Osmotic pressure

Osmotic pressure is the minimum pressure which needs to be applied to a solution to prevent the inward flow of its pure solvent across a semipermeable membrane.[1] It is also defined as the measure of the tendency of a solution to take in pure solvent by osmosis. Potential osmotic pressure is the maximum osmotic pressure that could develop in a solution if it were separated from its pure solvent by a semipermeable membrane.

Osmosis occurs when two solutions, containing different concentration of solute, are separated by a selectively permeable membrane. Solvent molecules pass preferentially through the membrane from the low-concentration solution to the solution with higher solute concentration. The transfer of solvent molecules will continue until equilibrium is attained.[1][2]

Osmosis diagram
Osmosis in a U-shaped tube.

Theory and measurement

Pfeffer Osmotische Untersuchungen-1-3
A Pfeffer cell used for early measurements of osmotic pressure

Jacobus van 't Hoff found a quantitative relationship between osmotic pressure and solute concentration, expressed in the following equation.

where is osmotic pressure, i is the dimensionless van 't Hoff index, C is the molar concentration of solute, R is the ideal gas constant, and T is the temperature in kelvins. This formula applies when the solute concentration is sufficiently low that the solution can be treated as an ideal solution. The proportionality to concentration means that osmotic pressure is a colligative property. Note the similarity of this formula to the ideal gas law in the form where n is the total number of moles of gas molecules in the volume V, and n/V is the molar concentration of gas molecules. Harmon Northrop Morse and Frazer showed that the equation applied to more concentrated solutions if the unit of concentration was molal rather than molar.[3]

For more concentrated solutions the van 't Hoff equation can be extended as a power series in solute concentration, C. To a first approximation,

where is the ideal pressure and A is an empirical parameter. The value of the parameter A (and of parameters from higher-order approximations) can be used to calculate Pitzer parameters. Empirical parameters are used to quantify the behaviour of solutions of ionic and non-ionic solutes which are not ideal solutions in the thermodynamic sense.

The Pfeffer cell was developed for the measurement of osmotic pressure.


Osmotic pressure on blood cells diagram
Osmotic pressure on red blood cells

Osmotic pressure measurement may be used for the determination of molecular weights.

Osmotic pressure is an important factor affecting cells. Osmoregulation is the homeostasis mechanism of an organism to reach balance in osmotic pressure.

  • Hypertonicity is the presence of a solution that causes cells to shrink.
  • Hypotonicity is the presence of a solution that causes cells to swell.
  • Isotonicity is the presence of a solution that produces no change in cell volume.

When a biological cell is in a hypotonic environment, the cell interior accumulates water, water flows across the cell membrane into the cell, causing it to expand. In plant cells, the cell wall restricts the expansion, resulting in pressure on the cell wall from within called turgor pressure. Turgor pressure allows herbaceous plants to stand upright. It is also the determining factor for how plants regulate the aperture of their stomata. In animal cells excessive osmotic pressure can result in cytolysis.

Osmotic pressure is the basis of filtering ("reverse osmosis"), a process commonly used in water purification. The water to be purified is placed in a chamber and put under an amount of pressure greater than the osmotic pressure exerted by the water and the solutes dissolved in it. Part of the chamber opens to a differentially permeable membrane that lets water molecules through, but not the solute particles. The osmotic pressure of ocean water is about 27 atm. Reverse osmosis desalinates fresh water from ocean salt water.

Derivation of the van 't Hoff formula

Consider the system at the point when it has reached equilibrium. The condition for this is that the chemical potential of the solvent (since only it is free to flow toward equilibrium) on both sides of the membrane is equal. The compartment containing the pure solvent has a chemical potential of , where is the pressure. On the other side, in the compartment containing the solute, the chemical potential of the solvent depends on the mole fraction of the solvent, . Besides, this compartment can assume a different pressure, . We can therefore write the chemical potential of the solvent as . If we write , the balance of the chemical potential is therefore:


Here, the difference in pressure of the two compartments is defined as the osmotic pressure exerted by the solutes. Holding the pressure, the addition of solute decreases the chemical potential (an entropic effect). Thus, the pressure of the solution has to be increased in an effort to compensate the loss of the chemical potential.

In order to find , the osmotic pressure, we consider equilibrium between a solution containing solute and pure water.


