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Chapter 3: Problem 119

Hemoglobin \(\left(\mathrm{C}_{2952} \mathrm{H}_{4664} \mathrm{~N}_{812} \mathrm{O}_{832} \mathrm{~S}_{8} \mathrm{Fe}_{4}\right)\) is the oxy- gen carrier in blood. (a) Calculate its molar mass. (b) An average adult has about \(5.0 \mathrm{~L}\) of blood. Every milliliter of blood has approximately \(5.0 \times 10^{9}\) erythrocytes, or red blood cells, and every red blood cell has about \(2.8 \times 10^{8}\) hemoglobin molecules. Calculate the mass of hemoglobin molecules in grams in an average adult.

Short Answer

Expert verified
Step 1 yields the Molar Mass of Hemoglobin. Step 2 gives the total number of Hemoglobin molecules in an average adult. Finally, Step 3 uses these results to determine the mass of Hemoglobin molecules in an average adult.

Step by step solution

01

Calculate Molar Mass of Hemoglobin

Each molecule of Hemoglobin consists of 2952 atoms of Carbon, 4664 atoms of Hydrogen, 812 atoms of Nitrogen, 832 atoms of Oxygen, 8 atoms of Sulfur, and 4 atoms of Iron. The molar mass of Hemoglobin is therefore calculated as: \(2952 \times \mathrm{Molar \; Mass} \; of \; Carbon + 4664 \times \mathrm{Molar \; Mass} \; of \; Hydrogen + 812 \times \mathrm{Molar \; Mass} \; of \; Nitrogen + 832 \times \mathrm{Molar \; Mass} \; of \; Oxygen + 8 \times \mathrm{Molar \; Mass} \; of \; Sulfur + 4 \times \mathrm{Molar \; Mass} \; of \; Iron\).
02

Calculate Number of Hemoglobin Molecules in an Average Adult

An average adult has about \(5.0 \mathrm{~L}\) of blood, every milliliter of blood contains approximately \(5.0 \times 10^{9}\) erythrocytes, and every red blood cell has about \(2.8 \times 10^{8}\) hemoglobin molecules. We can then calculate the total number of Haemoglobin molecules as: \(5.0 \mathrm{~L} \times 1000 \mathrm{~mL/L} \times 5.0 \times 10^{9} \mathrm{~cells/mL} \times 2.8 \times 10^{8} \mathrm{~molecules/cell}\).
03

Calculate the Mass of Hemoglobin Molecules in an Average Adult

To calculate the mass of Hemoglobin molecules in an average adult, the amount of hemoglobin molecules from Step 2 needs to be converted to grams using the Molar Mass from Step 1 and Avogadro’s law (\(1 \mathrm{~mole} \; = \; 6.022 \times 10^{23} \mathrm{~molecules}\)). The mass of hemoglobin molecules in an average adult can therefore be calculated by multiplying the total number of molecules with the molar mass and dividing by Avogadro's number.

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Most popular questions from this chapter

If we know the empirical formula of a compound, what additional information do we need to determine its molecular formula?

Propane \(\left(\mathrm{C}_{3} \mathrm{H}_{8}\right)\) is a component of natural gas and is used in domestic cooking and heating. (a) Balance the following equation representing the combustion of propane in air.$$\mathrm{C}_{3} \mathrm{H}_{8}+\mathrm{O}_{2} \longrightarrow \mathrm{CO}_{2}+\mathrm{H}_{2} \mathrm{O}$$ (b) How many grams of carbon dioxide can be produced by burning 3.65 moles of propane? Assume that oxygen is the excess reactant in this reaction.

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