Question

Hemoglobin \(\left(\mathrm{C}_{2952} \mathrm{H}_{4664} \mathrm{~N}_{812} \mathrm{O}_{832} \mathrm{~S}_{8} \mathrm{Fe}_{4}\right)\) is the oxygen 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

(a) Molar mass: 645719.792 g/mol. (b) 7500 g of hemoglobin in an average adult.

Step-by-step solution

Define the Molar Mass Formula

To find the molar mass of a compound, sum the products of the atomic masses of each element and its respective subscript in the chemical formula.

Calculate Molar Mass of Hemoglobin

Given the formula \( ext{C}_{2952} ext{H}_{4664} ext{N}_{812} ext{O}_{832} ext{S}_{8} ext{Fe}_{4}\), calculate the molar mass:- Carbon: \(2952 \times 12.01\)- Hydrogen: \(4664 \times 1.008\)- Nitrogen: \(812 \times 14.01\)- Oxygen: \(832 \times 16.00\)- Sulfur: \(8 \times 32.07\)- Iron: \(4 \times 55.85\)Add all values to get the molar mass: \[ \text{Molar mass} = (2952 \times 12.01) + (4664 \times 1.008) + (812 \times 14.01) + (832 \times 16.00) + (8 \times 32.07) + (4 \times 55.85) = 66052 + 4704.512 + 11371.32 + 13312 + 256.56 + 223.4 = 645719.792 \ ext{g/mol}.\]

Calculate Number of Hemoglobin Molecules

Each milliliter of blood contains approximately \(5.0 \times 10^{9}\) red blood cells, and each red blood cell has about \(2.8 \times 10^{8}\) hemoglobin molecules.First calculate the total number of hemoglobin molecules in 5.0 L of blood (5000 mL): \[ \text{Total hemoglobin molecules} = 5.0 \times 10^{9} \times 2.8 \times 10^{8} \times 5000.\] This results in \(7.0 \times 10^{21}\) hemoglobin molecules.

Convert Hemoglobin Molecules to Moles

Use Avogadro's number \(6.022 \times 10^{23}\) to convert molecules to moles: \[ \text{Moles of hemoglobin} = \frac{7.0 \times 10^{21}}{6.022 \times 10^{23}} = 1.162 \times 10^{-2} \text{ moles}.\]

Calculate Mass of Hemoglobin

To find the mass, multiply the moles of hemoglobin by its molar mass:\[ \text{Mass of hemoglobin} = 1.162 \times 10^{-2} \times 645719.792 \text{ g/mol} = 7500 \text{ grams (approximately)}.\]

Key concepts

Molar Mass

Understanding molar mass is essential in chemistry as it helps in determining the amount of a substance present in a sample. Molar mass is the mass of one mole of a substance, and it's computed by summing up the atomic masses of all atoms in a compound's formula. For instance, the molar mass of hemoglobin, which contains carbon, hydrogen, nitrogen, oxygen, sulfur, and iron, requires summing up each element's contribution based on its atomic mass and quantity listed in the formula.

The atomic masses are approximately: Carbon (12.01 g/mol), Hydrogen (1.008 g/mol), Nitrogen (14.01 g/mol), Oxygen (16.00 g/mol), Sulfur (32.07 g/mol), and Iron (55.85 g/mol). Calculate the contribution of each element by multiplying its atomic mass by the number of atoms and then add them all together to find the compound's total molar mass. This process reveals the molar mass of hemoglobin as approximately 645,720 grams per mole.

Red Blood Cells

Red blood cells, also known as erythrocytes, are crucial for transporting oxygen throughout the body. Each milliliter of blood contains about 5 billion red blood cells and each cell is packed with hemoglobin molecules. Hemoglobin is the protein responsible for oxygen transport and is thus critical for maintaining life.

To thoroughly understand the magnitude of these numbers, consider that an average adult has roughly 5 liters of blood. In total, this sums to an extraordinary number of red blood cells. Each cell containing vast quantities of hemoglobin reflects the efficiency and power of biological systems to support oxygen needs at a molecular level.

Avogadro's Number

Avogadro's number is a fundamental constant in chemistry, equal to approximately 6.022 x 10^23. It represents the number of units in one mole of any substance. These units could be atoms, molecules, ions, or other chemical entities.

When calculating the total hemoglobin molecules within an average adult's blood volume, Avogadro's number converts these vast quantities into moles. It allows us to shift from a microscopic view of millions and billions of molecules to a macroscopic and more practical scale of moles, making it easier to calculate and understand the mass and quantities in reactions and biological systems.

Chemistry Calculations

Chemistry calculations often combine precision with logical steps to unravel complex problems. In the context of hemoglobin and red blood cells, calculations bridge biochemical systems with quantitative analysis.

Calculations begin by defining the problem, such as determining the mass of hemoglobin in a given blood volume. Start by assessing the total number of molecules, converting that into moles using Avogadro's number, then finally into mass using molar mass.

• Define and gather data, such as formula and constants.
• Convert molecule counts to moles with Avogadro's constant.
• Calculate mass using the formula: Mass = Moles x Molar Mass.

These chemistry calculations ensure the precise determination of substances in blood, which is vital for understanding physiological chemistry and developing medical insights.