The concentration of cholesterol (C₂₇H₄₆O) in blood is approximately 5.0 mM. How many grams of cholesterol are in 250 mL of blood?

Verified step by step guidance

1. Identify the molar mass of cholesterol (C_{27}H_{46}O) by adding the atomic masses of all the atoms in the formula: 27 carbon atoms, 46 hydrogen atoms, and 1 oxygen atom.
2. Convert the concentration from millimoles per liter (mM) to moles per liter (M) by recognizing that 1 mM = 0.001 M.
3. Calculate the number of moles of cholesterol in 250 mL of blood by using the formula: \( \text{moles} = \text{concentration (M)} \times \text{volume (L)} \). Remember to convert 250 mL to liters.
4. Use the number of moles calculated to find the mass of cholesterol using the formula: \( \text{mass (g)} = \text{moles} \times \text{molar mass (g/mol)} \).
5. Ensure all units are consistent and check calculations for accuracy.

Key Concepts

Molarity and Concentration

Molarity is a measure of concentration defined as the number of moles of solute per liter of solution. In this case, a concentration of 5.0 mM (millimolar) indicates that there are 5.0 millimoles of cholesterol per liter of blood. Understanding molarity is essential for converting between volume and mass of a solute.

Molecular Weight

The molecular weight of a compound is the sum of the atomic weights of all atoms in its molecular formula. For cholesterol (C₂₇H₄₆O), the molecular weight can be calculated using the periodic table. This value is crucial for converting moles of cholesterol to grams, as it allows for the determination of how much mass corresponds to a given number of moles.

Unit Conversion

Unit conversion is the process of converting one unit of measurement to another. In this problem, it involves converting the concentration from millimoles per liter to grams, and the volume from milliliters to liters. Mastery of unit conversion is vital for accurately calculating the mass of cholesterol in the specified volume of blood.