 610 mL = 0.610 L

What to find:

The grams of cholesterol in 610 mL of blood.

Step-by-step solution:

Step 1: Determine the moles of cholesterol.

The number of moles of cholesterol in the blood can be calculated using the molarity formula, which is

`\begin{gathered} Molarity=\frac{Moles}{Volume\text{ }in\text{ }L} \\ \\ Moles=Molarity* Volume\text{ }in\text{ }L \\ \\ Moles=0.005\text{ }M*0.610\text{ }L \\ \\ Moles=3.05*10^(-3)\text{ }mol \end{gathered}`

Step 2: Calculate the molar mass of cholesterol.

Using the atomic masses of (H = 1.00784, C = 12.011, O = 15.999) from the periodic table, the molar mass of cholesterol is calculated as follows:

`\begin{gathered} C_(27)H_(46)O=(27*12.011)+(46*1.00784)+15.999 \\ \\ C_(27)H_(46)O=324.297+46.36064+15.999 \\ \\ C_(27)H_(46)O=386.68\text{ }g\text{/}mol \end{gathered}`

Step 3: Determine the grams of Cholesterol.

The grams of cholesterol in 610 mL of blood will be:

`\begin{gathered} Mass=Moles* Molar\text{ }mass \\ \\ Mass=3.05*10^(-3)\text{ }mol*386.68\text{ }g\text{/}mol \\ \\ Mass=1.179\text{ }grams\approx1.0\text{ }gram \end{gathered}`

Hence, the grams of cholesterol in 610 mL of blood to one significant figure is 1.0 g.