We can write the left hand side as:


where is the activity coefficient of the solvent. The product is also known as the activity of the solvent, which for water is the water activity . The addition to the pressure is expressed through the expression for the energy of expansion:


where is the molar volume (m³/mol). Inserting the expression presented above into the chemical potential equation for the entire system and rearranging will arrive at:


If the liquid is incompressible the molar volume is constant, , and the integral becomes . Thus, we get


The activity coefficient is a function of concentration and temperature, but in the case of dilute mixtures, it is often very close to 1.0, so


For aqueous solutions of salts, ionisation must be taken into account. For example, 1 mole of NaCl ionises to 2 moles of ions.

See also


  1. ^ a b Voet, Donald; Judith Aadil; Charlotte W. Pratt (2001). Fundamentals of Biochemistry (Rev. ed.). New York: Wiley. p. 30. ISBN 978-0-471-41759-0.
  2. ^ Atkins, Peter W.; de Paula, Julio (2010). "Section 5.5 (e)". Physical Chemistry (9th ed.). Oxford University Press. ISBN 978-0-19-954337-3.
  3. ^ Lewis, Gilbert Newton (1908-05-01). "The Osmotic Pressure of Concentrated Solutions and the Laws of the Perfect Solution". Journal of the American Chemical Society. 30 (5): 668–683. doi:10.1021/ja01947a002. ISSN 0002-7863.

External links

Candied fruit

Candied fruit, also known as crystallized fruit or glacé fruit, has existed since the 14th century. Whole fruit, smaller pieces of fruit, or pieces of peel, are placed in heated sugar syrup, which absorbs the moisture from within the fruit and eventually preserves it. Depending on size and type of fruit, this process of preservation can take from several days to several months. This process allows the fruit to retain its quality for a year.The continual process of drenching the fruit in syrup causes the fruit to become saturated with sugar, preventing the growth of spoilage microorganisms due to the unfavourable osmotic pressure this creates.Fruits that are commonly candied include dates, cherries, pineapple, and a root, ginger. The principal candied peels are orange and citron; these with candied lemon peel are the usual ingredients of mixed chopped peel (which may also include glacé cherries).

Recipes vary from region to region, but the general principle is to boil the fruit, steep it in increasingly strong sugar solutions for a number of weeks, and then dry off any remaining water.

Colligative properties

In chemistry, colligative properties are properties of solutions that depend on the ratio of the number of solute particles to the number of solvent molecules in a solution, and not on the nature of the chemical species present. The number ratio can be related to the various units for concentration of solutions. The assumption that solution properties are independent of nature of solute particles is only exact for ideal solutions, and is approximate for dilute real solutions. In other words, colligative properties are a set of solution properties that can be reasonably approximated by assuming that the solution is ideal.

Here we consider only properties which result from the dissolution of nonvolatile solute in a volatile liquid solvent. They are essentially solvent properties which are changed by the presence of the solute. The solute particles displace some solvent molecules in the liquid phase and therefore reduce the concentration of solvent, so that the colligative properties are independent of the nature of the solute. The word colligative is derived from the Latin colligatus meaning bound together.Colligative properties include:

Relative lowering of vapor pressure

Elevation of boiling point

Depression of freezing point

Osmotic pressureFor a given solute-solvent mass ratio, all colligative properties are inversely proportional to solute molar mass.

Measurement of colligative properties for a dilute solution of a non-ionized solute such as urea or glucose in water or another solvent can lead to determinations of relative molar masses, both for small molecules and for polymers which cannot be studied by other means. Alternatively, measurements for ionized solutes can lead to an estimation of the percentage of dissociation taking place.

Colligative properties are mostly studied for dilute solutions, whose behavior may often be approximated as that of an ideal solution.

Gibbs–Donnan effect

The Gibbs–Donnan effect (also known as the Donnan's effect, Donnan law, Donnan equilibrium, or Gibbs–Donnan equilibrium) is a name for the behaviour of charged particles near a semi-permeable membrane that sometimes fail to distribute evenly across the two sides of the membrane. The usual cause is the presence of a different charged substance that is unable to pass through the membrane and thus creates an uneven electrical charge. For example, the large anionic proteins in blood plasma are not permeable to capillary walls. Because small cations are attracted, but are not bound to the proteins, small anions will cross capillary walls away from the anionic proteins more readily than small cations.

Thus, some ionic species can pass through the barrier while others cannot. The solutions may be gels or colloids as well as solutions of electrolytes, and as such the phase boundary between gels, or a gel and a liquid, can also act as a selective barrier. The electric potential arising between two such solutions is called the Donnan potential.

The effect is named after the American physicist Josiah Willard Gibbs and the British chemist Frederick G. Donnan.The Donnan equilibrium is prominent in the triphasic model for articular cartilage proposed by Mow and Lai, as well as in electrochemical fuel cells and dialysis.

