Problem 83 - Chemistry: An Atoms-Focused Approach

Question

Arterial blood contains about \(0.25 \mathrm{g}\) of oxygen per liter at \(37^{\circ} \mathrm{C}\) and standard atmospheric pressure. What is the Henry's law constant, in \(\operatorname{mol} /(\mathrm{L} \cdot \mathrm{atm}),\) for \(\mathrm{O}_{2}\) dissolution in blood at \(37^{\circ} \mathrm{C} ?\)

Step-by-Step Solution

Answer

Answer: The Henry's law constant for the dissolution of oxygen in blood at 37°C is approximately 0.037203 mol/(L*atm).

Step 1: Convert grams to moles

Given that arterial blood contains 0.25 g of oxygen per liter, we will now find out how many moles this corresponds to. The molar mass of oxygen is 16 g/mol, so for O2, it is 32 g/mol. Number of moles (n) = (mass of O₂) / (molar mass of O₂) n = 0.25 g / 32 g/mol = 0.0078125 mol

Step 2: Calculate the concentration of O₂ in blood

Since we have found the number of moles (n = 0.0078125 mol) in 1 liter of blood, the concentration of oxygen in blood (C) in mol/L is: C = 0.0078125 mol/L

Step 3: Use Henry's Law to find the constant

As mentioned above, the standard atmospheric pressure is assumed. Under standard atmospheric conditions, the partial pressure of oxygen (P) at sea level is approximately 0.21 atm. Now, we can use the Henry's law formula to find the constant (k). C = k * P 0.0078125 mol/L = k * 0.21 atm To find k, we will divide the concentration by the partial pressure: k = 0.0078125 mol/L / 0.21 atm ≈ 0.037203 mol/(L*atm)

Step 4: Report the Henry's law constant

The Henry's law constant for the dissolution of oxygen in blood at 37°C is approximately 0.037203 mol/(L*atm).

Key Concepts

Oxygen Solubility

Understanding oxygen solubility is key to grasping how gases dissolve in liquids. Solubility indicates how much of a particular substance (in this case, oxygen) can dissolve in a solvent—in our scenario, this solvent is blood. Conditions such as temperature and pressure significantly impact solubility.

In the bloodstream, the solubility of oxygen is vital for delivering adequate oxygen to tissues. Oxygen solubility is higher at lower temperatures, and it decreases as temperature increases. In blood at body temperature, oxygen dissolves in small amounts per liter, contributing to the oxygen supply needed by tissues alongside oxygen bound to hemoglobin.

Molar Mass of Oxygen

To understand the conversion from grams to moles, you need to know the molecular make-up of oxygen. Oxygen is present in the atmosphere as \({\text{O}}_{2}\), meaning each molecule consists of two oxygen atoms. The atomic mass of a single oxygen atom is approximately 16 g/mol.

Thus, the molar mass of oxygen gas (\({\text{O}}_{2}\)) becomes 32 g/mol. This value is crucial for calculating the number of moles from a given mass, as shown in the solution.

• Molar Mass of \({\text{O}}\) = 16 g/mol
• Molar Mass of \({\text{O}}_{2}\) = 32 g/mol

Understanding molar mass is essential for converting the mass of oxygen into moles, facilitating further concentration calculations.

Partial Pressure of Oxygen

The term "partial pressure" refers to the pressure exerted by a single type of gas in a mixture of gases. For oxygen in the atmosphere, this accounts for approximately 21% of the total atmospheric pressure.

At sea level, with a total atmospheric pressure of 1 atm, oxygen has a partial pressure of about 0.21 atm. This pressure is a measure of the concentration of oxygen available to dissolve in blood. It directly influences how much oxygen can be absorbed by the blood through Henry's Law, playing an essential role in situations like calculating gas exchange across respiratory membranes.

Concentration Calculation

Calculating concentration involves determining how much solute (oxygen, in this case) is present in a specified volume of solvent (here, blood).

The solution process begins by using the number of moles obtained from the mass of oxygen. Knowing that 0.25 g of oxygen equates to 0.0078125 moles, it is crucial to understand what this means in terms of concentration in the bloodstream:

• Concentration (C) = Number of moles/Volume
• In this problem: C = 0.0078125 mol/L

The concentration forms a fundamental part of Henry's Law application: \({C = k \times P}\), where 'C' is the concentration, 'k' is the Henry's Law constant, and 'P' is the partial pressure.