Problem 1 - Physics

Question

Hemoglobin has a molecular mass of \(64500 \mathrm{u}\). Find the mass (in \(\mathrm{kg}\) ) of one molecule of hemoglobin.

Step-by-Step Solution

Answer

The mass of one molecule of hemoglobin is \(1.071 \times 10^{-22} \text{ kg}\).

Step 1: Understand the Molecular Mass Unit

The molecular mass of a substance expressed in atomic mass units (u) is the mass of one molecule of that substance in terms of a scale where the carbon-12 atom is set to 12 u. 1 u is equivalent to \(1.66053906660 \times 10^{-27}\) kg.

Step 2: Use the Molecular Mass of Hemoglobin

The problem states that the molecular mass of hemoglobin is 64500 u. This means that one molecule of hemoglobin has a mass of 64500 u in the atomic mass unit scale.

Step 3: Convert Molecular Mass to Kilograms

To find the mass of one molecule of hemoglobin in kilograms, multiply the molecular mass (64500 u) by the conversion factor for atomic mass units to kilograms: \(64500 \times 1.66053906660 \times 10^{-27} \text{ kg/u}\).

Step 4: Perform the Calculation

Carry out the multiplication: \(64500 \times 1.66053906660 \times 10^{-27} = 1.071245224 \times 10^{-22} \text{ kg}\). Thus, the mass of one molecule of hemoglobin is \(1.071 \times 10^{-22} \text{ kg}\).

Key Concepts

Atomic Mass Unit

Atomic mass unit, often abbreviated as \'u\', is a standard unit of measure used in chemistry and physics to express the mass of atoms and molecules. It provides a simple way to compare different elements and compounds by establishing a common scale where the carbon-12 isotope is assigned a mass of exactly 12 atomic mass units. This is helpful, as elements and compounds can have very different masses at the atomic level.

To put it into perspective:

• 1 atomic mass unit is defined as one twelfth the mass of a carbon-12 atom.
• 1 u is approximately equal to \(1.66053906660 \times 10^{-27}\) kilograms.

This tiny mass is effective for calculating molecular masses in a manageable way, especially when dealing with large molecules like hemoglobin.

Mass Conversion

Mass conversion involves changing the units in which the mass of an object is expressed. This is critical when working with atomic-scale masses, as scientists often switch between atomic mass units and kilograms to relate microscopic masses to more familiar macroscopic units.

The process is simple and requires a known conversion factor:

• The conversion factor from atomic mass units to kilograms is \(1.66053906660 \times 10^{-27}\text{ kg/u}\).

To convert molecular mass to kilograms, you multiply the given mass in atomic mass units by the conversion factor. For example, the hemoglobin molecule's mass in kilograms can be found by multiplying its atomic mass unit value (64500 u) by \(1.66053906660 \times 10^{-27}\) to obtain \(1.071 \times 10^{-22}\) kilograms. This straightforward multiplication provides a clear pathway to represent the tiny mass in a more tangible unit like kilograms.

Hemoglobin Molecule

The hemoglobin molecule is a large and complex protein found in red blood cells, and it plays a vital role in transporting oxygen from the lungs to the rest of the body. Understanding its structure and mass is important in both medical and biochemistry fields.

Hemoglobin comprises multiple subunits and has a relatively high molecular mass of 64500 atomic mass units. This considerable mass is due to the molecule's intricate structure, which includes iron atoms crucial for oxygen transport.

• Each hemoglobin molecule contains four iron atoms that bind to oxygen molecules.
• Its high mass allows it to effectively carry oxygen throughout the bloodstream, highlighting its critical biological function.

Knowing the molecular mass of hemoglobin also aids in studying various blood-related health conditions, making it essential for scientific and medical research.