Air entering the lungs ends up in tiny sacs called alveoli. It is from the alveoli that oxygen diffuses into the blood. The average radius of the alveoli is 0.0050 cm and the air inside contains 14 per cent oxygen. Assuming that the pressure in the alveoli is 1.0atm and the temperature is 37^oC, calculate the number of oxygen molecules in one of the alveoli.

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6 x 1013

1024

1.7 x 1022

1.7 x 1012

answer is D.

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Detailed Solution

Volume of alveoli $= \frac{4}{3} {πR}^{3}$
$\begin{array}{l} = \frac{4}{3} \times 3 .14 \times {(5 \times 10^{- 3})}^{3} mL \\ = 5 .23 \times 10^{- 10} mL \\ = 5 .23 \times 10^{- 7} L \end{array}$
$\begin{array}{l} n_{O_{2}} = \frac{14}{100} \times n_{air} = 0 .14 \times \frac{PV}{RT} \\ = 0 .14 \times 1 \times \frac{5 .23 \times 10^{- 10}}{0 .0821 \times 310} \\ = 2 .87 \times 10^{- 12} \end{array}$
$\begin{array}{l} Molecules = 2 .87 \times 6 .02 \times 10^{23} \times 10^{- 12} \\ = 1 .7 \times 10^{12} \end{array}$