Biomedical Engineering Reference
In-Depth Information
where
C
is the concentration difference of the solute across the semipermeable
membrane (moles/liter). Equation (2.16) is called Van't Hoff's equation and is for
a single solute. A common method of dealing with departures from ideal dilute
solutions is to use the osmotic coefficient,
Δ
φ
. With the osmotic coefficient, the Van't
Hoff equation is written as:
πφ
=
RT
Δ
C
where
φ
is the molal osmotic coefficient. For nonelectrolytes such as glucose,
φ
>
1
at physiologi cal concentrations. For electrolytes,
1 due to the electrical interac-
tions between the ions (e.g., NaCl at physiological concentrations has an osmotic
coefficient of 0.93). For macromolecules, the deviation becomes much more dra-
matic; hemoglobin has an osmotic coefficient of 2.57, and that of the parvalbumin
present in frog myoplasm is nearly 3.7.
φ
<
EXAMPLE 2.10
Using the values given in Example 2.5, calculate the osmotic pressure due to each compo-
nent. (These results are inaccurate because of electrical effects.)
Solution: For albumin
4.5g
1,000 mL
1 mol
3
C
*
*
0.6 * 10
−
mol/L
=
=
100 mL
1L
75,000g
Assuming Van't Hoff's law,
π
=
RT
Δ
C
(
) (
)
0.082 L.atm/mol.
K
* 273
37
K
* 0.6 * 10
−
3
mol/L
0.01525 atm
=
+
=
760 mmHg
0.01525 atm *
11.6 mmHg
→
=
1 atm
2.4.4 Osmometers
Monitoring osmolality is important for improving patient care by direct measure-
ment of body fluid osmolarity, transfusion and infusion solutions, and kidney func-
tion. Further, osmotic pressure measurements are used to determine the molecular
weights of proteins and other macromolecules. Van't Hoff's equation establishes a
linear relationship between concentration and osmotic pressure, the slope of which
is dependent upon temperature. If the dilute ideal solution contains
N
ideal solutes
then
N
∑
(2.17)
π
=
RT
C
Si
,
i
=
1
Equation (2.17) can also be written in terms of the mass concentration
ρ
S
