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

Ch.9 Solutions

McMurry - Fundamentals of General, Organic, and Biological Chemistry 8th Edition

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McMurry 8th Edition

Ch.9 Solutions

문제 14

9장, 문제 14

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

검증된 단계별 안내

Step 1: Understand the problem. We are tasked with finding the mass of cholesterol (C₂₇H₄₆O) in grams, given its concentration in millimolar (mM) and the volume of blood in milliliters (mL).

Step 2: Convert the concentration from millimolar (mM) to molar (M). Recall that 1 mM = 10⁻³ M. Multiply the given concentration (5.0 mM) by 10⁻³ to express it in mol/L.

Step 3: Calculate the number of moles of cholesterol in the given volume of blood. Use the formula: \( \text{moles} = \text{concentration (M)} \times \text{volume (L)} \). Convert the volume from mL to L by dividing by 1000 (since 1 L = 1000 mL).

Step 4: Determine the molar mass of cholesterol (C₂₇H₄₆O). Add the atomic masses of all the atoms in the molecular formula: \( 27 \times \text{atomic mass of C} + 46 \times \text{atomic mass of H} + 1 \times \text{atomic mass of O} \). Use the periodic table to find the atomic masses (C = 12.01 g/mol, H = 1.008 g/mol, O = 16.00 g/mol).

Step 5: Calculate the mass of cholesterol in grams. Use the formula: \( \text{mass (g)} = \text{moles} \times \text{molar mass (g/mol)} \). Multiply the number of moles (from Step 3) by the molar mass (from Step 4) to find the mass of cholesterol in the given volume of blood.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Molarity

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

Molecular Weight

Molecular weight is the mass of one mole of a substance, expressed in grams per mole (g/mol). For cholesterol (C₂₇H₄₆O), the molecular weight is approximately 386.65 g/mol. This value is crucial for converting moles of cholesterol into grams, allowing for the calculation of the total mass present in a given volume of blood.

Volume Conversion

Volume conversion involves changing the measurement of volume from one unit to another, such as from milliliters (mL) to liters (L). Since molarity is expressed in moles per liter, it is necessary to convert the volume of blood (250 mL) into liters (0.250 L) to accurately calculate the amount of cholesterol in grams using the concentration and molecular weight.