The Donnan effect is extra osmotic pressure attributable to cations (Na+ and K+) attached to dissolved plasma proteins.

Harmon Northrop Morse

Harmon Northrop Morse (October 15, 1848 – September 8, 1920) was an American chemist. Today he is known as the first to have synthesized paracetamol, but this substance only became widely used as a drug decades after Morse's death. In the first half of the 20th century he was best known for his study of osmotic pressure, for which he was awarded the Avogadro Medal in 1916. The Morse equation for estimating osmotic pressure is named after him.


Hemodynamics or hæmodynamics is the dynamics of blood flow. The circulatory system is controlled by homeostatic mechanisms, such as hydraulic circuits are controlled by control systems. Hemodynamic response continuously monitors and adjusts to conditions in the body and its environment. Thus hemodynamics explains the physical laws that govern the flow of blood in the blood vessels.

Blood flow ensures the transportation of nutrients, hormones, metabolic wastes, O2 and CO2 throughout the body to maintain cell-level metabolism, the regulation of the pH, osmotic pressure and temperature of the whole body, and the protection from microbial and mechanical harms.Blood is a non-Newtonian fluid, best studied using rheology rather than hydrodynamics. Blood vessels are not rigid tubes, so classic hydrodynamics and fluids mechanics based on the use of classical viscometers are not capable of explaining hemodynamics.The study of the blood flow is called hemodynamics. The study of the properties of the blood flow is called hemorheology.

Oncotic pressure

Oncotic pressure, or colloid osmotic pressure, is a form of osmotic pressure induced by proteins, notably albumin, in a blood vessel's plasma (blood/liquid) that displaces water molecules, thus creating a relative water molecule deficit with water molecules moving back into the circulatory system within the lower pressure venous end of capillaries. It has the opposing effect of both hydrostatic blood pressure pushing water and small molecules out of the blood into the interstitial spaces within the arterial end of capillaries and interstitial colloidal osmotic pressure. These interacting factors determine the partition balancing of total body extracellular water between the blood plasma and the larger extracellular water volume outside the blood stream.

It has a major effect on the pressure across the glomerular filter. However, this concept has been strongly criticised and attention has been shifted to the impact of the intravascular glycocalyx layer as major player.


Osmoconformers are marine organisms that maintain an internal environment which is osmotic to their external environment. This means that the osmotic pressure of the organism's cells is equal to the osmotic pressure of their surrounding environment. By minimizing the osmotic gradient, this subsequently minimizes the net influx and efflux of water into and out of cells. Even though osmoconformers have an internal environment that is isosmotic to their external environment, the types of ions in the two environments differ greatly in order to allow critical biological functions to occur.An advantage of osmoconformation is that such organisms don’t need to expend as much energy as osmoregulators in order to regulate ion gradients. However, to ensure that the correct types of ions are in the desired location, a small amount of energy is expended on ion transport. A disadvantage to osmoconformation is that the organisms are subject to changes in the osmolarity of their environment.


An osmoreceptor is a sensory receptor primarily found in the hypothalamus of most homeothermic organisms that detects changes in osmotic pressure. Osmoreceptors can be found in several structures, including two of the circumventricular organs – the vascular organ of the lamina terminalis, and the subfornical organ. They contribute to osmoregulation, controlling fluid balance in the body. Osmoreceptors are also found in the kidneys where they also modulate osmolality.


Osmoregulation is the passive regulation of the osmotic pressure of an organism's body fluids, detected by osmoreceptors, to maintain the homeostasis of the organism's water content; that is, it maintains the fluid balance and the concentration of electrolytes (salts in solution) to keep the fluids from becoming too diluted or concentrated. Osmotic pressure is a measure of the tendency of water to move into one solution from another by osmosis. The higher the osmotic pressure of a solution, the more water tends to move into it. Pressure must be exerted on the hypertonic side of a selectively permeable membrane to prevent diffusion of water by osmosis from the side containing pure water.

Organisms in aquatic and terrestrial environments must maintain the right concentration of solutes and amount of water in their body fluids; this involves excretion (getting rid of metabolic nitrogen wastes and other substances such as hormones that would be toxic if allowed to accumulate in the blood) through organs such as the skin and the kidneys.


Osmosis () is the spontaneous net movement of solvent molecules through a selectively permeable membrane into a region of higher solute concentration, in the direction that tends to equalize the solute concentrations on the two sides. It may also be used to describe a physical process in which any solvent moves across a selectively permeable membrane (permeable to the solvent, but not the solute) separating two solutions of different concentrations. Osmosis can be made to do work. Osmotic pressure is defined as the external pressure required to be applied so that there is no net movement of solvent across the membrane. Osmotic pressure is a colligative property, meaning that the osmotic pressure depends on the molar concentration of the solute but not on its identity.

