Problem 83 - Chemistry Matter and Change

Question

Blood You have 15 g of hemoglobin in every 100 \(\mathrm{mL}\) of your blood. 10.0 \(\mathrm{mL}\) of your blood can carry 2.01 \(\mathrm{mL}\) of oxygen. How many milliters of oxygen does each gram of hemoglobin carry?

Step-by-Step Solution

Answer

Each gram of hemoglobin carries approximately 1.34 mL of oxygen.

Step 1: Convert grams of hemoglobin/100 mL of blood to grams/mL

First, let's convert 15 g of hemoglobin per 100 mL of blood into a ratio of grams per mL: \( \frac{15 \ \text{g}}{100 \ \text{mL}} = 0.15 \ \text{g/mL} \)

Step 2: Calculate oxygen carrying capacity per 100 mL of blood

We know that 10 mL of blood can carry 2.01 mL of oxygen. In 100 mL, it would be ten times as much: \(10 \times 2.01 \ \text{mL} = 20.1 \ \text{mL} \ \text{of O₂} \)

Step 3: Divide the oxygen carrying capacity in 100 mL of blood by the amount of hemoglobin in grams

We have 15 g of hemoglobin in 100 mL of blood, which can carry 20.1 mL of oxygen. We need to find how much oxygen each gram of hemoglobin can carry: \( \frac{20.1 \ \text{mL}}{15 \ \text{g}} \)

Step 4: Calculate oxygen carrying capacity per gram of hemoglobin

Now, we just need to perform the division to find our final answer: \( \frac{20.1 \ \text{mL}}{15 \ \text{g}} = 1.34 \ \frac{\text{mL}}{\text{g}} \ \text{of O₂} \) So, each gram of hemoglobin carries approximately 1.34 mL of oxygen.

Key Concepts

Hemoglobin Function

Hemoglobin is a vital protein found in red blood cells that has a crucial function in the respiratory system: carrying oxygen from the lungs to the body's tissues and facilitating the return of carbon dioxide from the tissues back to the lungs. It is composed of four subunits, each containing an iron atom that binds oxygen, with one hemoglobin molecule having the capacity to carry up to four oxygen molecules.

This capacity to bind oxygen is quantified in terms of the oxygen-carrying capacity of hemoglobin. This characteristic is key to sustaining life, as oxygen is mandatory for cellular respiration, a process that cells use to generate energy. When we measure how much oxygen one gram of hemoglobin can carry, as in our original exercise, we are essentially evaluating hemoglobin's efficacy and efficiency at fulfilling its oxygen transport role.

Stoichiometry in Biology

Stoichiometry, common in chemistry and physics, also plays a pivotal role in biological processes, where it involves the quantification of relationships between different molecules in biochemical reactions. In the context of the exercise, stoichiometry allows us to calculate the oxygen carrying capacity of hemoglobin, which is a fundamental understanding in respiratory physiology.

By applying stoichiometric calculations, we can establish the ratio of oxygen to hemoglobin and determine how efficient the protein is at oxygen transport. This understanding can lead to insights on physiological conditions or diseases, for example, anemia, where hemoglobin's oxygen carrying capacity might be compromised. Stoichiometry in biology is thus not only a quantitative tool but also a bridge to qualitative analysis of biological health and function.

Molar Concentration

Molar concentration, often referred to as molarity, is the measure of the concentration of a solute in a given volume of solution, typically expressed in moles per liter (\( \text{mol/L} \) or M). In the exercise provided, while molar concentration is not directly referenced, understanding it can enhance comprehension of the solution.

Molar concentration can be used to describe the concentration of hemoglobin in blood, enabling comparisons and calculations in medical diagnostics. The oxygen carrying capacity of hemoglobin can also be analyzed in molar terms; for example, each mole of hemoglobin can bind a certain number of moles of oxygen. Understanding hemoglobin's molarity in the blood and its stoichiometric relationship to oxygen can provide a more in-depth view of the underlying biological processes and how they may be affected by different conditions or treatments.