Gas equation problem

[Stefan Borović]

Back in class we had the following problem:

 

The air we breathe is about 21% oxygen, by volume. Exhaled air contains about 14% of oxygen. The absorption of oxygen within the lungs takes place in tiny spherical compartments called alveoli which have a diameter of the order of 0.1 mm. Estimate the number of oxygen molecules absorbed in one breath in each of the alveoli. (Assume that body temperature is 37°C.)

[math]n= \frac{pV}{RT}= \frac{101325 Jm^{-3}\times 5.23\times 10^{-13}m^{3}}{8.3145JK^{-1}mol^{-1}\times 310.15K}[/math]

[math]n=2.06\times 10^{-11} mol [/math]

[math]N= 1.24\times 10^{-13} molecules[/math]

I assumed that the pressure inside the alveoli is 1 atm, that [math]r= \frac{d}{2}[/math] and calculated the volume using [math]V= \frac{4}{3} r^{3} \pi[/math]

Now, [math]21 \% - 14 \% = 7\%[/math] and [math]7 \% \times N= 8.7 \times 10^{11}[/math] End-of-chapter solution is [math]6.9 \times 10^{12}molecules[/math]

What am I doing wrong?

 

@admin: It seems to me now that this should better be in the general Chemistry thread?

Edited June 6, 2012 by Stefan Borović

[Enthalpy]

I get the same figures as yours (except 10⁺¹³ molecules, not 10^-13).