Principles of Modern Chemistry
Principles of Modern Chemistry
8th Edition
ISBN: 9781305079113
Author: David W. Oxtoby, H. Pat Gillis, Laurie J. Butler
Publisher: Cengage Learning
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Chapter 11, Problem 1P

A patient has a “cholesterol count” of 214. Like manyblood-chemistry measurements,this result is measured inunits of milligrams per deciliter ( mg dL 1 ) .
Determine the molar concentration of cholesterol inthis patient’s blood, taking the molar mass of cholesterolto be 386.64 g mol 1 .

  1. Estimate the molality of cholesterol in the patient’sblood.
  2. If 214 is a typical cholesterol reading among men inthe United States, determine the volume of such bloodrequired to furnish 8.10 g of cholesterol.

(a)

Expert Solution
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Interpretation Introduction

Interpretation: The molar concentration of cholesterol in blood of patient needs to be calculated by taking molar mass of cholesterol equal to 386.64 g/mol.

Concept Introduction: The molar concentration or molarity of a substance is number of moles of solute in 1 L of the solution.

Explanation of Solution

The cholesterol count of patient is 214 mg dL-1.

Thus, molar concentration of cholesterol (mol/L) can be calculated as follows:

  C=XM

Here, C is molar concentration, X is cholesterol count and M is molar mass.

Substitute the values,

  C=XM=214 mg/dL1 dL101L103 g1 mg386.64 g/mol=0.005535 mol/L=5.535×103 mol/L

Therefore, molar concentration of cholesterol is 5.535×103 mol/L .

(b)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation: The molality of cholesterol in the patient’s blood needs to be estimated.

Concept Introduction: The molality of a substance is number of moles of a substance in 1 kg of solvent.

Explanation of Solution

It is related to molarity of solution or molar concentration of solution as follows:

  m=1000×MM×Mb1000×d

Here, M is molarity, Mb is molar mass of solute and d is density of solution.

In the given case, solute is cholesterol and solvent is blood. The relation between molarity (molar concentration) and molality of solution is as follows:

  m=1000×MM×Mb1000×d

Here, molarity of solution is 5.535×103 mol/L . The density of solution is 0.994 g/mL (density of blood) and molar mass of cholesterol is 386.64 g/mol.

Substitute the values,

  m=10005.535×103 mol/L5.535×103 mol/L386.64 g/mol1000×0.994 g/mL=5.535 0.005535×607.36=1.65 m

Thus, the molality of solution is 1.65 m .

(c)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation: The volume of blood required to furnish 8.10 g of cholesterol needs to be calculated.

Concept Introduction: To calculate the volume of blood requited for given mass of cholesterol, unitary method can be used. Here, mass of cholesterol in 1 dL of blood is given thus, volume of blood required for given mass of cholesterol can be calculated.

Explanation of Solution

The cholesterol count of patient is 214 mg dL-1. Thus, in 1 dL of blood there is 214 mg of cholesterol.

The volume of blood required for 8.10 g of cholesterol will be:

  V=8.10 g214 mgdL103 g1 mg=37.850 dL101 L1 dL=3.785 L

Therefore, volume of blood required is 3.785 L .

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Solutions: Crash Course Chemistry #27; Author: Crash Course;https://www.youtube.com/watch?v=9h2f1Bjr0p4;License: Standard YouTube License, CC-BY