A young male adult takes in about 5.0 ×10^-4 m^3 of fresh air during a normal breath. Fresh air

step 1 In the question, it was asked to find the number of molecules of oxygen in one breath. We will l

A young male adult takes in about 5.0 ×10^-4 m^3 of fresh...

A young male adult takes in about $5.0 \times 10^{-4} \mathrm{m}^{3}$ of fresh air during a normal breath. Fresh air contains approximately $21 \%$ oxygen. Assuming that the pressure in the lungs is $1.0 \times 10^{5}$ Pa and that air is an ideal gas at a temperature of $310 \mathrm{K},$ find the number of oxygen molecules in a normal breath.

Key Concepts

Avogadro's Number

Avogadro's number, approximately 6.022 x 10^23, is the number of particles in one mole of a substance. This constant is crucial for converting the number of moles obtained through the ideal gas law into the number of individual molecules, which is often required for problems involving gas contents at the molecular level.

Partial Pressure and Mixtures of Gases

In a mixture of gases, each component gas contributes to the total pressure in proportion to its concentration. In problems where the percentage of a particular gas (like oxygen) is known, the ideal gas law can be used on the partial pressure or the fraction of the volume to determine the number of moles or molecules of that specific gas.

Ideal Gas Law

The ideal gas law relates the pressure, volume, number of moles, and temperature of a gas with the equation PV = nRT. This equation is fundamental in understanding how a gas behaves under different conditions and is used to calculate the amount of substance (in moles) in a given volume at a specific pressure and temperature.

Mole Concept

The mole is a unit that represents a specific number of particles, typically atoms or molecules, and provides a bridge between the macroscopic measurements of a gas (like volume, pressure, and temperature) and the microscopic count of particles. Calculating the number of moles allows conversion into the actual number of molecules using Avogadro’s number.

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