Problem 119 - Chemistry

Question

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.

Step-by-Step Solution

Answer

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 1: 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: \(2952 \times \mathrm{Molar \; Mass} \; of \; Carbon + 4664 \times \mathrm{Molar \; Mass} \; of \; Hydrogen + 812 \times \mathrm{Molar \; Mass} \; of \; Nitrogen + 832 \times \mathrm{Molar \; Mass} \; of \; Oxygen + 8 \times \mathrm{Molar \; Mass} \; of \; Sulfur + 4 \times \mathrm{Molar \; Mass} \; of \; Iron\).

Step 2: 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: \(5.0 \mathrm{~L} \times 1000 \mathrm{~mL/L} \times 5.0 \times 10^{9} \mathrm{~cells/mL} \times 2.8 \times 10^{8} \mathrm{~molecules/cell}\).

Step 3: 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.

Key Concepts

Hemoglobin Structure

Hemoglobin is a complex protein that plays a crucial role in transporting oxygen from the lungs to the cells throughout our body. Its structure consists of four subunits, each containing a heme group.
These heme groups contain iron atoms and are critical for the protein's ability to bind and release oxygen efficiently.

• Composition: Hemoglobin is made up of 2952 carbon atoms, 4664 hydrogen atoms, 812 nitrogen atoms, 832 oxygen atoms, 8 sulfur atoms, and 4 iron atoms.
• Function: The iron within the heme groups is responsible for binding oxygen, making it vitally important for our survival.

Understanding this structure is essential for comprehending how hemoglobin accomplishes its task of oxygen transport effectively, which is fundamental to the functioning of red blood cells.

Red Blood Cells

Red blood cells, also known as erythrocytes, are the carriers of hemoglobin in the bloodstream. These cells are biconcave in shape, which increases their surface area and allows for a more efficient exchange of gases.
In a single milliliter of blood, there are about 5.0 billion red blood cells, each equipped with a large number of hemoglobin molecules.

• Amount in Blood: An average adult has about 5 liters of blood, equating to a vast number of red blood cells that constantly circulate through the body.
• Role: Their primary job is to transport oxygen from the lungs to tissues and help in the removal of carbon dioxide.

Understanding the sheer volume of red blood cells and their role provides insight into the body's ability to sustain oxygen levels and overall health.

Avogadro's Number

Avogadro's number is a key constant in chemistry that is fundamental to understanding how molecules are quantified in moles. Defined as approximately 6.022 x 10²³ molecules per mole, it allows chemists to scale experiments up from the atomic and molecular level to quantities that can be seen and measured.
Avogadro's number plays a crucial role in calculating the mass of hemoglobin because it links the total number of molecules (as discussed in the original exercise) to a tangible mass in grams.

• Purpose: It is used to convert mole quantities to molecular numbers, essential for calculations involving large complex molecules like hemoglobin.
• Application: In practical chemistry, Avogadro's number helps in understanding reactions and mass of substances based on molecular proportions.

By applying Avogadro's number, we can accurately calculate the mass of hemoglobin molecules in an adult's body, highlighting the importance of precise molecular knowledge in real-world applications.