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Ch.10 - Gases: Their Properties & Behavior
Chapter 10, Problem 65

The average oxygen content of arterial blood is approximately 0.25 g of O2 per liter. Assuming a body temperature of 37 °C, how many moles of oxygen are transported by each liter of arterial blood? How many milliliters?

Verified step by step guidance
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Step 1: Begin by identifying the given information. You have 0.25 g of O2 per liter of arterial blood, and you need to find out how many moles of O2 this corresponds to.
Step 2: Use the molar mass of oxygen (O2) to convert grams to moles. The molar mass of O2 is approximately 32.00 g/mol. Use the formula: \( \text{moles of O2} = \frac{\text{mass of O2 (g)}}{\text{molar mass of O2 (g/mol)}} \).
Step 3: Substitute the given mass of O2 (0.25 g) and the molar mass of O2 (32.00 g/mol) into the formula to calculate the moles of O2.
Step 4: To find out how many milliliters of O2 gas are transported, use the ideal gas law. At body temperature (37 °C or 310 K) and assuming standard pressure, use the ideal gas law equation: \( PV = nRT \).
Step 5: Rearrange the ideal gas law to solve for volume (V): \( V = \frac{nRT}{P} \). Use the calculated moles of O2 (n), the ideal gas constant (R = 0.0821 L·atm/mol·K), and standard pressure (P = 1 atm) to find the volume in liters, then convert to milliliters.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). For oxygen (O2), the molar mass is approximately 32 g/mol, calculated from the atomic mass of oxygen (16 g/mol) multiplied by two, since O2 consists of two oxygen atoms. Understanding molar mass is essential for converting between grams and moles in chemical calculations.
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Mole Concept

The mole is a fundamental unit in chemistry that quantifies the amount of substance. One mole contains Avogadro's number of entities, approximately 6.022 x 10^23 particles, whether they are atoms, molecules, or ions. This concept allows chemists to relate mass to the number of particles, facilitating calculations involving chemical reactions and stoichiometry.
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Volume and Density Relationships

The relationship between mass, volume, and density is crucial in determining how much of a substance is present in a given volume. Density is defined as mass per unit volume (e.g., g/L). In this context, knowing the mass of oxygen in grams allows us to calculate the volume it occupies using the ideal gas law or density relationships, which is important for understanding how gases behave in biological systems.
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