Osmotic pressure relationships

The body s normal daily sodium requirement is 1.0 to 1.5 mEq/kg (80 to 130 mEq, which is 80 to 130 mmol) to maintain a normal serum sodium concentration of 136 to 145 mEq/L (136 to 145 mmol/L).15 Sodium is the predominant cation of the ECF and largely determines ECF volume. Sodium is also the primary factor in establishing the osmotic pressure relationship between the ICF and ECF. All body fluids are in osmotic equilibrium and changes in serum sodium concentration are associated with shifts of water into and out of body fluid compartments. When sodium is added to the intravascular fluid compartment, fluid is pulled intravascularly from the interstitial fluid and the ICF until osmotic balance is restored. As such, a patient s measured sodium level should not be viewed as an index of sodium need because this parameter reflects the balance between total body sodium content and TBW. Disturbances in the sodium level most often represent disturbances of TBW. Sodium imbalances cannot be properly assessed without first assessing the body fluid status. 

In this example, we need to determine the molar mass (g/mol) of the gene fragment. This requires two pieces of information—the mass of the substance and the number of moles. We know the mass (7.95 mg), thus we need to determine the number of moles present. We will rearrange the osmotic pressure relationship to n 77 V/RT. We know the solute is a nonelectrolyte so i = 1. We can now enter the given values into the rearranged equation and perform a pressure and a volume conversion ... 

The natural tendency is for the solvent to flow in the direction that will equalize the concentrations. It turns out, however, that if a certain pressure, called the osmotic pressure, is imposed on the more concentrated solution, flow of the solvent can be forced in the direction from the more concentrated to the more dilute solution. Example 19.1 illustrates the osmotic pressure relationship, and points out how rapidly the osmotic pressure falls off with increasing molecular weight of the solute. 

For the case of pure solvent on the low pressure side of the membrane, the osmotic pressure relationship is... 

The bicarbonate ions are replaced in the plasma by chloride ions that diffuse out of the blood cells. This step, called the chloride shift, maintains charge balance and osmotic pressure relationships between the plasma and red blood cells. 

As in osmotic pressure experiments, polymer concentations are usually expressed in mass volume units rather than in the volume fraction units indicated by the Einstein equation. For dilute solutions, however, Eq. (8.100) shows that

partial molar volume of the polymer in solution, and M is the molecular weight of the polymer. Substituting this relationship for (pin Eq. (9.9)gives... 

When the superfluid component flows through a capillary connecting two reservoirs, the concentration of the superfluid component in the source reservoir decreases, and that in the receiving reservoir increases. When both reservoirs are thermally isolated, the temperature of the source reservoir increases and that of the receiving reservoir decreases. This behavior is consistent with the postulated relationship between superfluid component concentration and temperature. The converse effect, which maybe thought of as the osmotic pressure of the superfluid component, also exists. If a reservoir of helium II held at constant temperature is coimected by a fine capillary to another reservoir held at a higher temperature, the helium II flows from the cooler reservoir to the warmer one. A popular demonstration of this effect is the fountain experiment (55). 

Chapters 7 to 9 apply the thermodynamic relationships to mixtures, to phase equilibria, and to chemical equilibrium. In Chapter 7, both nonelectrolyte and electrolyte solutions are described, including the properties of ideal mixtures. The Debye-Hiickel theory is developed and applied to the electrolyte solutions. Thermal properties and osmotic pressure are also described. In Chapter 8, the principles of phase equilibria of pure substances and of mixtures are presented. The phase rule, Clapeyron equation, and phase diagrams are used extensively in the description of representative systems. Chapter 9 uses thermodynamics to describe chemical equilibrium. The equilibrium constant and its relationship to pressure, temperature, and activity is developed, as are the basic equations that apply to electrochemical cells. Examples are given that demonstrate the use of thermodynamics in predicting equilibrium conditions and cell voltages. 

Colligative properties measure average relative molar masses, M, and in the case of osmotic pressure, II, the important relationship is ... 

In the osmotic pressure method, the activity of the solvent in the dilute solution is restored to that of the pure solvent (i.e., unity) by applying a pressure m on the solution. According to a well-known thermodynamic relationship, the change in activity with pressure is given by... 

But for any arbitrary polymer concentration C2 there will be another osmotic pressure due to the previously considered polymer-solvent interaction and to the associated elastic reaction of the network. Recalling the general relationship tz= — (mi —mi)/vi, we may calculate oTo from Eq. (38). At equilibrium the total osmotic pressure arising from the effects of all solutes must be zero, i.e., — JCq. Hence from Eqs. 

Here Jv is the volumetric flow rate of fluid per unit surface area (the volume flux), and Js is the mass flux for a dissolved solute of interest. The driving forces for mass transfer are expressed in terms of the pressure gradient (AP) and the osmotic pressure gradient (All). The osmotic pressure (n) is related to the concentration of dissolved solutes (c) for dilute ideal solutions, this relationship is given by... 

In case of solutions of high Molecular weight compounds, the selection of semi-permeable membrane is easier, because the solvent and the solute molecules are quite different in their size. The relationship between the Osmotic pressure of solution of a macromolecular compound and the Molecular weight is widely used for determination of Molecular weights and in the study of the interaction between the solvent and the solute molecules in the solution. 

For this reason, the relationship between the reduced Osmotic pressure p/C and the concentration is generally expressed in the form of virial equation as given below ... 

In the next example, we will examine the colligative property of osmotic pressure. This will require us to use the relationship 1r = i(nRT/V). 

The analogue to one-component thermodynamics applies to the nature of the variables. So Ay S, U and V are all extensive variables, i.e. they depend on the size of the system. The intensive variables are n and T -these are local properties independent of the mass of the material. The relationship between the osmotic pressure and the rate of change of Helmholtz free energy with volume is an important one. The volume of the system, while a useful quantity, is not the usual manner in which colloidal systems are handled. The concentration or volume fraction is usually used ... 

Analysis of polyelectrolytes in the semi-dilute regime is even more complicated as a result of inter-molecular interactions. It has been established, via dynamic light-scattering and time-dependent electric birefringence measurements, that the behavior of polyelectrolytes is qualitatively different in dilute and semi-dilute regimes. The qualitative behavior of osmotic pressure has been described by a power-law relationship, but no theory approaching quantitative description is available. 

Finally, at the level of pair interactions, after the differentiation of the osmotic pressure Ft with respect to biopolymer concentration c, we get the following widely used form of the scattering equation, showing clearly the relationship between AR and the measured quantities Mw, RG... 

Equation (20) provides the relationship we have sought between osmotic pressure and concentration. If the solution is ideal, we may replace activity by mole fraction. Then Equation (20) becomes... 

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 ... 

Two additional relationships are fairly evident. The experimental osmotic pressure is the sum of the pressure contributions of the individual components ... 

In reverse osmosis both solvent and solute diffuse because of gradients in their chemical potentials. For the solvent there is no gradient of chemical potential at an osmotic pressure of x at applied pressures p greater than 7r, there is such a gradient that is proportional to the difference p — ir. To a first approximation, the gradient of the solute chemical potential is independent of p and depends on the difference between concentrations on opposite sides of the membrane. This leads to the result that the fraction of solute retained varies as [1 + const./(p — 7r)] 1. Verify that the following data for a reverse osmosis experiment with 0.1 M NaCl and a cellulose acetate membrane follow this relationship ... 

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