Biomedical Engineering Reference
In-Depth Information
where
n
is the number of moles and
C
is the concentration. Absolute pressure refers
to the pressure measured relative to a perfect vacuum. Using ideal gas, one mole
of air at a standard temperature and pressure (STP), which are 273°C and 1 atm,
occupies a volume of 22.415L (or 359.05 ft
3
). The ideal gas approximation is ad-
equate for most of the biomedical applications involving gases, which occurs above
0°C and near 1 atmosphere.
EXAMPLE 2.3
Mary Joy is inhaling 500 mL of air with each breath at a rate of 12 breaths per minute. The
molar compositions of the inspired and expired gases are as given in the table.
The inspired gas is at 25°C and 1 atm, and the expired gas is at body temperature and
pressure (i.e., 37°C and 1 atm). Nitrogen is not transported into or out of the blood in the
lungs.
(a) Calculate the masses of O
2
, CO
2
, and H
2
O transferred from the
pulmonary gases to the blood or vice versa (specify which) per minute.
(b) Calculate the volume of air exhaled per milliliter inhaled.
Species
O
2
CO
2
N
2
H
2
O
Inspired gas (%)
21
0
77
2
Expired gas (%)
15
4
75
6
(c) At what rate (g/min) is Mary Joy losing weight by breathing?
Solution: The volume of gases changes with temperature and pressure. However,
number of moles does not change if there is no reaction. Hence, the first step is to convert
volume to moles.
At STP, 1 mol of gas occupies 22.414L.
Hence,
273( )
K
1 mol
n
6,000(mL/min) * 10
−
3
(L/mL)
*
0.245 mol/min
=
=
in
298( )
K
22.4L
Nitrogen is not absorbed by body fluids. Hence, the same amount of nitrogen
that enters the system leaves the system. Using this relation, total moles exhaled can be
calculated.
That is,
0.77*0.2246
=
0.75*
n
out
Rearranging,
n
out
=
0.252 mol exhaled/min
Knowing the total moles exhaled,
2
transferred to blood: (0.245*0.21
−
0.252*0.15 (mol O
2
/min)
=
0.439 g/min
CO
2
transferred from blood: (0.252*0.04 (molCO
2
/min))*44 g/mol
=
0.443 g/min
2
O transferred from blood: (0.252*0.06
−
0.245*0.02 (mol H
2
O/min))
=
0.184 g/
min.
By breathing, this individual is losing 0.184g in a minute.
