# Osmotic Pressure

Submitted by ChemPRIME Staff on Thu, 12/16/2010 - 14:09

Suppose we have a solutionA mixture of one or more substances dissolved in a solvent to give a homogeneous mixture. of sugarA small carbohydrate that either contains five or six carbon atoms or is a dimer of two units, each containing five or six carbon atoms. in water separated by a membrane from a sample of pure water. The membrane is porous, but the holes are not large enough to allow sucrose molecules to pass through from one side to the other while still being large enough to allow water molecules to pass freely through them. In such a situation, water molecules will be hitting one side of the membrane more often than the other. As a result, water molecules will move more often from right to left through the membrane in the animation than they will in the reverse direction. There will thus be a net flow of water from the compartment containing pure solventThe substance to which a solute is added to make a solution., through the membrane, into the compartment containing the sucrose. This is another example of the tendency for moving molecules to become more thoroughly mixed together. The following movie shows this process, called osmosisThe passage of solvent through a membrane that is impermeable to solute from a region of lower concentration of solute to a region of higher concentration of solute. The solvent moves from a region of higher concentration to one of lower concentration; the process corresponds with the spontaneous dilution of a solution that is mixed with another solution of lower (or zero) concentration..

Figure 1 This animation depicts osmosis on a molecular level. Above a membrane formed by white spheres is a solution made of a green solute and gray solvent. On the bottom is the pure solvent, shown in blue, so that it is easier to follow where solvent starting on each side ends up. Solvent can pass through the membrane, but the green solute cannot. More solvent moves from bottom to above the membrane, and the membrane itself is pushed down.

Osmosis occurs when two solutions of different concentrations are separated by a membrane which will selectively allow some species through it but not others. Then, material flows from the less concentratedIncreased the concentration of a mixture or solution (verb). Having a large concentration (adjective). to the more concentrated side of the membrane. A membrane which is selective in the way just described is said to be semipermeable. Osmosis is of particular importance in living organisms, since most living tissue is semipermeable in one way or another. In the movie, we have depicted a membrane which is selective purely because of the pore size. In biological systems, the semipermeability relies on a set of solute transporters and channels. The cell membrane is formed of a lipid bilayer with polar head groups facing out, and nonpolarDescribes a molecule with no net permanent dipole; this can occur when there is no separation of centers of positive and negative electrical charge or because there are bond dipoles that cancel each others' effects. A polar molecule will assume certain orientations more than others in an electric field. hydrocarbonA compound containing only the elements carbon and hydrogen. tails in the middle of the membrane. The consequence is that charged and polar substances cannot cross the membrane. Aquaporins are membrane proteins which allow water, but no other molecule, not even H3O+ to pass through. For other solutes and ions, there exist specific transporters, some which allow a solute to diffuse down a natural gradient, and others which actively pump ions or other solutes in or out of the cell. These transporters, pumps and channels can be gated and regulated as well, allowing a cell to respond to varying osmotic conditions.[1]

A simple demonstration of osmosis is provided by the behavior of red blood cells. If these are immersed in water and observed under the microscope, they will be seen to gradually swell and to finally burst. Osmotic flow occurs from the surrounding water into the more concentrated solutions inside the cell. If the blood cells are now immersed in a saturatedDescribes 1) a solution that contains the equilibrium concentration of a solute, or 2) an organic compound that contains no double or triple bonds (such as an alkane). solution of NaC1, osmosis occurs in the opposite direction, since the solution inside the cell is not as concentrated as that outside. Under the microscope, the blood cells can be seen to shrink and shrivel. In medical practice, any solution which is to be introduced into the blood must take the possibility of osmosis into account. Normal saline, a solution of 0.16 M NaCl (0.16 mol NaCl per dm3 of solution) is always employed for intravenous feeding or injection, because it has the same concentration of salts as blood serum.

Figure 2 An osmometer measures osmotic flow by determining the pressure needed to just stop osmosis. In this set up, a solution is placed into solvent, separated by a membrane. Solvent begins to flow into the solution, raising its level above that of the solvent. The column reaches a height where the pressure it exerts on the solution equals the pressure of solvent flowing in, and the column ceases to rise.
The tendency for osmotic flow to occur from a solvent to a solution is usually measured in terms of what is called the osmotic pressureThe pressure required to prevent solvent from passing through a semipermeable membrane from a region of lower concentration of solute to a region of higher concentration of solute. of the solution, symbol Π. This osmotic pressure is not a pressure which the solution itself exerts but is rather the pressure which must be applied to the solution (but not the solvent) from outside in order to just prevent osmosis from occurring. A simple method for measuring the osmotic pressure is shown in Fig. 2. The wider end of a funnel-shaped tube is covered with a membrane. The tube is filled with solution and placed in a container of the solvent. The height of the solution above the solvent increases until a maximum value is reached. The osmotic pressure is then the pressure exerted by the column of a solution of height h:

Π = ρgh

where ρ is the densityThe ratio of the mass of a sample of a material to its volume. of the solution and g is the gravitational acceleration. Experimentally the osmotic pressure is found to obey a law similar in form to the ideal gasA hypothetical gas for which the relationship among the pressure, volume, temperature, and chemical amount (moles) can be described by simple proportionalities summarized by the ideal gas equation, PV = nRT. law and hence easy to remember:

ΠV = nRT      (1)

where n is the amount of solute in volume V of solution. In practice it is more useful to have Eq. (1) in terms of the concentration of solute n/V. Accordingly we rearrange it to read

Π = n × V–1 RT

or      Π = cRT      (2)

Equation (2) is a very useful relationship since it means that we can find the concentration of any solution merely by measuring its osmotic pressure. This, in turn, allows us to find the molar massThe mass of a mole of substance; the same as molecular weight for molecular substances. of the solute. Suppose we have a solution in which a known mass of solute is dissolved in a known volume of solution. By measuring the osmotic pressure of this solution, we can find the concentration of solute and hence the amount of solute in the total volume. Since we already know the mass of solute, the molar mass follows immediately.

EXAMPLE A solution of 20.0 g of polyisobutylene in 1.00 dm3 of benzene was placed in an osmometer, similar to the one shown in Fig. 2, at 25°C. After equilibriumA state in which no net change is occurring, that is, in which the concentrations of reactants and products remain constant; chemical equilibrium is characterized by forward and reverse reactions occurring at the same rate. had been obtained, the height h was found to be 24.45 mm of benzene. Find the average molar mass of the polymerA large molecule containing a large number of repeating units; a substance formed from such molecules.. The density of the solution is 0.879 g cm–3.

Solution We must first find the osmotic pressure from the height h with the formula Π = ρgh. In doing this, it is most convenient to convert everything to SI baseIn Arrhenius theory, a substance that increases the concentration of hydroxide ions in an aqueous solution. In Bronsted-Lowry theory, a hydrogen-ion (proton) acceptor. In Lewis theory, a species that donates a pair of electrons to form a covalent bond. units.

\begin{align} & \Pi =\rho gh=\text{0}\text{.879}\frac{\text{g}}{\text{cm}^{\text{3}}}\text{ }\times \text{ 9}\text{.807}\frac{\text{m}}{\text{s}^{\text{2}}}\text{ }\times \text{ 24}\text{.45 mm} \ & \text{ }=210.8\frac{\text{g}}{\text{cm}^{\text{3}}}\frac{\text{m}}{\text{s}^{\text{2}}}\text{mm }\times \text{ }\frac{\text{1 kg}}{\text{1000 g}}\text{ }\times \text{ }\left( \frac{\text{100 cm}}{\text{1 m}} \right)^{\text{3}}\text{ }\times \text{ }\frac{\text{1 m}}{\text{1000 mm}} \ & \text{ }=\text{210}\text{.8}\frac{\text{kg m}^{\text{2}}}{\text{m}^{\text{3}}\text{ s}^{\text{2}}}=\text{210}\text{.8}\frac{\text{kg m}}{\text{s}^{\text{2}}}\text{ }\times \text{ }\frac{\text{1}}{\text{m}^{\text{2}}}=\text{210}\text{.8 N m}^{-\text{2}}=\text{210}\text{.8 Pa} \ \end{align}

Knowing Π, we can now calculate the concentration c by rewriting

Π = cRT

as      $\text{c}=\frac{\Pi }{RT}=\frac{\text{210}\text{.8 }\times \text{ 10}^{-\text{3}}\text{ kPa}}{\text{8}\text{.3143 J K}^{-\text{1}}\text{ mol}^{-\text{1}}\text{ }\times \text{ 298}\text{.15 K}}=\text{8}\text{.50 }\times \text{ 10}^{-5}\text{ mol dm}^{-\text{3}}$

For 1 dm3 of solution therefore,

nsolute = 8.50 × 10–5 mol

while      msolute = 20 g

Thus      $M_{\text{solute}}=\frac{\text{20 g}}{\text{8}\text{.50 }\times \text{ 10}^{-\text{5}}\text{ mol}}\text{2}\text{.35 }\times \text{ 10}^{\text{5}}\text{ g mol}^{-\text{1}}$

Note: An average polyisobutylene molecule thus has a molecular weightThe mass of one mole of molecules of a substance; the molar mass of a molecular substance. of close to a quarter of a million! Such a molecule is made from units, each with a molar mass of 56.10 g mol-1.

An average polyisobutylene chain is thus $\frac{\text{2}\text{.35 }\times \text{ 10}^{\text{5}}\text{ g mol}^{-\text{1}}}{\text{56}\text{.10 g mol}^{-\text{1}}}=\text{4189}$ units long.In other words the chain length is over 8000 carbon atomsThe smallest particle of an element that can be involved in chemical combination with another element; an atom consists of protons and neutrons in a tiny, very dense nucleus, surrounded by electrons, which occupy most of its volume. in this sample of polymer.

1. Nelson, D.L., Cox, M.M. Lehninger Principles of Biochemistry(5th ed.). New York: W.H. Freeman and Company, 2008. pp. 52,389,405.