Osmosis is a vital process in biological systems, as biological membranes are semipermeable. In general, these membranes are impermeable to large and polar molecules, such as ions, proteins, and polysaccharides, while being permeable to non-polar or hydrophobic molecules like lipids as well as to small molecules like oxygen, carbon dioxide, nitrogen, and nitric oxide. Permeability depends on solubility, charge, or chemistry, as well as solute size. Water molecules travel through the plasma membrane, tonoplast membrane (vacuole) or protoplast by diffusing across the phospholipid bilayer via aquaporins (small transmembrane proteins similar to those responsible for facilitated diffusion and ion channels). Osmosis provides the primary means by which water is transported into and out of cells. The turgor pressure of a cell is largely maintained by osmosis across the cell membrane between the cell interior and its relatively hypotonic environment.

Osmotic-controlled release oral delivery system

The osmotic-controlled release oral delivery system (OROS) is an advanced controlled release oral drug delivery system in the form of a rigid tablet with a semi-permeable outer membrane and one or more small laser drilled holes in it. As the tablet passes through the body, water is absorbed through the semipermeable membrane via osmosis, and the resulting osmotic pressure is used to push the active drug through the opening(s) in the tablet. OROS is a trademarked name owned by ALZA Corporation, which pioneered the use of osmotic pumps for oral drug delivery.

Osmotic concentration

Osmotic concentration, formerly known as osmolarity, is the measure of solute concentration, defined as the number of osmoles (Osm) of solute per litre (L) of solution (osmol/L or Osm/L). The osmolarity of a solution is usually expressed as Osm/L (pronounced "osmolar"), in the same way that the molarity of a solution is expressed as "M" (pronounced "molar"). Whereas molarity measures the number of moles of solute per unit volume of solution, osmolarity measures the number of osmoles of solute particles per unit volume of solution. This value allows the measurement of the osmotic pressure of a solution and the determination of how the solvent will diffuse across a semipermeable membrane (osmosis) separating two solutions of different osmotic concentration.

Peritubular capillaries

In the renal system, peritubular capillaries are tiny blood vessels, supplied by the efferent arteriole, that travel alongside nephrons allowing reabsorption and secretion between blood and the inner lumen of the nephron. Peritubular capillaries surround the proximal and distal tubules, as well as the loop of Henle, where they are known as vasa recta.Ions and minerals that need to be saved in the body are reabsorbed into the peritubular capillaries through active transport, secondary active transport, or transcytosis.

The ions that need to be excreted as waste are secreted from the capillaries into the nephron to be sent towards the bladder and out of the body.

Essentially, the peritubular capillaries reabsorb useful substances such as glucose and amino acids and secrete certain mineral ions and excess water into the tubule.

The majority of exchange through the peritubular capillaries occurs because of chemical gradients osmosis and hydrostatic pressure. Movement of water into the peritubular capillaries is due to the loss of water from the glomerulus during filtration, which increases the colloid osmotic pressure of the blood. This blood leaves the glomerulus via the efferent arteriole, which supplies the peritubular capillaries. The higher osmolarity of the blood in the peritubular capillaries creates an osmotic pressure which causes the uptake of water. Other ions can be taken up by the peritubular capillaries via solvent drag. Water is also driven into the peritubular capillaries due to the higher fluid pressure of the interstitium, driven by reabsorption of fluid and electrolytes via active transport, and the low fluid pressure of blood entering the peritubular capillaries due to the narrowness of the efferent arteriole.


Plasmolysis is the process in which cells lose water in a hypertonic solution. The reverse process, cytolysis, can occur if the cell is in a hypotonic solution resulting in a lower external osmotic pressure and a net flow of water into the cell. Through observation of plasmolysis and deplasmolysis, it is possible to determine the tonicity of the cell's environment as well as the rate solute molecules cross the cellular membrane.

