Osmotic Pressure of Electrolyte Solutions

The osmotic pressure of solutions are discussed here as an introduction to the concept of osmotic pressme in suspension [21]. The phenomena of osmotic pressure is illustrated by a semipermeable membrane filled with a sugar solution immersed in water. The pressure inside the membrane, p + it, is large than that in the water, p, according to the formula 

From a fundamental thermodynamic equation at constant T, we have dpi = Vidp, which becomes 

If the solution is ideal fli xi = 1 —jC2,whereji 2 s the mole fraction of the solute. If the solute is dilute (i.e., 2 1-0) then we can make 

C2[n2/Vl is the molar concentration of electrolyte. The formal analogy between the earlier van t Hoff equation and tiie ideal gas law should not go unnoticed. The solute molecules of numbers n2 are dispersed in the solvent analogous to the gas molecules dispersed in an empty space. The solvent is analogous to the empty space. 

001 M solution will have an osmotic pressure, tt, of 0.0244 atm, which corresponds to a column of water 24 cm high. The measurement of the osmotic pressure is useful to determine the molecular wei t, M2, of dilute ideal solutions for example, if W2 grams of solute is dissolved in a liter of solution then 

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These results show more clearly than Fq. (8.126)-of which they are special cases-the effect of charge and indifferent electrolyte concentration on the osmotic pressure of the solution. In terms of the determination of molecular weight of a polyelectrolyte by osmometry. ... 

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. 

If you were to add 50.0 g of sodium chloride, an electrolyte (NaCl, molar mass 58.44 g), to enough water to make 1.00 L of solution, what would be the osmotic pressure of the solution at 22°C ... 

The total osmolality or osmotic pressure of a solution is equal to the sum of the osmotic pressures or osmolalities of all solute species present. The electrolytes Na", Cr, and HCO3, which are present in relatively high concentration, make the greatest contribution to serum osmolality. Nonelectrolytes such as glucose and urea, which are present normally at lower molal concentrations, contribute less, and serum proteins contribute less than 0.5% of the total serum osmolality because even the most abundant protein is present at millimolar concentrations. 

The formation of micelles results in a sharp drop in the electrical conductivity per mole of the electrolyte. Suppose 100 sodium and 100 stearate ions were present individually. If the stearate ions aggregate into a micelle and the micelle binds 70 Na as counter ions, then there will be 30 Na ions and 1 micellar ion having a charge of —30 units a total of 31 ions. The same quantity of sodium stearate would produce 200 ions as individuals but only 31 ions if the micelle is formed. This reduction in the number of ions sharply reduces the conductivity. The formation of micelles also reduces the osmotic pressure of the solution. The average molar mass, and thus an estimate of the average number of stearate ions in the micelle, can be obtained from the osmotic pressure. 

A U. luO-L solution is made by dissolving u.44i gof CaCl2(s) in water, (a) Calculate the osmotic pressure of this solution at 27 "C, assuming that it is completely dissociated into its component ions, (b) The measured osmotic pressure of this solution is 2.56 atm at 27 C. Explain why it is less than the value calculated in (a), and calculate the van t Hoff factor, i, for the solute in this solution. (See the A Closer Look box on Colligative Properties of Electrolyte Solutions in Section 13.5.) (c) The enthalpy of solution for CaCl2 is AH = —81.3 kj/mol. If the final temperature of the solution is 27 °C, what was its initial temperature (Assume that the density of the solution is 1.00 g/mL, that its specific heat is 4.18 J/g-K, and that the solution loses no heat to its surroundings.)... 

Maron SH, Nakajima N (1959) A theory of the thermodynamic behavior of non-electrolyte solutions. II. Application to the system mbber-benzene. J Polym Sci 40 59-71 Maron SH, Nakajima N (1960) A theory of the thermodynamic behavior of non-electrolyte solutions. III. The osmotic pressure of polymer solutions. J Polym Sci 42 327-340 Orwall RA, Flory PJ (1967) Equation-of-state parameters for normal alkanes. Correlation with chain length. J Am Chem Soc 89 6814—6822 Prigogine I (1957a) The molecular theory of solution. North-Holland, Amsterdam Prigogine I (1957b) Molecular theory of solutions. Chapter 16. North-Holland, Amsterdam Rowlinson JS (1970) Structure and properties of simple liquids and solutions. Faraday Disc Chem Soc 49 30-42... 

Vapor pressure measurements yield the activity and/or osmotic coefficients of electrolyte solutions. The equilibrium condition T) = p p, T) for the solvent... 

The osmotic pressures of polyelectrolyte solutions are most often measured in the presence of a membrane permeable to solvent and small ions but not to polyelectrolyte. The chemical potentials of the added electrolyte and solvent on each side of the membrane in this instance match, a condition defining Donnan equilibrium (200). Assuming ideal chain mixing, the quantity measured here is the Donnan osmotic pressure which can be equated to the difference of the osmotic... 

