Biomedical Engineering Reference
In-Depth Information
¼
M
L
¼
c
0
ss
¼
245
M
c
i
ss
¼
Na
þ
o
þ
Cl
½
½
o
ð
142
þ
103
Þ
L
,
10
9
M
245
L
V
i
¼
q
i
28
giving a new cell volume of
c
i
ss
¼
¼
0
:
114 nL. Realistically, the cell cannot
shrink to this degree, and there are other ions inside and outside the cell that move to maintain
osmotic pressure at zero.
Osmotic pressure depends on the total number of particles per unit volume and not the
size of the particle or its atomic weight. On average, all particles in the solution exert the
same amount of pressure on the membrane; smaller particles move at higher velocities
and larger particles move at lower velocities, providing about the same energy.
Since osmotic pressure does not depend on the weight of the particles and only the
number of particles, the unit
(osm) is used. One osmole equals one mole of solute
particles. If a molecule dissociates into two ions, then it contributes two osmoles; if a mole-
cule dissociates into three ions, then it contributes three osmoles, and so on. For instance,
one mole of glucose contributes 1 osm, since glucose does not dissociate into multiple ions;
one mole of sodium chloride (
osmole
NaCl
) contributes 2 osm, since it dissociates into 2 ions; one
mole of sodium sulfate (
Na
2
SO
4
) contributes 3 osm, since it dissociates into 3 ions. Glucose
and sucrose do not dissociate into ions, so their osmolarity equals the number of moles. Body
fluids typically are observed in milliosmoles, so these units are expressed in mOsm.
Because concentrations are used in calculating osmotic pressures, we use the term
osmo-
larity
instead of osmoles. Osmolarity equals the number of osmoles per liter of solution. The
osmolarity (in mOsm/L) inside a mammalian cell is approximately 301.2, plasma is 301.8,
and the interstitial fluid is 300.8. The plasma has a slightly higher osmolarity than the inter-
stitial fluid because of the proteins that do not diffuse through the capillary wall. For
plasma and the interstitial fluid, 80 percent of the total osmolarity is due to
NaCl
. Within
the cell, 50 percent of the total osmolarity is due to
. A solution containing one osmo-
larity contains one mole of undissociated particles per liter of solution. If a solute dissoci-
ates into more than one particle, then the osmolarity is given by
KCl
Number of Dissociated Particles
1L Solution
and osmotic pressure in terms of osmolarity is
Moles
Osmolarity
¼
L
osm
L
mmHg
K
T
K
R
p
¼
c
ðÞ¼
62
:
3637
cT
mmHg
ð
7
:
18
Þ
mol
EXAMPLE PROBLEM 7.2
Find the osmolarity of 5 mM
NaCl
in 1 L of solution.
Solution
Since
Na
þ
and
Cl
in solution, the osmolarity is equal to 2 times the moles
NaCl
dissociates into
. Thus, a solution of 5
mM
L
forms a 10
mOsm
L
of
solution.
NaCl
NaCl
