Chemistry for Today: General, Organic, and Biochemistry
Chemistry for Today: General, Organic, and Biochemistry
9th Edition
ISBN: 9781305960060
Author: Spencer L. Seager, Michael R. Slabaugh, Maren S. Hansen
Publisher: Cengage Learning
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Chapter 24, Problem 24.67E
Interpretation Introduction

Interpretation:

The ketone present in the patient’s blood is to be stated. The number of ketone molecules in 1.0mL of patient’s blood is to be calculated.

Concept introduction:

Ketones are organic compounds containing carbonyl group. Both diabetic and non-diabetic human body contains some amount of ketone in it. Liver turns fat into ketones. High concentration of ketone in blood can be harmful.

Expert Solution & Answer
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Answer to Problem 24.67E

Acetone is present in the patient’s blood.

The number of ketone molecules in 1.0mL of patient’s blood is 5.18×1015.

Explanation of Solution

It is given that the molecular weight of ketone is 58.1g/mol.

The starting member of ketone family is acetone.

The molecular formula of acetone is C3H6O.

The molar mass of hydrogen is 1g/mol.

The molar mass of oxygen is 16g/mol.

The molar mass of carbon is 12g/mol.

Therefore, the molecular weight of acetone is calculated as shown below.

Molecular weight of acetone =(3×C+1×O+6×H)g/mol=(3×12+1×16+6×1)g/mol=(36+16+6)g/mol=58g/mol

The molecular weight of ketone present in patient’s blood is approximately equal to that of acetone. Therefore, acetone is present in the patient’s blood.

It is given that the concentration of ketone in 100mL of patient’s blood is 0.050mg.

Therefore, the concentration of ketone in 1.0mL of patient’s blood is 0.050100mg.

The conversion of 0.050mg to g is shown below.

0.050mg=0.050×103g

Therefore, the concentration of ketone in 100mL of patient’s blood is 0.050×103g.

Therefore, the concentration of ketone in 1.0mL of patient’s blood is 0.050×103100g.

The number of acetone molecules in 1.0mL of patient’s blood is calculated by the formula shown below.

Numberofketonemolecules=(Concentrationofketonein1.0mLofbloodMolecularweightofketone)×NA…(1)

Where,

NA is Avogadro’s constant.

The concentration of ketone in 1.0mL of patient’s blood is 0.050×103100g.

The molecular weight of ketone is 58.1g/mol.

The value of NA is 6.022×1023mol-1.

Substitute the value of concentration of ketone in 1.0mL blood, molecular weight of ketone and NA in equation (1).

Numberofketonemolecules=(Concentrationofketonein1.0mLofbloodMolecularweightofketone)×NA=(0.050×103100g58.1g/mol)×6.022×1023mol-1=5.18×108×1023=5.18×1015

Therefore, the number of ketone molecules in 1.0mL of patient’s blood is 5.18×1015.

Conclusion

Acetone is present in the patient’s blood and the number of ketone molecules in 1.0mL of patient’s blood is 5.18×1015.

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Chapter 24 Solutions

Chemistry for Today: General, Organic, and Biochemistry

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