Osmotic pressure of a solution

In Chap. 8 we saw how the equilibrium osmotic pressure of a solution is related to AG for the mixing process whereby the solution is formed. Any difference in the concentration of the solution involves a change in AG j, ... 

It is a necessary consequence of the reversibility of osmotic processes that the osmotic pressure is independent of the nature of the septum used to measure it. For, suppose there are two semiperineable septa [a] and [/3], and let the osmotic pressures of a solution when separated from pure solvent under a given pressure by these septa be Pa and Pp. Then if we separate a volume 8V of solvent through [a], the work Pa V is spent on the system, and if the solvent is readmitted through [3] the work PpSV is done by the system. The isothermal cycle being now completed, we have ... 

If we now assume that the osmotic pressure of a solution has its origin in the bombardment of the semipermeable diaphragm by the molecules of the solute, we shall, if the same reasoning is applied which led to (1), obtain ... 

If we assume, with Nernst (1893), that the osmotic pressure of a solute (being independent of the nature of the solvent provided... 

The same van t Hoff responsible for the i factor showed that the osmotic pressure of a solution is related to the molarity, c, of the solute in the solution ... 

The van t Ho ff equation is used to determine the molar mass of a solute from osmotic pressure measurements. This technique, which is called osmometry, involves the determination of the osmotic pressure of a solution prepared by making up a known volume of solution of a known mass of solute with an unknown molar mass. Osmometry is very sensitive, even at low concentrations, and is commonly used to determine very large molar masses, such as those of polymers. 

Acrylic resins are polymeric materials used to make warm yet lightweight garments. The osmotic pressure of a solution prepared by dissolving 47.7 g of an acrylic resin in enough water to make 500. mL of solution is 0.325 atm at 25°C. (a) What is the average molar mass of the polymer ... 

The activity coefficient of the solvent remains close to unity up to quite high electrolyte concentrations e.g. the activity coefficient for water in an aqueous solution of 2 m KC1 at 25°C equals y0x = 1.004, while the value for potassium chloride in this solution is y tX = 0.614, indicating a quite large deviation from the ideal behaviour. Thus, the activity coefficient of the solvent is not a suitable characteristic of the real behaviour of solutions of electrolytes. If the deviation from ideal behaviour is to be expressed in terms of quantities connected with the solvent, then the osmotic coefficient is employed. The osmotic pressure of the system is denoted as jz and the hypothetical osmotic pressure of a solution with the same composition that would behave ideally as jt. The equations for the osmotic pressures jt and jt are obtained from the equilibrium condition of the pure solvent and of the solution. Under equilibrium conditions the chemical potential of the pure solvent, which is equal to the standard chemical potential at the pressure p, is equal to the chemical potential of the solvent in the solution under the osmotic pressure jt,... 

Electrolytes regulate body water volumes by establishing osmotic pressure which is proportional to the total number of particles in solution. The osmotic pressure of a solution is expressed in units of milliosmoles (mOsm). Osmolar concentrations reflects the number of particles (molecules as well as ions) of total solutes per volume of solution, which in turn determines the osmotic pressure of the solution. 

The tension or osmotic pressure of a solution also, ionic strength, usually measured as weight percentage. Often the tonicity of a solution is presented as relative to some physiological solution (e.g., blood plasma). See Hypertonic Hypotonic Isotonic Isotonic Buffers... 

The experimental verification of Gibbs theorem. Since the osmotic pressure of a solution is generally difficult to measure, it is simplest to choose a case such that Raoult s law holds good and the concentration of the solution may be used in place of osmotic pressure. The solution should therefore be dilute and should be a true solution the solute, that is, must be dispersed as simple molecules and not as molecular aggregates like soap micelles. These conditions were obtained by Donnan and Barker Proc. 

A) Osmotic pressure of a solution is the force that has to be exerted to halt osmosis. Begin with the formula nV = nRT, where rr represents the pressure measured in atmospheres. T = 273 + 27°C = 300K. 

