Anatomy and Physiology - Introduction to Biomedical Engineering - page 83

cell, 1 nl, is very small relative to the volume of the solution. In other words, changes in the
cell's volume have no measurable effect on the volume of the external solution. What will
happen to the volume of the cell as it achieves equilibrium?
At equilibrium, the osmolarity inside the cell must equal the osmolarity outside the cell.
The initial osmolarity inside the cell is 0.2 Osm, since the proteins do not dissociate into smal-
ler units. The osmolarity outside the cell is 0.1 Osm due to the sucrose solution. A 0.2 Osm
solution has 0.2 moles of dissolved particles per liter of solution, while a 0.1 Osm solution
has half as many moles of dissolved particles per liter. The osmolarity inside the cell must
decrease by a factor of 2 in order to achieve equilibrium. Since the plasma membrane will
not allow any of the protein molecules to leave the cell, this can only be achieved by dou-
bling the cell's volume. Thus, there will be a net movement of water across the plasma
membrane until the cell's volume increases to 2 nl and the cell's internal osmolarity is
reduced to 0.1 Osm—the same as the osmolarity of the external solution. The water moves
down its concentration gradient by diffusing from where it is more highly concentrated in
the 0.1 M sucrose solution to where it is less concentrated in the 0.2 M protein solution in
the cell.

EXAMPLE PROBLEM 3.2
What would happen to the model cell in Figure 3.6 if it were placed in pure water?

Solution
Water can pass through the plasma membrane and would flow down its concentration gradi-
ent from where it is more concentrated (outside of the cell) to where it is less concentrated (inside
of the cell). Eventually, enough water would move into the cell to rupture the plasma membrane,
since the concentration of water outside the cell would be higher than the concentration of water
inside the cell as long as there were proteins trapped within the cell.

EXAMPLE PROBLEM 3.3
Assume that the model cell in Figure 3.6 has an initial volume of 2 nl and contains 0.2 M
protein. The cell is placed in a large volume of 0.2 M NaCl. In this model, neither Na þ nor Cl
can cross the plasma membrane and enter the cell. Is the 0.2 M NaCl solution hypotonic, isotonic,
or hypertonic relative to the osmolarity inside the cell? Describe what happens to the cell as it
achieves equilibrium in this new environment. What will be the final osmolarity of the cell? What
will be its final volume?

Solution
The osmolarity inside the cell is 0.2 Osm. The osmolarity of the 0.2 M NaCl solution is 0.4 Osm
(0.2 Osm Na þ þ 0.2 Osm Cl ). Thus, the NaCl solution is hypertonic relative to the osmolarity

inside the cell (osmolarity outside >

osmolarity inside ). Since none of the particles (protein, Na þ ,
and Cl ) can cross the membrane, water will move out of the cell until the osmolarity inside
Continued