Question

The air entering the lungs passes through tiny sacs called alveoli, from which oxygen diffuses into the blood. The average radius of the alveoli is 0.0050 cm, and the air inside contains 14 mole percent oxygen. Assuming that the pressure in the alveoli is 1.0 atm and the temperature is ${37}^{O}C$; calculate the number of oxygen molecules in one of the alveoli. $(R=0.08206L-atmmo{l}^{-1}{K}^{-1},6.023\times {10}^{23}moleculesmol{e}^{-1})$

• A. $1.7\times {10}^{11}$ oxygen molecules
• B. $1.7\times {10}^{13}$ oxygen molecules
• C. $1.7\times {10}^{12}$ oxygen molecules
• D. $1.7\times {10}^{10}$ oxygen molecules

Answer 1

The correct option is C $1.7\times {10}^{12}$ oxygen molecules

Radius, $r=0.0050cm$
$T=273+37=310K$
The volume of one alveolus $=V=\left(4/3\right)\pi r^3$ $=\left(4/3\right).3.12(0.0050cm{)}^3$
$=5.2\times {10}^{7}c{m}^3$
But $1L={10}^{3}c{m}^3$
Hence $V=5.2\times {10}^7\times {10}^{3}L=5.2\times {10}^{10}L$
No of moles, $n$ of air in one alveolus can be calculated from $PV=nRT$
$n=PV/RT$
$=(1.0atm\times 5.2\times {10}^{10}L)/(0.08206Latmmo{l}^{-1}{K}^{-1}\times 310K)$
$=2.0\times {10}^{11}mol$
$1$ mol of oxygen $=6.022\times {10}^{23}$ molecules
$2.0\times {10}^{10}$ mol of oxygen $=2.0\times {10}^{11}\times 6.022\times {10}^{23}$ molecules
$=12.044\times {10}^{12}$ molecules
Air inside the alveolus is 14% oxygen,
Therefore no of oxygen molecules $=\left(14/100\right)\times 12.044\times {10}^{12}$
$=1.69\times {10}^{12}$ oxygen molecules