Question

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

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

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

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.

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.

Key concepts

Cholesterol Conversion

Understanding cholesterol conversion is important for assessing cholesterol levels in different units. Cholesterol levels are often measured in milligrams per deciliter (mg/dL), but converting it to moles per liter (mol/L) can provide more insights related to molecular concentrations. The conversion requires two main steps:

• Convert mg/dL to g/L by multiplying by 0.001 to change milligrams to grams and dividing by 0.1 to change deciliters to liters. For example, 40 mg/dL equals 40 mg * 0.001 g/mg * 0.1 L/dL = 0.4 g/L.
• Use the molar mass to convert from g/L to mol/L. Divide the cholesterol grams per liter by its molar mass (386.73 g/mol). For example, 40 g/L becomes 40 g/L / 386.73 g/mol = 0.103 mol/L.

This conversion helps in biochemical calculations and understanding variations in individuals' cholesterol levels.

HDL Cholesterol Levels

HDL, or high-density lipoprotein cholesterol, is sometimes called the 'good' cholesterol. It helps remove other forms of cholesterol from your bloodstream, playing a protective role against heart disease. HDL levels are usually measured in mg/dL but can also be calculated in mol/L for precision in scientific contexts.

• Healthy HDL levels range from 40 mg/dL to 59 mg/dL.
• In mol/L, this range converts to approximately 0.103 mol/L to 0.152 mol/L, reflecting the biochemical concentration more precisely.

Keeping track of HDL cholesterol levels in different units can be beneficial for those managing their cardiovascular health, as it provides a clearer picture of cholesterol dynamics.

Molecular Formula

A molecular formula represents the number and type of atoms in a molecule. For cholesterol, this is \(\text{C}_{27} \text{H}_{46} \text{O}\), indicating it contains 27 carbon atoms, 46 hydrogen atoms, and a single oxygen atom.

• The molecular formula aids in calculating the molar mass, a critical figure in chemical conversion.
• For cholesterol, its molar mass is calculated as 386.73 g/mol using the atomic masses (C = 12.01 g/mol, H = 1.01 g/mol, O = 16.00 g/mol).

Knowing the molecular formula and molar mass allows for conversions between mass and moles, essential for understanding molecular quantities in scientific experiments.