Question
Air entering the lungs ends up in tiny sacs called alveoli. From the alveoli, the 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 $$1.0\,atm$$ and the temperature is $${37^ \circ }C,$$ calculate
the number of oxygen molecules in one of the alveoli.
A.
$$6 \times {10^{13}}$$
B.
$${10^{24}}$$
C.
$$1.7 \times {10^{22}}$$
D.
$$1.7 \times {10^{12}}$$
Answer :
$$1.7 \times {10^{12}}$$
Solution :
$$\eqalign{
& {\text{Volume of alveoli}}\, = \frac{4}{3}\pi {R^3} \cr
& = \frac{4}{3} \times 3.14 \times {\left( {5 \times {{10}^{ - 3}}} \right)^3}\,mL \cr
& = 5.23 \times {10^{ - 7}}mL = 5.23 \times {10^{ - 7}}L \cr
& {n_2} = \frac{{14}}{{100}} \times {n_{air}} = 0.14 \times \frac{{PV}}{{RT}} \cr
& = 0.14 \times 1 \times \frac{{5.23 \times {{10}^{ - 10}}}}{{0.0821 \times 310}} \cr
& = 2.87 \times {10^{ - 12}} \cr
& {\text{Molecules}} = 2.87 \times 6.02 \times {10^{23}} \times {10^{ - 12}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 1.7 \times {10^{12}} \cr} $$