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 s $0.0050cm$ and the air inside contains $14$ 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.

• A. $6\times {10}^{13}$
• B. ${10}^{24}$
• C. $1.7\times {10}^{22}$
• D. $1.7\times {10}^{12}$

Answer 1

Answer: (D)

$1.7\times {10}^{12}$

Radius of alveoli $=0.0050$ cm

Contains $14\%$ $O_2$.

$P=1.0\text{a}tm$

$T={37}^{\circ }C=37+273=310K$

$\begin{array}{cc}\text{Volume of alveoli}& =\frac{4}{3}\pi r^3\\ & =\frac{4}{3}\times 3.14(0.0050cm{)}^3\\ & =5.236\times {10}^{-7}{cm}^3\end{array}$

Now: we find the no. of moles(n)

using $PV=nRT$

$\{$ where $R=0.082\frac{\text{Latm}}{\text{mol.}k}$

$\begin{array}{cc}n& =\frac{PV}{RT}=\frac{1\times 5.236\times {10}^{-7}}{0.082\times 310\times 1000}\\ n& =2.058\times {10}^{-11}mol\end{array}$

Here, alveoli consists of $14\%O_2$, we find

no. of molecules of $O_2$

$\begin{array}{cc}\therefore \text{No of molecules of}{O}_2& =2.058\times {10}^{-11}\times \frac{14}{100}\times \frac{6\times {10}^{23}}{1}\\ & =1.7\times {10}^{12}\text{molecules}{O}_2\end{array}$

Thus, one alveoli contains $1.7\times {10}^{12}$ moleculesof $O_2$.