Problem 138 - Chemistry The Molecular Science

Question

An adult human body contains \(6.0 \mathrm{~L}\) blood, which contains about \(15.5 \mathrm{~g}\) hemoglobin per \(100.0 \mathrm{~mL}\) blood. The molar mass of hemoglobin is approximately \(64,500 \mathrm{~g} / \mathrm{mol}\) and there is 4 mol iron per 1 mol hemoglobin. A news item claims that there is sufficient iron in the hemoglobin of the body that this iron, if it were in the form of metallic iron, could make a 3 -in. iron nail that weighs approximately \(3.7 \mathrm{~g}\). Show sufficient calculations to either support or refute the claim.

Step-by-Step Solution

Answer

The claim is false; 3.2144 g of iron is not enough for a 3.7 g nail.

Step 1: Calculate the total mass of hemoglobin in the blood

First, we determine the total mass of hemoglobin in the entire blood volume. The adult body contains 6.0 L (or 6000 mL) of blood. Since each 100 mL of blood contains 15.5 g of hemoglobin, we calculate:\[ \text{Total mass of hemoglobin} = 6000 \, \text{mL} \times \frac{15.5 \, \text{g}}{100 \, \text{mL}} = 930 \, \text{g} \]

Step 2: Calculate the number of moles of hemoglobin

Using the molar mass of hemoglobin, we convert the total mass from grams to moles. The molar mass of hemoglobin is 64,500 g/mol. Thus:\[ \text{Number of moles of hemoglobin} = \frac{930 \, \text{g}}{64,500 \, \text{g/mol}} \approx 0.0144 \, \text{mol} \]

Step 3: Calculate the total moles of iron in the hemoglobin

Since there are 4 moles of iron per mole of hemoglobin, we multiply the moles of hemoglobin by four to find the moles of iron:\[ \text{Number of moles of iron} = 0.0144 \, \text{mol} \times 4 = 0.0576 \, \text{mol} \]

Step 4: Calculate the mass of iron

Using the molar mass of iron (approximately 55.85 g/mol), calculate the total mass of iron in grams:\[ \text{Mass of iron} = 0.0576 \, \text{mol} \times 55.85 \, \text{g/mol} \approx 3.2144 \, \text{g} \]

Step 5: Compare the mass of iron to the mass of a 3-inch nail

Compare the calculated iron mass with the 3.7 g provided as the mass of the 3-inch nail. The mass of iron in the blood is approximately 3.2144 g.

Key Concepts

Understanding Molar Mass

The molar mass of a substance is a crucial concept in chemistry. It tells us how much one mole of that substance weighs in grams. This is especially useful when dealing with large and complex molecules, like hemoglobin.

- **Definition**: Molar mass is the mass of one mole of a given substance, usually expressed in grams per mole (g/mol). - **Importance**: It aids in converting grams to moles and vice versa. This conversion is crucial for stoichiometric calculations in chemical reactions.

Let's consider hemoglobin, a large protein in red blood cells responsible for carrying oxygen. The molar mass of hemoglobin is given as 64,500 g/mol. This means that each mole of hemoglobin weighs 64,500 grams. By knowing its molar mass, we can determine the number of moles in a given mass, which is a pivotal step in chemical calculations involving hemoglobin.

Iron Content in Blood

Iron plays a vital role in the human body, particularly in the formation of hemoglobin. Hemoglobin contains iron, which binds oxygen molecules, allowing red blood cells to transport oxygen throughout the body. Understanding the iron content in blood is key to assessing nutritional and health conditions.

- **Functional Role**: Iron is crucial for oxygen transport due to its presence in hemoglobin. This makes it essential for the respiratory function of blood. - **Hemoglobin Composition**: Each molecule of hemoglobin can bind four molecules of iron. This means that for every mole of hemoglobin, we have four moles of iron in the blood.

In our calculation exercise, knowing how much iron is contained in hemoglobin will help determine whether the claim about making a nail from the body's iron content is feasible. We calculated that the hemoglobin in the blood yields approximately 3.2144 grams of iron. Understanding this sheds light on how much iron is necessary for human health and in industrial contexts.

Mastering Chemical Calculations

Chemical calculations allow us to quantitatively analyze substances and reactions. They are foundational to both academic and practical chemistry.

- **Why It Matters**: Calculations enable chemists to predict outcomes, produce desired chemical products, and meet safety and efficiency demands. - **Common Tools Used**: Molar mass, mole-to-mole conversions, and concentration calculations are among the most commonly used tools.

The exercise demonstrated several chemical calculations:

• We calculated the total mass of hemoglobin present using given concentration data.
• Next, we converted the mass of hemoglobin to moles using its molar mass.
• Then, by using the ratio of iron to hemoglobin, we determined the moles of iron.
• Finally, with the molar mass of iron, we obtained the mass in grams.

Such a series of steps showcases how chemical calculations are essential in correlating measurements with chemical composition, ultimately confirming or disproving hypotheses. Here, it helped us understand if the iron content in human blood could indeed make a 3-inch nail.