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Chapter 4: Problem 40

High-density lipoprotein (HDL) cholesterol is the “good” cholesterol because adequate levels reduce the risk of heart disease and stroke. HDL levels between 40. and 59 mg/dL are typical for a healthy individual. What is this range of HDL cholesterol in units of mol/L? The formula for cholesterol is \(\mathrm{C}_{27} \mathrm{H}_{46} \mathrm{O}\)

Short Answer

Expert verified
The range of HDL cholesterol in units of mol/L is from 0.103 mol/L to 0.152 mol/L.

Step by step solution

01

1. Find the molar mass of cholesterol

Using the molecular formula C27H46O, we first need to find the molar mass of cholesterol. To do this, multiply the atomic mass of each element by the number of its atoms in a molecule and add up the resulting values for each element: Molar mass of cholesterol (M) = (27 * atomic mass of carbon) + (46 * atomic mass of hydrogen) + (atomic mass of oxygen) Using the atomic masses of C (12.01 g/mol), H (1.01 g/mol), and O (16.00 g/mol), we can calculate M: M = (27 * 12.01) + (46 * 1.01) + (16.00)= 324.27 + 46.46 + 16.00 = 386.73 g/mol
02

2. Convert the range of HDL cholesterol from mg/dL to g/L

We have the range of HDL cholesterol levels between 40 and 59 mg/dL. To convert this into g/L, we apply the following conversions: 1 mg = 0.001 g 1 dL = 0.1 L The conversion factor for mg to g is 0.001 and for dL to L is 0.1, so we can convert the lower and upper values of the range as follows: 40 mg/dL = 40 * 0.001 g/dL = 4 g/dL 4 g/dL = 4 / 0.1 g/L = 40 g/L 59 mg/dL = 59 * 0.001 g/dL = 5.9 g/dL 5.9 g/dL = 5.9 / 0.1 g/L = 59 g/L Thus, the range of HDL cholesterol in g/L is from 40 g/L to 59 g/L.
03

3. Calculate the range of HDL cholesterol in mol/L

Now we have the range of HDL cholesterol in g/L, and we can convert it to mol/L using the molar mass (M) of cholesterol that we calculated earlier: Lower limit (40 g/L): Number of moles = mass of cholesterol (g) / molar mass of cholesterol (g/mol) Number of moles = 40 g / 386.73 g/mol = 0.103 mol/L Upper limit (59 g/L): Number of moles = mass of cholesterol (g) / molar mass of cholesterol (g/mol) Number of moles = 59 g / 386.73 g/mol = 0.152 mol/L The range of HDL cholesterol in units of mol/L is from 0.103 mol/L to 0.152 mol/L.

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Most popular questions from this chapter

The blood alcohol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\) level can be determined by tirrating a sample of blood plasma with an acidic potassium dichromate solution, resulting in the production of \(\mathrm{Cr}^{3+}(a q)\) and carbon dioxide. The reaction can be monitored because the dichromate ion \(\left(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}\right)\) is orange in solution, and the \(\mathrm{Cr}^{3+}\) ion is green. The unbalanced redox equation is $$\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(a q)+\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(a q) \rightarrow \mathrm{Cr}^{3+}(a q)+\mathrm{CO}_{2}(g)$$ If 31.05 \(\mathrm{mL}\) of 0.0600\(M\) potassium dichromate solution is required to titrate 30.0 \(\mathrm{g}\) of blood plasma, determine the mass percent of alcohol in the blood.

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