Question

Air enters in the lungs in a tiny cavity called alveoli. Oxygen diffuses into our blood from alveoli. The average radius of alveoli is $0.005cm$ and air inside it contains $21$% $O_2$ and $79$% $N_2$. Assuming that the pressure in the alveoli is $1atm$ at body temperature of ${37}^{\circ }C$.

Number of $O_2$ molecules in one alveoli is :

• A. $2.6\times {10}^{12}$
• B. $2.6\times {10}^{13}$
• C. $2.6\times {10}^{14}$
• D. $2.6\times {10}^{15}$

Answer 1

The correct option is A $2.6\times {10}^{12}$

The average radius of alveoli is 0.005 cm
Volume of single alveoli is $V=\frac{4}{3}\pi r^3=\frac{4}{3}\times 3.1416\times (0.005cm{)}^3=5.23\times {10}^{-7}c{m}^3$
Number of air moles in one alveoli is
$n=\frac{PV}{RT}$
$n=\frac{1atm\times 5.23\times {10}^{-7}c{m}^3\times \frac{1d{m}^3}{1000c{m}^3}}{0.08206Latm/molK\times (37+273.15)K}$
$n=2.055\times {10}^{-11}$
Number of $O_2$ moles in one alveoli is $n^{\prime }=\frac{21}{100}\times 2.055\times {10}^{-11}=4.32\times {10}^{-12}$
Number of $O_2$ molecules in one alveoli is $6.023\times {10}^{23}\times 4.32\times {10}^{-12}=2.6\times {10}^{12}$