Question

A sample of hemoglobin is found to be \(0.335 \%\) iron. If hemoglobin contains one iron atom per molecule, what is the molar mass of hemoglobin? What is the molar mass if there are four iron atoms per molecule?

Short answer

With one iron atom per molecule, the molar mass is about 16676.12 g/mol. With four iron atoms, it is about 4169.03 g/mol.

Step-by-step solution

Understand the Problem

We need to find the molar mass of hemoglobin based on the percentage of iron present. We'll calculate it for two scenarios: when hemoglobin contains one iron atom per molecule and when it contains four iron atoms per molecule.

Calculate Molar Mass with One Iron Atom

First, determine the mass of the iron in the hemoglobin sample that corresponds to the given percentage. If the sample is 100 g, then it contains 0.335 g of iron. The atomic mass of iron is approximately 55.85 g/mol. Thus, the molar mass of hemoglobin when it contains one iron atom is given by \[ \text{Molar mass of hemoglobin} = \frac{55.85\, \text{g/mol}}{0.00335} \approx 16676.12\, \text{g/mol} \]

Calculate Molar Mass with Four Iron Atoms

Assuming there are four iron atoms per molecule of hemoglobin, the total iron mass per molecule is 4 times the atomic mass of iron. Therefore, the percentage weight contribution of iron for four iron atoms is 4 times 0.335%. Thus, the molar mass of hemoglobin is computed as\[ \text{Molar mass of hemoglobin} = \frac{4 \times 55.85\, \text{g/mol}}{0.00335} \approx 4169.03\, \text{g/mol} \] since the contribution of iron is now 1.34% (4 times 0.335%).

Key concepts

Understanding Hemoglobin

Hemoglobin is an essential protein found in red blood cells. It carries oxygen from the lungs to other parts of the body and returns carbon dioxide back to the lungs to be exhaled. This protein is vital for maintaining healthy physiological functions and is mainly composed of four subunits. Each subunit contains a heme group, which binds oxygen. Hemoglobin's ability to efficiently bind oxygen is primarily due to its iron atom content. Understanding the composition of hemoglobin in relation to its iron atoms aids in calculating its molar mass, a key aspect in biological and chemical studies.

Exploring Iron Atoms in Hemoglobin

Iron atoms are central to hemoglobin's function, playing a critical role in its oxygen-carrying capacity. In its natural form, hemoglobin heterocyclic ring structures known as hemes contain iron ions. Each iron atom is capable of binding a single oxygen molecule, which is crucial for oxygen transport within the bloodstream. Depending on the biological state of hemoglobin, there can be a variation in the number of iron atoms per molecule, typically, either one or several iron atoms. These variations significantly impact the calculation of hemoglobin's molar mass, as each scenario yields a different molar mass based on the number of iron atoms.

Calculating Percentage Composition

Percentage composition is a method that tells us the makeup of a compound in terms of the percentage of each constituent element. For hemoglobin, it is expressed as the percentage contribution of iron to the overall mass of hemoglobin. In the calculation process, if the iron content is given as 0.335%, it means in every 100 grams of hemoglobin, there are 0.335 grams of iron. When evaluating different scenarios, such as hemoglobin containing one iron atom versus four, the percentage composition changes and this significantly influences the resulting molar mass of hemoglobin. High accuracy in determining the percentage composition is crucial as it directly affects the calculation outcomes.

Understanding Atomic Mass

Atomic mass is a fundamental concept in chemistry that refers to the mass of an atom, usually expressed in unified atomic mass units (u) or grams per mole (g/mol). For iron, the atomic mass is approximately 55.85 g/mol. This value is indispensable when calculating the molar mass of compounds like hemoglobin. By knowing the atomic mass of iron, it is possible to determine how much iron contributes to the total mass of hemoglobin, which helps in calculating the compound's molar mass under different conditions. Accurate use of atomic mass ensures reliable calculations, aiding chemists and biologists in understanding the molecular weight of such vital biomolecules.