Problem 13 - General Chemistry: Principles and Modern Applications

Question

The hemoglobin content of blood is about \(15.5 \mathrm{g} / 100 \mathrm{mL}\) blood. The molar mass of hemoglobin is about \(64,500 \mathrm{g} / \mathrm{mol},\) and there are four iron (Fe) atoms in a hemoglobin molecule. Approximately how many Fe atoms are present in the 6 Lof blood in a typical adult?

Step-by-Step Solution

Answer

The number of Fe atoms present in the blood of a typical adult is approximately \(3.381 \times 10^{25}\)

Step 1: Convert the quantity of blood to mL

An adult has 6 L of blood, which converts to \(6000 \mathrm{mL}\) since \(1 \mathrm{L} = 1000 \mathrm{mL}\).

Step 2: Find the mass of hemoglobin in this volume

If there is \(15.5 \mathrm{g}\) of hemoglobin in \(100 \mathrm{mL}\) of blood, then in \(6000 \mathrm{mL}\) of blood there will be \( \xi = \frac{6000 \times 15.5}{100} = 930 \mathrm{g} \) of hemoglobin, where \(\xi\) refers to the required quantity of hemoglobin.

Step 3: Convert the mass of hemoglobin to moles

Knowing that the molar mass of hemoglobin is \(64500 \mathrm{g/mol}\), the molar quantity \(\eta\) of hemoglobin is found using the formula: \(\eta = \frac{\xi}{64500} = 0.014 \mathrm{mol}\)

Step 4: Calculate the number of Fe atoms

Each molecule of hemoglobin contains 4 atoms of Fe. Therefore, the number of iron atoms is \(4 \times \eta \times 6.022 \times 10^{23} = 3.381 \times 10^{25}\)

Key Concepts

Understanding Hemoglobin

Hemoglobin is a crucial protein found in red blood cells, responsible for carrying oxygen from the lungs to other parts of the body. It also transports carbon dioxide back to the lungs to be exhaled. Hemoglobin's structure consists of four subunits, each containing an iron atom, which is vital for its oxygen-carrying capacity.
- The presence of iron atoms in hemoglobin is what allows it to bind with oxygen molecules efficiently. - Iron atoms give blood its distinctive red color when bound to oxygen. - This protein functions as an essential tool in maintaining adequate levels of oxygen in tissues and organs. Understanding hemoglobin at a molecular level can help us appreciate its role in respiration and its importance to overall health.

What is Molar Mass?

Molar mass is a central concept in chemistry that represents the mass of one mole of a substance. One mole equals Avogadro's number, which is approximately 6.022 x 10^23 entities, be they atoms, molecules, or ions. The molar mass provides the bridge between the mass of a material and the amount of moles present. - By knowing the molar mass, we can convert grams into moles, making it easier to work with chemical equations. - For hemoglobin, the molar mass is about 64,500 g/mol, which means one mole of hemoglobin weighs approximately 64,500 grams. - Calculating the molar mass involves summing the atomic masses of all atoms in a molecule's formula. This concept is indispensable for converting between the mass of substances used or produced in a reaction and the number of molecules or atoms involved.

Calculating Iron Atoms in Blood

Calculating the number of iron atoms in a given sample of hemoglobin involves several steps, as you've seen in the problem example. Here's how the process unfolds neatly: - First, determine the total amount of hemoglobin in a specified blood volume using the given mass of hemoglobin per 100 mL of blood. - Next, convert this mass to moles using the molar mass of hemoglobin. - Finally, calculate the number of iron atoms by knowing that each hemoglobin molecule contains four iron atoms. Since one mole consists of Avogadro's number of molecules (approximately 6.022 x 10^23), multiplying the number of moles by Avogadro's number tells us how many molecules are present, and hence the total number of iron atoms is calculated by further multiplying by 4 (as there are 4 iron atoms per molecule). This method allows chemists to understand how alterations at the molecular level affect large-scale biological processes.