Question

In the lungs, the respiratory membrane separates tiny sacs of air (pressure 1.00x105Pa) from the blood in the capillaries. These sacs are called alveoli. The average radius of the alveoli is 0.012 cm, and the air inside contains 20% oxygen. Assuming that the air behaves as an ideal gas at 300K, find the number of oxygen molecules in one of these sacs.

Boltzmann constant =1.38 ×10−23 J K

Answer 1

The pressure and temperature of the air inside an alveolus are known, and its volume can be determined since we know the radius. Thus, the ideal gas law in the form PV = NkT can be used directly to find the number N of air particles inside one of the sacs. The number of oxygen molecules is 14% of the number of air particles.

The volume of a spherical sac is V = 4/3πr^3

N = PV/kT

= {(1.00 x 10^5 Pa)(4/3 * π(0.012 x 10^-2 m)^3)}/{(1.38 x 10^-23 J/K)(300 K)}

= 1.75 x 10^14 (number of air particles)

The number of oxygen molecules is 20% of this number: 0.20 N = 3.5 x 10^13

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