Reverse osmosis. Reverse osmosis involves manipulation of the osmotic pressure of a solution. If a solution containing n moles of solute particles in a volume V (in m3) of solution is separated from pure solvent by a semiperme-able membrane (i.e., a membrane through which solvent molecules, but not solute particles, can pass), an osmotic pressure n pascals develops across the membrane, the pure solvent being the high pressure side (Fig. 14.2a). 

Since both the osmotic pressure of a solution and the pressure-volume-temperature behavior of a gas are described by the same formal relationship of Equation (25), it seems plausible to approach nonideal solutions along the same lines that are used in dealing with nonideal gases. The behavior of real gases may be written as a power series in one of the following forms for n moles of gas ... 

Write the equation of state for the osmotic pressure of a solution that behaves ideally. 

In Chapter 3 we developed expressions for the equilibrium osmotic pressure of a solution as a function of its concentration. Equation (3.34) may be written... 

From the above relationship, the osmotic pressure of a solution containing 1 mol of solute per liter should be 22.4 atm at 273.15 K. This concentration is called one osmoll" (i.e., Osm 1" ), with one-thousandth ofthe unit being called a millios-mol (i.e., mOsm 1" ). Thus, the osmotic pressure of a 1 mOsm solution would be... 

The osmotic pressure of a solution is a colligative property, i.e. it is proportional to the number of solute particles present in the solution, rather than to their weight. It is usually determined by measuring another colligative property, the depression of freezing point relative to water. 

The osmotic pressure of a solution is defined by Glasstone (1) as the excess pressure which must be applied to a solution to prevent the passage into it of solvent when they are separated by a perfectly semipermeable membrane. Actually no membrane is... 

The osmotic pressure of a solution of a synthetic polyisobutylene in benzene was determined at 25°C. A sample containing 0.20 g of solute per 100 mL of solution developed a rise of 2.4 mm at osmotic equilibrium. The density of the solution was 0.88 g/mL. What is the molar mass of the polyisobutylene The osmotic pressure is equal to that of a column of the solution 2.4 mm high. By the formula in Chapter 5,... 

Osmotic pressure (symbolized as capital pi, II) results from the potential drive for the concentration of water to equalize. Osmotic pressure is a colligative property, and the osmotic pressure of a solution increases with increasing solute concentration. The relationship between osmotic pressure and concentration is given by ... 

The osmotic pressure of a solute is the hydrostatic pressure that must be applied to a solution in order to increase the activity, a. (or fugacity, designated f, introduced by G. N. Lewis as a measure of thermodynamic escaping tendency . It is an effective gas pressure corrected for deviations from the perfect gas laws) of the solvent sufficiently to balance its decrease caused by the presence of the solute. Equilibrium is established through a membrane permeable only to the solvent. This pressure is, by integrating... 

Osmosis is the selective passage of particular components of a solution through a semipermeable membrane. Usually, it is the solvent that passes through the membrane, because the solute is blocked. However, some membranes also allow small solute molecules to pass through as well and only block the passage of macromolecular solute molecules. The osmotic pressure of a solution is the pressure difference produced at equilibrium across the membrane, with the solution on one side of the membrane and pure solvent on the other side. As shown in Fig. 4, the reduced activity of the solvent in solution is compensated for by an increase in the pressure of the solution ... 

The osmotic pressure of a solution of non-interacting molecules or ions at the zero concentration limit is determined by the total molar concentration of solute species. In this hypothetical state, a solution of a polyelectrolyte may contain highly charged polyions at concentration c and monovalent counterions at a concentration where c is the molar concentration of the polyelectrolyte and z is the number of counterions per polyion. Since the total molar concentration is c (z +1) c z for z l, the ideal osmotic pressure is... 

