Respuesta :
Answer
The grams of cholesterol in 610 mL of blood to one significant figure = 1.0 g
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
[tex]\begin{gathered} Molarity=\frac{Moles}{Volume\text{ }in\text{ }L} \\ \\ Moles=Molarity\times Volume\text{ }in\text{ }L \\ \\ Moles=0.005\text{ }M\times0.610\text{ }L \\ \\ Moles=3.05\times10^{-3}\text{ }mol \end{gathered}[/tex]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:
[tex]\begin{gathered} C_{27}H_{46}O=(27\times12.011)+(46\times1.00784)+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}[/tex]Step 3: Determine the grams of Cholesterol.
The grams of cholesterol in 610 mL of blood will be:
[tex]\begin{gathered} Mass=Moles\times Molar\text{ }mass \\ \\ Mass=3.05\times10^{-3}\text{ }mol\times386.68\text{ }g\text{/}mol \\ \\ Mass=1.179\text{ }grams\approx1.0\text{ }gram \end{gathered}[/tex]Hence, the grams of cholesterol in 610 mL of blood to one significant figure is 1.0 g.
