Table 3.1 Body

Fluids

Fluid Fluid

Volume% of Body

Weight

Intracellular

25 liters 36 wt %

Extracellular

15 liters 21 wt %

Interstitial

12 liters

17 wt %

Plasma

3 liters

4 wt %

Transcellular

   --------          

Total 40 liters 57 wt %

Source: Data from A.C. Guyton, Textbook of Medical Physiology,

8th ed. (Philadelphia: W. B. Saunders Co., 1991), 275

Table 3.2Osmolar Solutes Found in the Extracellular and

Intracellular Fluids

Solute Plasma Interstitial Intracellular

(mOsm/L) (mOsm/L) (mOsm/L)

Na+ 143 140 14

K+ 4.2 4.0 140

Ca++ 1.3 1.2 0

Mg++ 0.8 0.7 20

Cl- 108 108 10

HCO3- 24 28.3 10

HPO4-- , H2PO4

-- 2 2 11

SO4-- 0.5 0.5 1

Phosphocreatine 45

Carnosine 14

Amino acids 2 2 8

Creatine 0.2 0.2 9

Lactate 1.2 1.2 1.5

Adenosine Triphosphate 5

Hexose Monophosphate 3.7

Glucose 5.6 5.6

Protein 1.2 0.2 4

Urea 4 4 4

Others 4.8 3.9 11

Total (mOsmoles/liter) 302.8 301.8 302.2

Corrected Osmolar Activity (mOsmoles/liter)

282.5 281.3 281.3

Total Osmotic Pressure at 37C (mmHg) 5450 5430 5430

Source: Data from A.C. Guyton, Textbook of Medical Physiology, 8th ed. (Philadelphia:W.B. Saunders Co., 1991) , 277

Example 2.14 Consider the situation shown in Figure 2.5 where on side A of the

membrane we have a solution that has a water mole fraction of 0.99. On side B of the

membrane we have pure water. If the temperature is 25 oC and side B is at 1 atmosphere

pressure, estimate the pressure needed on side A to stop the osmosis of water from region

A. What would happen if the pressure on side A was increased to a value above this

pressure?

SOLUTION Assuming the solution in region A is an ideal solution we can use Equation

2.147 to calculate the osmotic pressure of region A, ie.

atm6.130.01x

gmol

m10x18

K298Pa 101,325

atm1x

K gmol

m Pa314.8

PP3

6-

3

BA

Therefore the pressure in region A would have to be 14.6 atm to prevent the osmosis of

water from region B into region A. If the pressure in region A is greater than 14.6 atm,

then water will move from region A into region B and this process is called reverse

osmosis.

Since small pressures are easy to measure, the osmotic pressure is also useful for

determining the molecular weight of macromolecules. For example, letting msolute

represent the mass concentration (g/liter) of the solute in the solution, then from Equation

2.147 we can write the molecular weight of the solute (MWsolute) in terms of the osmotic

pressure of the solution as follows

solutesolute

mRTMW (2.149)

Example 2.15 The osmotic pressure of a solution containing a macromolecule is

equivalent to the pressure exerted by 8 cm of water. The mass concentration of

the protein in the solution is 15 g/liter. Estimate the molecular weight of this

macromolecule.

SOLUTION We can use Equation 2.149 to estimate the molecular weight as

follows.

OHft33.91

atm1x

in12

ft1x

cm2.54

in1xOHcm8

Pa101,325

atm1

m

cm100x

cm1000

liter1x

liter

g15xK298x

Kmol

Pam314.8

MW

22

3

3

3

3

solute

MWsolute = 47400 g/mol

Example 3.1 Calculate the filtration flowrate (cm3/sec) of a pure fluid across a 100

cm2 membrane. Assume the viscosity () of the fluid is 1.8 cP. The porosity of the

membrane is 40% and the thickness of the membrane is 500 microns. The pores run

straight through the membrane and these pores have a radius of 0.225 microns. The

pressure drop applied across the membrane is 75 psi. ( Recall that 14.7 psi = 1 atm =

101325 Pa (or N m-2) , that 1 N = 1 kg m sec-2, and from Chapter 4 we have for the

viscosity that 1 cP = 0.001 N sec m-2 = 0.001 Pa sec).

SOLUTION To find the filtration flowrate we will use Equations 3.4 and 3.7. Since

there are no retained solutes there are no osmotic effects and the effective pressure

drop across the membrane is equal to the applied pressure drop of 75 psi. From the

information about the membrane we first calculate the value of the hydraulic

conductance as shown below.

sec54.14

1017.5100sec

10813.2

4.3

sec10813.2

05.0sec0018.08

1025.240.0

:7.3

1017.51

101325

7.14

175,sec0018.08.1

,05.0500,1025.2225.0,4.0

3

527

7

25

5

5

cmQ

PacmPa

cmQ

Equationfromand

Pa

cm

cmPa

cmL

Equationinvaluesthesengsubstitutinow

Paatm

Pa

psi

atmpsiPandPacP

cmmicronstcmmicronsRS

A

P

mp