Several hundred experiments were carried out to determine the relation between the fall in pressure and the nature of the electrolyte. It turned out that both the nature of the anion and that of the cathion are factors. Hofmeister and Pauli t have arranged several anions in the descending order of their reducing effect on the osmotic pressure of protein solutions. SO4 > Cl > NO3 > Br > I > CNS. Both series of experiments point to the conclusion that the reduced pressure is due to partial coagulation of the particles. 

Since proteins are colloidal electrolytes, they also played a pivotal role at this Meeting. F.G. Donnan discussed measurements of the electrovalency and osmotic pressure of protein solutions. G.S. Adair of Cambridge applied the theories of J. Willard Gibbs [6] to protein systems. 

Example Osmotic Pressure in Electrolyte Solutions. In this example we begin by studying osmotic pressure from a somewhat different angle than before. The spherical cell in Fig. 3.16 is submerged inside a water (or solvent) reservoir kept at constant temperature, T, and pressure, P. The water passes freely between the cell, which has a constant volume V, and the reservoir. A suitable mechanism allows to add electrolyte (or solute) to the cell. Contrary to the water the electrolyte, which we assume fully dissociated into its ions, cannot pass the cell s wall. We know from our previous discussion of osmotic pressure that the total pressure inside the cell will rise to P+n. The dependence of osmotic pressure, n, on solute concentration follows via the Gibbs-Duhem equation (2.168) applied to the interior of the cell, i.e. 

No experiments appear to have been made with such cells, although the equation has been verified with oxygen at different partial pressures in admixture with nitrogen, with platinum electrodes and hot solid glass as electrolyte (Haber and Moser). A similar case is that of two amalgams of a metal, of different concentrations, as electrodes, and a solution of a salt of the metal as electrolyte (G. Meyer, 1891). Here we must take the osmotic pressures of the metals in the amalgams, Pi, P2, and, for an 7i-valent metal ... 

Numerous measurements of the conductivity of aqueous solutions performed by the school of Friedrich Kohhansch (1840-1910) and the investigations of Jacobns van t Hoff (1852-1911 Nobel prize, 1901) on the osmotic pressure of solutions led the young Swedish physicist Svante August Arrhenius (1859-1927 Nobel prize, 1903) to establish in 1884 in his thesis the main ideas of his famous theory of electrolytic dissociation of acids, alkalis, and salts in solutions. Despite the sceptitism of some chemists, this theory was generally accepted toward the end of the centnry. 

Van t Hoff introduced the correction factor i for electrolyte solutions the measured quantity (e.g. the osmotic pressure, Jt) must be divided by this factor to obtain agreement with the theory of dilute solutions of nonelectrolytes (jt/i = RTc). For the dilute solutions of some electrolytes (now called strong), this factor approaches small integers. Thus, for a dilute sodium chloride solution with concentration c, an osmotic pressure of 2RTc was always measured, which could readily be explained by the fact that the solution, in fact, actually contains twice the number of species corresponding to concentration c calculated in the usual manner from the weighed amount of substance dissolved in the solution. Small deviations from integral numbers were attributed to experimental errors (they are now attributed to the effect of the activity coefficient). 

The osmotic pressure of an electrolyte solution jt can be considered as the ideal osmotic pressure jt decreased by the pressure jrel resulting from electric cohesion between ions. The work connected with a change in the concentration of the solution is n dV = jt dV — jrel dV. The electric part of this work is then JteldV = dWcl, and thus jzc] = (dWei/dV)T,n. The osmotic coefficient 0 is given by the ratio jt/jt, from which it follows that... 

Since osmotic pressure depends upon the number of particles of solute(s) in solution, the osmotic pressure of an electrolyte is directly proportional to the degree (or extent) of dissociation. The dissociation factor, symbolized by the letter i, can be calculated by dividing the total number of particles (which include undissociated molecules and ions) in a solution by the number of particles before dissociation, i.e.,... 

As in the analogous case of gases (Section 2.4), corrections for nonideality can be obtained by measurements of osmotic pressure at different solute concentrations, with extrapolation toward the infinite-dilution limit. For electrolytes, the correction for ionic dissociation is important. 

Data collected with membranes of this type played an important part in the formulation of present-day solution theory—so much so that the authors have used this theory without hesitation to compute osmotic pressures of solutions whose osmotic pressures have never been precisely measured. Such a solution is sea water. The copper ferrocyanide membrane is leaky to solutions of strong electrolytes. Some data have been obtained on weak solutions of strong electrolytes by the Townend method (16), but no one has made precise measurements on the osmotic pressure of sea water. 

By application of this equation, it is possible to calculate osmotic pressures for ionic solutions. Van t Hoff also observed that i approaches the number of ions as the molecule dissociates in an increasingly dilute solution. Moreover, the deviations of concentrated electrolyte solutions from ideal behavior can be obtained from Raoult s law.8... 

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