The question of the osmotic relationship between a cestode and its environment is complicated by the fact that some substances can pass through membranes by means other than diffusion (p. 42). Hence the actual osmotic pressure of a solution as measured by physico-chemical means may not be as significant to a worm as the actual content to which the tegument of the worm is permeable - using the word in its widest sense as indicated above. The reason for this is that substances in the medium which (theoretically) contribute to the total osmotic pressure of the medium do not actually exert osmotic pressure across the tegument of the worm, which separates the worm from its environment. 

An enzyme has four identical and independent binding sites for its substrate. The osmotic pressure of a solution of the enzyme was measured and found to be 2.4 x 10 3 atm at 20°C. The binding equilibrium between the enzyme and its substrate was carried out in a dialysis bag at 20°C. The concentration of unbound substrate outside the dialysis bag and the total substrate concentration inside the bag were found to be 1.0 xIO 4 and 3.0 x Qr M, respectively. Calculate the equilibrium constant for the binding of the substrate to the enzyme at 20°C. 

If IT is the osmotic pressure of a solution in which the mole fraction of the solvent is or then, the condition for equilibrium for the chemical potential of the solvent on both sides of the osmometer membrane gives... 

The osmotic pressure of a solute in a solvent is given by the expression... 

Osmotic pressure is another property due to dissolved substances. The presence of solute particles lowers the ability of solvent molecules to pass through a semipermeable membrane. Osmotic pressure is very important in biological systems, and an application of the theory behind osmotic pressure allows for the purification of seawater. The osmotic pressure of a solution, IT, is proportional to the molarity (the number of moles per liter) ... 

Another obvious requirement of a nonaqueous solvent is chemical stability under a variety of conditions. Thus, methanol, especially after standing in the presence of air, may contain small amounts of formaldehyde which can react with groups on proteins and nucleic acids. Forma-mide, A, A-dimethylformamide, and related compounds, are slowly decomposed by acid or base in the solvent, and the possibility exists that such decomposition may be catalyzed to some extent by a protein dissolved in the solvent. Thus Rees and Singer (1956) found that the apparent osmotic pressure of a solution of insulin in lV,A -dimethylformamide continually increased over a period of a week at 25°C but reached equilibrium at 13.8°C, which might have been due to the slow decomposition of the solvent on the solution side of the osmotic membrane at the higher temperature. 

This is based on the concept of a membrane permeable to water, but not to solute molecules. For example, if a sucrose solution is placed on one side and pure water on the other, then a passive driving force will be created and water will diffuse across the membrane into the sucrose solution, since the effective water concentration in the sucrose solution wiU be lower. The tendency for water to diffuse into the sucrose solution could be counteracted by applying a hydrostatic pressure equivalent to the passive driving force. Thus, the osmotic pressure of a solution is the excess hydrostatic pressure required to prevent the net flow of water into a vessel containing the solution. The SI unit of osmotic pressure is the pascal. Pa (=kgm s ). Older sources may use atmospheres, or bars, and conversion factors are given in Box 9.1 (p. 72). Osmotic pressure and osmolality can be interconverted using the expression 1 osmol kg = 2.479 MPa at 25 °C. 

As osmosis proceeds, pressure builds up on the side of the membrane where volume has increased. Ultimately, the pressure prevents more water from entering, so osmosis stops. The osmotic pressure of a solution is the pressure needed to prevent osmosis into the solution. It is measured in comparison with pure solvent. The osmotic pressure is directly related to the different heights of the liquid on either side of the membrane when no more change in volume occurs. Osmotic pressure depends on the temperature and the original concentration of solute. Interestingly, it does not depend on what is dissolved. Two solutions of different solutes, for example alcohol and sugar, will each have the same osmotic pressure, provided they have the same concentration. Osmotic pressure is therefore a colligative property of solutions, one which depends only on the concentration of dissolved particles, not on their chemical identity. 

The osmotic pressure of a solution can thus be calculated from the vapour pressures of the solvent and of the solution. 

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