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Chapter 3: Problem 92

(a) One molecule of the antibiotic penicillin G has a mass of $5.342 \times 10^{-21} \mathrm{~g}$. What is the molar mass of penicillin G? (b) Hemoglobin, the oxygen-carrying protein in red blood cells, has four iron atoms per molecule and contains \(0.340 \%\) iron by mass. Calculate the molar mass of hemoglobin.

Short Answer

Expert verified
The molar mass of penicillin G is approximately \(3.214 \times 10^3\ \mathrm{g/mol}\), and the molar mass of hemoglobin is approximately \(6.56 \times 10^4\ \mathrm{g/mol}\).

Step by step solution

01

Determine the mass of one mole of penicillin G molecules

Multiply the given mass of a single penicillin G molecule by Avogadro's number, which is the number of particles (atoms, ions, or molecules) in one mole of any substance. $$ MolarMass= MassOfSingleMolecule \times Avogadro's Number $$ \(MolarMass= 5.342 \times 10^{-21} \mathrm{~g} \times 6.022\times10^{23}\mathrm{~particles/mol}\)
02

Calculate the molar mass of penicillin G

Perform the multiplication to find the molar mass of penicillin G. $$ MolarMass \approx 3.214 \times 10^3\ \mathrm{g/mol} $$ The molar mass of penicillin G is approximately \(3.214 \times 10^3\ \mathrm{g/mol}\). (b) Calculating the molar mass of hemoglobin
03

Determine the total mass of iron in one hemoglobin molecule

To do this, we will use the molar mass of iron, Fe, which is approximately 55.85 g/mol. Since there are four iron atoms in one molecule of hemoglobin, we can calculate its total mass of iron as follows: $$ TotalMassOfIronInHemoglobinMolecule= 4 \times MolarMassOfIron $$ $$ TotalMassOfIronInHemoglobinMolecule = 4 \times 55.85 \mathrm{~g/mol} $$
04

Calculate the molar mass of hemoglobin based on the percentage of iron

Hemoglobin contains 0.340% iron by mass, and we have calculated the total mass of iron in one hemoglobin molecule. Now we can find the molar mass of hemoglobin, knowing the mass of iron and the percentage: $$ MolarMassOfHemoglobin = \frac{TotalMassOfIronInHemoglobinMolecule}{PercentageOfIron} $$ $$ MolarMassOfHemoglobin = \frac{4 \times 55.85 \mathrm{~g/mol}}{0.00340} $$
05

Calculate the final molar mass of hemoglobin

Calculate the molar mass of hemoglobin: $$ MolarMassOfHemoglobin \approx 6.56 \times 10^4\ \mathrm{g/mol} $$ The molar mass of hemoglobin is approximately \(6.56 \times 10^4\ \mathrm{g/mol}\).

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Most popular questions from this chapter

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