Reverse osmosis

Reverse osmosis (RO) is a water purification technology that uses a partially permeable membrane to remove ions, molecules and larger particles from drinking water. In reverse osmosis, an applied pressure is used to overcome osmotic pressure, a colligative property, that is driven by chemical potential differences of the solvent, a thermodynamic parameter. Reverse osmosis can remove many types of dissolved and suspended chemical species as well as biological ones (principally bacteria) from water, and is used in both industrial processes and the production of potable water. The result is that the solute is retained on the pressurized side of the membrane and the pure solvent is allowed to pass to the other side. To be "selective", this membrane should not allow large molecules or ions through the pores (holes), but should allow smaller components of the solution (such as solvent molecules, i.e., water, H2O) to pass freely.In the normal osmosis process, the solvent naturally moves from an area of low solute concentration (high water potential), through a membrane, to an area of high solute concentration (low water potential). The driving force for the movement of the solvent is the reduction in the free energy of the system when the difference in solvent concentration on either side of a membrane is reduced, generating osmotic pressure due to the solvent moving into the more concentrated solution. Applying an external pressure to reverse the natural flow of pure solvent, thus, is reverse osmosis. The process is similar to other membrane technology applications.

Reverse osmosis differs from filtration in that the mechanism of fluid flow is by osmosis across a membrane. The predominant removal mechanism in membrane filtration is straining, or size exclusion, where the pores are 0.01 micrometers or larger, so the process can theoretically achieve perfect efficiency regardless of parameters such as the solution's pressure and concentration. Reverse osmosis instead involves solvent diffusion across a membrane that is either nonporous or uses nanofiltration with pores 0.001 micrometers in size. The predominant removal mechanism is from differences in solubility or diffusivity, and the process is dependent on pressure, solute concentration, and other conditions. Reverse osmosis is most commonly known for its use in drinking water purification from seawater, removing the salt and other effluent materials from the water molecules.


Sap is a fluid transported in xylem cells (vessel elements or tracheids) or phloem sieve tube elements of a plant. These cells transport water and nutrients throughout the plant.

Sap is distinct from latex, resin, or cell sap; it is a separate substance, separately produced, and with different components and functions.

Starling equation

The Starling equation for fluid filtration is named for the British physiologist Ernest Starling, who is also recognised for the Frank–Starling law of the heart. The classic Starling equation has in recent years been revised. The Starling principle of fluid exchange is key to understanding how plasma fluid (solvent) within the bloodstream (intravascular fluid) moves to the space outside the bloodstream (extravascular space). Starling can be credited with identifying that the "absorption of isotonic salt solutions (from the extravascular space) by the blood vessels is determined by this osmotic pressure of the serum proteins." (1896)

Transendothelial fluid exchange occurs predominantly in the capillaries, and is a process of plasma ultrafiltration across a semi-permeable membrane. It is now appreciated that the ultrafilter is the endothelial glycocalyx layer whose interpolymer spaces function as a system of small pores, radius circa 5 nm. Where the endothelial glycocalyx overlies an inter endothelial cell cleft, the plasma ultrafiltrate may pass to the interstitial space. Some continuous capillaries may feature fenestrations that provide an additional subglycocalyx pathway for solvent and small solutes. Discontinuous capillaries as found in sinusoidal tissues of bone marrow, liver and spleen have little or no filter function.

The rate at which fluid is filtered across vascular endothelium (transendothelial filtration) is determined by the sum of two outward forces, capillary pressure () and interstitial protein osmotic pressure (), and two absorptive forces, plasma protein osmotic pressure () and interstitial pressure (). The Starling equation describes these forces in mathematical terms. It is one of the Kedem–Katchalski equations which bring nonsteady state thermodynamics to the theory of osmotic pressure across membranes that are at least partly permeable to the solute responsible for the osmotic pressure difference (Staverman 1951; Kedem and Katchalsky 1958). The second Kedem–Katchalsky equation explains the trans endothelial transport of solutes, .

Glomerular capillaries have a continuous glycocalyx layer in health and the total transendothelial filtration rate of solvent () to the renal tubules is normally around 125 ml/ min (about 180 litres/ day). Glomerular capillary is more familiarly known as the glomerular filtration rate (GFR). In the rest of the body's capillaries, is typically 5 ml/ min (around 8 litres/ day), and the fluid is returned to the circulation via afferent and efferent lymphatics.


Tonicity is a measure of the effective osmotic pressure gradient, as defined by the water potential of two solutions separated by a semipermeable membrane. In other words, tonicity is the relative concentration of solutes dissolved in solution which determine the direction and extent of diffusion. It is commonly used when describing the response of cells immersed in an external solution.

Unlike osmotic pressure, tonicity is influenced only by solutes that cannot cross the membrane, as only these exert an effective osmotic pressure. Solutes able to freely cross the membrane do not affect tonicity because they will always be in equal concentrations on both sides of the membrane. It is also a factor affecting imbibition.

There are three classifications of tonicity that one solution can have relative to another: hypertonic, hypotonic, and isotonic.

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