# Osmotic pressure: definition, van ‘t Hoff factor, and examples

In solution, solvent molecules tend to move from a region of higher concentration to one of lower concentration. When two different solutions are separated by a semipermeable membrane, namely, a membrane that allows certain ions or molecules to pass, in this case the solvent molecules, a net flow of solvent molecules from the side with higher concentration to the side with lower concentration will occur. This net flow through the semipermeable membrane produces a pressure called osmotic pressure, indicated as Π, that can be defined as the force that must be applied to prevent the movement of the solvent molecules through a semipermeable membrane.

Osmotic pressure, together with boiling point elevation, freezing point depression, and vapor pressure lowering, is one of the four colligative properties of solutions, properties that do not dependent of the chemical properties of the solute particles, namely ions, molecules or supramolecular structures, but depend only on the number of solute particles present in solution.
For a solutions of n solutes, the equation that describes osmotic pressure is the sum of the contributions of each solute:

Π = RT(i1c1 + i2c2 + … + incn)

The equation is known as the van ’t Hoff equation, where:

• T is the absolute temperature in Kelvin;
• R is the ideal gas constant = 8.314 J/mol K;
• c is the molar concentration of the solute;
• i is the van ’t Hoff factor.

## van ’t Hoff factor

The van ‘t Hoff factor is a measure of the degree of dissociation of solutes in solution, and is described by the equation:

i = 1 + α(n-1)

where:

• α is the degree of dissociation of the solute molecules, equal to the ratio between the moles of the solute molecules that have dissociated and the number of the original moles, and is comprised between 0, for substances that do not ionize or dissociate in solution, and 1, for substances that completely dissociate or ionize;
• n is the number of ions formed from the dissociation of the solute molecule.

For non ionizable compounds, such as glucose, glycogen or starch, n = 1, and i = 1, whereas for compounds that completely dissociate, such as strong acids and strong bases or salts, the van ‘t Hoff factor is a whole number greater than one, as α = 1 and n is equal to at least 2. For example, if we consider sodium chloride, NaCl, potassium chloride, KCl, or calcium chloride, CaCl2, in dilute solution:

NaCl → Na+ + Cl
KCl → K+ + Cl
CaCl2 → Ca2+ + 2 Cl

So in the first two cases i = 2, whereas with calcium chloride, i = 3.
Finally, for substances that do not completely ionize, such as weak acids and weak bases, i is not an integer.

The product of the van ’t Hoff factor and the molar concentration of the solute particles, ic, is the osmolarity of the solution, namely, the concentration of the solute particles osmotically active per liter of solution.

## Osmotic pressure, osmosis, and plasma membranes

Osmosis can be defined as the net movement or flow of solvent molecules through a semipermeable membrane driven by osmotic pressure differences across the membrane, to try to equal the concentration of the solute on the two sides of the membrane itself. In biological systems, water is the solvent and plasma membranes are the semipermeable membranes.
Plasma membranes allow water molecules to pass, due to protein channels, known as aquaporins, as well as small non-polar molecules that diffuse rapidly across them, whereas they are impermeable to ions and macromolecules.
Inside the cell there are macromolecules, such as nucleic acids, proteins, glycogen, and supramolecular aggregates, for example multienzyme complexes, but also ions in a higher concentration than that of the extracellular environment. This causes osmotic pressure to drive water from outside to inside the cell. If this net flow of water toward the inside of the cell is not counterbalanced, cell swells, and plasma membrane is distended until the cell bursts, that is, an osmotic lysis occurs. Under physiological conditions, this does not happen because during evolution several mechanisms have been developed to oppose, and in some cases even exploit, these osmotic forces. Two of these are energy-dependent ion pumps and, in plants, bacteria and fungi, the cell wall.

### Energy dependent ion pumps

Ion pumps reduce, at the expense of ATP, the intracellular concentrations of specific ions with respect to their concentrations in the extracellular environment, thereby creating an unequal distribution of the ions across the plasma membrane, namely, an ion gradient. In this way the cell counterbalances the osmotic forces due to the ions and macromolecules trapped inside it. An example of energy-dependent ion pump is Na+/K+ ATPase, which reduces the concentration of Na+ inside the cell relative to the outside.

### Cell wall

Plant cells are surrounded by an extracellular matrix, the cell wall, that, being non expandable and positioned next to the plasma membrane, allows cell to resist osmotic forces that would cause its swelling and finally the lysis. How?
Inside mature plant cells, the vacuoles are the largest organelles, occupying about 80% of the total cell volume. Large quantities of solutes, for the most part organic and inorganic acids, are accumulated within them and osmotically draw water, causing their swelling. In turn, this causes the tonoplast, the membrane that surrounds the vacuole, to press the plasma membrane against the cell wall, that mechanically opposes to these forces and avoids the osmotic lysis. This osmotic pressure is called turgor pressure, and can reach up 2 MPa, that is, 20 atmospheres, a value about 10 times higher than the air pressure in tires. It is responsible for the rigidity of non woody parts of plants, is involved in plant growth, as well as in:

• wilting of vegetables, due to its reduction;
• plants movements, such as:
• the circadian movements of the leaves;
• the movements of the leaves of Dionaea muscipula, the Venus flytrap, or of the leaves of the sensitive plants such as Mimosa pudica.

