Problem 28 - Chemistry: An Atoms-Focused Approach

Question

A typical adult body contains \(6.0 \mathrm{L}\) of blood. The hemoglobin content of blood is about \(15.5 \mathrm{g} /\) \(100.0 \mathrm{mL}\) of blood. The approximate molar mass of hemoglobin is \(64,500 \mathrm{g} / \mathrm{mol} .\) How many moles of hemoglobin are present in a typical adult?

Step-by-Step Solution

Answer

Answer: Approximately 0.0144 moles of hemoglobin are present in a typical adult body.

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

First, we need to find out the total mass of hemoglobin in the blood. We know that there are 15.5 g of hemoglobin per 100 mL of blood. Since the adult has 6.0 L of blood, let's first convert the blood volume into milliliters (mL): \(6.0 \mathrm{L} \times \dfrac{1000 \mathrm{mL}}{1 \mathrm{L}} = 6000 \mathrm{mL}\) Now, using the previously given hemoglobin content, we can calculate the total mass of hemoglobin present in 6000 mL of blood as follows: \(\dfrac{15.5 \mathrm{g}}{100.0 \mathrm{mL}} \times 6000 \mathrm{mL} =\) \(15.5 \mathrm{g} \times \dfrac{6000 \mathrm{mL}}{100.0 \mathrm{mL}} = 930 \mathrm{g}\)

Step 2: Calculating the number of moles of hemoglobin

We have determined the total mass of hemoglobin in the adult body to be 930 g. To find the number of moles of hemoglobin, we will use the molar mass of hemoglobin, which is 64,500 g/mol. Using the molar mass, we can convert the mass of hemoglobin to moles using the following formula: \(\text{moles of hemoglobin} = \dfrac{\text{mass (g)}}{\text{molar mass (g/mol)}}\) Substituting the given values, we get: \(\text{moles of hemoglobin} = \dfrac{930 \mathrm{g}}{64,500 \mathrm{g/mol}} \approx 0.0144 \mathrm{mol}\) Hence, there are approximately 0.0144 moles of hemoglobin present in a typical adult body.

Key Concepts

Hemoglobin

Hemoglobin is a crucial component in our blood responsible for transporting oxygen from the lungs to the rest of the body. This protein is found in red blood cells and contains iron, which binds to oxygen molecules. Hemoglobin not only delivers oxygen to tissues but also carries carbon dioxide back to the lungs to be exhaled. Its role is vital for maintaining life and supporting bodily functions. Hemoglobin levels can vary based on several factors including age, sex, and overall health. An inadequate amount of hemoglobin can lead to health conditions such as anemia, which results in a person's feeling fatigued or weak.

Molar Mass

Molar mass is a fundamental concept in chemistry that relates the mass of a substance to the amount of substance in moles. It's calculated by summing the atomic masses of all the atoms in a molecule. For hemoglobin, the molar mass is approximately 64,500 g/mol. This means one mole of hemoglobin weighs 64,500 grams. The molar mass helps in converting between grams and moles, which is essential in chemical calculations and stoichiometry.

• To find out how many moles are in a given sample, we use the formula: \[ \text{moles} = \frac{\text{mass (grams)}}{\text{molar mass (g/mol)}} \]
• For hemoglobin, this calculation allows us to translate the physical mass measured in a sample into chemical quantities.

This translation is vital for understanding how substances interact in chemical reactions.

Blood Composition

Blood is a complex bodily fluid comprising cells, nutrients, and other components suspended in plasma. It consists of several main components: red blood cells, white blood cells, platelets, and plasma. Each component serves a specific role in maintaining health and function.

• Red blood cells: These cells contain hemoglobin and are responsible for oxygen transport.
• White blood cells: They play a significant role in the body's immune response.
• Platelets: Essential for blood clotting and wound healing.
• Plasma: The liquid part of blood, carrying nutrients, hormones, and waste products.

Understanding blood composition is crucial for medical professionals to diagnose and treat various health conditions. It enables the assessment of overall health and provides insights into how our bodies function and react to different circumstances.