Question

Chemical analysis shows that the oxygen-carrying protein hemoglobin is 0.34 percent Fe by mass. What is the minimum possible molar mass of hemoglobin? The actual molar mass of hemoglobin is about \(65,000 \mathrm{~g}\). How would you account for the discrepancy between your minimum value and the experimental value?

Short answer

The minimum molar mass of hemoglobin is approximately 16,393 g/mol, differing from the actual 65,000 g/mol due to structural complexity and multiple iron atoms.

Step-by-step solution

Understanding the Problem

To find the minimum possible molar mass of hemoglobin based on iron content, we need to use the percentage of iron and assume iron is a critical component in the smallest possible unit of hemoglobin.

Calculating the Number of Moles of Iron

Given that hemoglobin is 0.34% iron by mass, for every 100 grams of hemoglobin, there are 0.34 grams of iron. We need to calculate the number of moles of iron present. The molar mass of iron (Fe) is about 55.85 g/mol.Number of moles of iron = \(\frac{0.34}{55.85}\approx 0.0061\) moles.

Determining the Minimum Molar Mass of Hemoglobin

The minimum assumption is that each molecule of hemoglobin contains only one iron atom. Thus, to find the simplest formula weight of hemoglobin, we assume 1 mole of hemoglobin contains 1 mole of iron.Therefore, the molecular weight is determined as: \(\frac{100}{0.0061} \approx 16,393 \, \text{g/mol}\).

Comparing with Experimental Molar Mass

Given the calculated minimum molar mass (16,393 g/mol) and the experimental molar mass (65,000 g/mol), the discrepancy can be attributed to the presence of multiple iron atoms in each hemoglobin molecule, or other structural complexities not considered by our minimum assumption.

Key concepts

Iron Content in Hemoglobin

Hemoglobin is a complex protein that plays a crucial role in transporting oxygen throughout the body. One of its most significant components is iron. The presence of iron is essential because it binds oxygen molecules, enabling hemoglobin to function efficiently. In chemical analysis, hemoglobin is found to be 0.34% iron by mass. This means that in every 100 grams of hemoglobin, there are 0.34 grams of iron. This percentage is critically important when determining the molar mass of hemoglobin.
Iron's role isn't merely passive but pivotal, anchoring oxygen and ensuring it can be transported where needed. Understanding the proportion of iron helps to unveil some of the molecular structure and functioning of hemoglobin. This information is useful when conducting experiments and making further calculations.

Molar Mass Calculation

Calculating the molar mass of hemoglobin based on its iron content involves several steps. It begins with calculating the number of moles of iron present in a given amount of hemoglobin. The molar mass of iron is approximately 55.85 g/mol. To find the number of moles in 0.34 grams of iron, you use the formula:
\[ \text{Number of moles of iron} = \frac{0.34 \text{ grams}}{55.85 \text{ g/mol}} \approx 0.0061 \text{ moles} \]
This calculation helps determine how many moles of hemoglobin correspond to iron content, assuming each hemoglobin molecule contains one atom of iron.
Next, we find the minimum possible molar mass of hemoglobin. Since 0.0061 moles of iron represent 100 grams of hemoglobin, the molar mass calculation for hemoglobin is:
\[ \text{Minimum molar mass of hemoglobin} = \frac{100}{0.0061} \approx 16,393 \text{ g/mol} \]
This value only provides a minimum estimate, assuming each hemoglobin unit carries one iron atom.

Chemical Analysis of Proteins

The chemical analysis of proteins like hemoglobin helps scientists better understand their structure and function. Proteins are complex molecules made from chains of amino acids, and chemical analysis allows researchers to dissect these chains to identify key components such as iron. Techniques like mass spectrometry and spectroscopy are often used.
Understanding the role and quantity of elements like iron within a protein helps in revealing how these proteins interact within biological systems. The specifics of protein chemistry are integral in fields like medicine and biotechnology, where insights into protein structures can lead to new therapies and advancements in diagnostics.

Discrepancy in Experimental Values

A calculated molar mass of hemoglobin based on iron content gives a value around 16,393 g/mol as a minimum. In contrast, experimental methods measure hemoglobin's molar mass to be about 65,000 g/mol.
This significant difference, or discrepancy, arises because the initial calculations oversimplify hemoglobin's structure. Hemoglobin is not only composed of single iron atoms but includes multiple iron atoms per molecule, complex tertiary and quaternary structures, as well as various amino acids linked in precise sequences.
Discrepancies in values often underline the necessity for understanding the broader context of chemical structures and molecular chemistry. They highlight how theoretical calculations may need adjustments when considering practical, real-world data and analyses. Students and scientists must remain prudent and mindful of these differences when interpreting calculated results versus experimental findings.