Even in bacteria and fungi, the plasma membrane is surrounded by a cell wall that stably withholds the internal pressure, then preventing osmotic lysis of the cell.

### Isotonic, hypotonic, and hypertonic solutions

By comparing the osmotic pressure of two solutions separated by a semipermeable membrane, it is possible to define three types of solutions, briefly described below.

• The solutions are isotonic when they have the same osmotic pressure.
• If the solutions have different osmotic pressures, that with the higher osmotic pressure is defined hypertonic with respect to the other.
• If the solutions have different osmotic pressures, that with the lower osmotic pressure is defined hypotonic with respect to the other.

In biological systems, the cytosol is the reference solution; then, if we place a cell in a:

• isotonic solution, no net flow of water occurs into or out of the plasma membrane;
• hypertonic solution, there is a net flow of water out of the cell, therefore the cell loses water and shrinks;
• hypotonic solution, there is a net flow of water into the cell, the cell swells and can burst, i.e., an osmotic lysis can occur.

In addition to ion pumps and the cell wall, in the course of evolution multicellular organisms have developed another mechanism to oppose the osmotic forces: to surround the cells with an isotonic solution or close to isotonicity that prevents, or at least limits, a net inflow or outflow of water. An example is plasma, that is, the liquid component of blood, which, due to the presence of salts and proteins, primarily albumin in humans, has an osmolarity similar to that of the cytosol.

## Osmotic pressure, starch and glycogen

Living organisms store glucose in the form of polymers, glycogen in animals, fungi, bacteria, and starch in photoautotrophs, but not in the free form. In this way, they avoid that the osmotic pressure exerted by the stores of carbohydrates becomes too high. Indeed, since osmotic pressure, like the other colligative properties, depends only on the number of solute molecules, storing millions of glucose units in the form of a significantly lower number of polysaccharides allows to avoid an excessive pressure. Here are some examples.

• A gram of polysaccharide, e.g. glycogen or starch, composed of 1000 glucose units has an effect on osmotic pressure lower than that of a milligram of free glucose.
• In hepatocyte, if the glucose stored in the form of glycogen was present in the free form, its concentration would be about 0.4 M, whereas the polysaccharide concentration of about 0.04 μM, and this would cause a net flow of water inside the cell such as to lead to osmotic lysis.
Furthermore, even if osmotic lysis could be avoided, there would be problems with the transport of glucose into the cell. In humans, under physiological conditions, blood glucose levels range from 3.33 to 5.56 mmol/L (60-100 mg/dL); if glucose was present in the free form, its intracellular concentration would be 120 to 72 times greater than that of the blood, and its transport into the hepatocyte would entail a large energy expenditure.

## Osmotic diarrhea

In the presence of diseases that cause non-absorbed and osmotically active solutes accumulation in the distal portion of the small intestine and in the colon, a condition known as osmotic diarrhea occurs.
Causes can be, for example, bacterial infections, pancreatic diseases, celiac disease, an autoimmune enteropathy due to gluten intake in genetically predisposed subjects, or a congenital deficiency of one of the disaccharidases of the brush border of enterocytes, such as in lactose intolerance. In these conditions, an incomplete carbohydrate digestion can occur as a consequence of a deficit of alpha-amylase and/or of one or more disaccharidases. Moreover, unabsorbed osmotically active solutes pass into the colon where they can be fermented by bacteria of gut microbiota, which is part of the human microbiota, resulting in production of excessive gas, such as hydrogen, carbon dioxide and methane, and short-chain fatty acids, mainly butyric acid, aceticacid and propioni acid. This causes a condition known as osmotic-fermentative diarrhea.
Osmotic diarrhea can also result from the use of osmotic laxatives such as polyethylene glycol or PEG, and magnesium sulfate.
Osmotically active solutes deriving from incomplete digestion, and osmotic laxatives lead to an increase in intraluminal osmotic pressure and inhibit the normal absorption of water and electrolytes, causing a reduction in the consistency of the stool and an increase in intestinal motility.

## Osmotic pressure, galactosemia, and cataracts

Galactose, glucose and fructose are the monosaccharides that are absorbed in the intestine.
Galactose is metabolized mostly in the liver, and to a lesser extent by other organs and tissues. After conversion to UDP-glucose and UDP-galactose through the Leloir pathway, it can be used for both anabolic and catabolic purposes.
Mutations in one of the genes encoding the enzymes of the Leloir pathway leads to an accumulation of galactose and causes galactosemia, a genetic metabolic disorder whose only treatment is a galactose-restricted diet.
The accumulation of the monosaccharide fuels alternative metabolic pathways that lead to the synthesis of the galactose-related chemicals galactitol and galactonate.
The symptoms of galactosemia include cataracts, and the synthesis and accumulation of galactitol in the lens of the eye seems to be one of the triggers. Why? Galactitol is a poorly metabolized polyol, and, due to its poor lipophilicity does not diffuse through cell membranes and accumulates inside the cell. Being osmotically active, its accumulation causes an increase in intracellular osmotic pressure and then a net flow of water into the cell. Such osmotic effect seems to be one of the mechanisms through which galactitol contributes to the development of galactosemic cataracts.

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