Movement of Molecules Across Cell Membranes
109
and 1 mol of chloride ions, producing 2 mol of solute particles.
This lowers the water concentration twice as much as 1 mol of
glucose. By the same reasoning, if a 1 M MgCl
2
solution were
to dissociate completely, it would lower the water concentra-
tion three times as much as would a 1 M glucose solution.
Because the water concentration in a solution depends
upon the number of solute particles, it is useful to have a con-
centration term that refers to the total concentration of solute
particles in a solution, regardless of their chemical composi-
tion. The total solute concentration of a solution is known as
its
osmolarity.
One
osmol
is equal to 1 mol of solute par-
ticles. Thus, a 1 M solution of glucose has a concentration of
1 Osm (1 osmol per liter), whereas a 1 M solution of sodium
chloride contains 2 osmol of solute per liter of solution. A liter
of solution containing 1 mol of glucose and 1 mol of sodium
chloride has an osmolarity of 3 Osm. A solution with an
osmolarity of 3 Osm may contain 1 mol of glucose and 1 mol
of sodium chloride, or 3 mol of glucose, or 1.5 mol of sodium
chloride, or any other combination of solutes as long as the
total solute concentration is equal to 3 Osm.
Although osmolarity refers to the concentration of sol-
ute particles, it also determines the water concentration in
the solution because the higher the osmolarity, the lower the
water concentration. The concentration of water in any two
solutions having the same osmolarity is the same because the
total number of solute particles per unit volume is the same.
Let us now apply these principles governing water con-
centration to osmosis of water across membranes.
Figure 4–17
shows two 1-L compartments separated by a membrane per-
meable to
both
solute and water. Initially the concentration of
solute is 2 Osm in compartment 1 and 4 Osm in compart-
ment 2. This difference in solute concentration means there is
also a difference in water concentration across the membrane:
53.5 M in compartment 1 and 51.5 M in compartment 2.
Therefore, a net diffusion of water from the higher concen-
tration in 1 to the lower concentration in 2 will take place,
and a net diffusion of solute in the opposite direction, from
2 to 1. When diffusion equilibrium is reached, the two com-
partments will have identical solute and water concentrations,
3 Osm and 52.5 M, respectively. One mol of water will have
diffused from compartment 1 to compartment 2, and 1 mol
of solute will have diffused from 2 to 1. Since 1 mol of solute
has replaced 1 mol of water in compartment 1, and vice versa
in compartment 2, no change in the volume occurs for either
compartment.
If the membrane is now replaced by one
permeable to
water but impermeable to solute
(
Figure 4–18
), the same
concentrations
of water and solute will be reached at equi-
librium as before, but a change in the
volumes
of the com-
partments will also occur. Water will diffuse from 1 to 2, but
there will be no solute diffusion in the opposite direction
because the membrane is impermeable to solute. Water will
continue to diffuse into compartment 2, therefore, until the
water concentrations on the two sides become equal. The sol-
ute concentration in compartment 2 decreases as it is diluted
by the incoming water, and the solute in compartment 1
becomes more concentrated as water moves out. When the
water reaches diffusion equilibrium, the osmolarities of the
Water molecule
Solute molecule
Pure water
(high water concentration)
Solution
(low water concentration)
Figure 4–16
The addition of solute molecules to pure water lowers the water
concentration in the solution.
in water, the concentration of water in the resulting solution
is less than that of pure water. A given volume of a glucose solu-
tion contains fewer water molecules than an equal volume of
pure water because each glucose molecule occupies space for-
merly occupied by a water molecule (
Figure 4–16
). In quan-
titative terms, a liter of pure water weighs about 1000 g, and
the molecular weight of water is 18. Thus, the concentration of
water in pure water is 1000/18 = 55.5 M. The decrease in water
concentration in a solution is approximately equal to the concen-
tration of added solute. In other words, one solute molecule will
displace one water molecule. The water concentration in a 1 M
glucose solution is therefore approximately 54.5 M rather than
55.5 M. Just as adding water to a solution will dilute the solute,
adding solute to a solution will “dilute” the water.
The greater
the solute concentration, the lower the water concentration.
It is essential to recognize that the degree to which the
water concentration is decreased by the addition of solute
depends upon the
number
of particles (molecules or ions) of
solute in solution (the solute concentration) and not upon the
chemical nature
of the solute. For example, 1 mol of glucose in
1 L of solution decreases the water concentration to the same
extent as does 1 mol of an amino acid, or 1 mol of urea, or 1
mol of any other molecule that exists as a single particle in
solution. On the other hand, a molecule that ionizes in solu-
tion decreases the water concentration in proportion to the
number of ions formed. For example, many simple salts disso-
ciate nearly completely in water. For simplicity’s sake, we will
assume the dissociation is 100 percent at body temperature
and at concentrations found in the blood. Therefore, 1 mol of
sodium chloride in solution gives rise to 1 mol of sodium ions
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