Osmotic pressure calculation example

Osmotic pressure effects can be substantial. For example, the waters of the oceans contain dissolved salts at a total ionic molarity of about 1.13 M. The osmotic pressure of ocean water can be calculated ... 

From the assumptions made in deducing it, it appears that this formula is inapplicable to any but dilute solutions. At higher concentrations the discrepancies become considerable between the osmotic pressures actually measured and those calculated from Van t Hoff s equation. The following figures for cane sugar may serve as an example —... 

When the activity of the solvent is determined from a colligative property, then g can be calculated with Equation (19.44). If we use osmotic pressure as an example, we can combine Equation (15.33) and Equation (16.1) to obtain the expression... 

In later chapters we will see a few more examples of explicit calculations. Specifically we will present the calculation of the single-chain density correlation function in Appendix A 15.2 and the calculation of the osmotic pressure in Appendix A 17,1. 

Recently a new method for formation of monodisperse emulsions that creates high capillary pressures, involving osmotic stress technique, has been introduced [73]. It proves to be most reliable for the purpose. Preliminary calculations showed that the emulsion films in such monodisperse systems rupture in a narrow range of critical disjoining pressure. For example, NaDoS emulsion films rupture in the range from 1 to 1.3-105 Pa, which is analogous to foam films from the same surfactant solution. Unfortunately, the foam film type has not been considered. 

In our current example, the osmotic pressure of the phloem solution decreases from 1.7 MPa in the leaf to 0.7 MPa in the root (Fig. 9-18). Such a large decrease in n is consistent with the phloem s function of delivering photosynthetic products to different parts of a plant. Moreover, our calculations indicate that flow is in the direction of decreasing concentration but that diffusion is not the mechanism. (Although the total concentration decreases in the direction of flow, the c - of every solute does not necessarily do so.) Finally, we note the importance of removing solutes from the phloem solution at a sink, either by active transport or by diffusion into the cells near the conducting cells of the phloem. 

The following example will illustrate the application of equations (9) to (12) to numerical calculations. Let us calculate, by means of equations (9) and (11), the osmotic pressures at 100 and at 0° of aqueous solutions, whose boiling points are... 

Values of electrolyte activities, as measured by osmotic pressures, freezing point depression, and other experimental methods are in the literature (References 5 and 6, for example) or one can calculate activity coefficients based on models of molecular-level interactions between ions in electrolyte solutions. For illustrative purposes, mean molal activity coefficients for various salts at different aqueous molal (mj concentrations at 25°C are listed in Table 26.3 [7]. 

Example You are required to calculate the molecular weight of a polymer by measurements of its osmotic pressure in solution. At infinite dilution, measured graphically from your experiments, the equation below applies ... 

EXAMPLE 9 Calculate the osmotic pressure of a 0.100 M solution of a nonionic solute at 25°C. 

The osmotic pressure can be calculated from the solution concentration at any temperature. How do we determine "solution concentration" Recall that osmosis is a colligative property, dependent on the concentration of solute particles. Again, it becomes necessary to distinguish between solutions of electrolytes and nonelectrolytes. For example, a 1 M glucose solution consists of 1 mol of particles per liter glucose is a nonelectrolyte. A solution of 1 M NaCl produces 2 mol of particles per liter (1 mol of Na+ and 1 mol of CH). AIM CaClj solution is 3 M in particles (1 mol of Ca + and 2 mol of CH per liter). 

In systems 1-solvent, 2-polymer, and 3-poly-mer, any method that determines either AG or its derivatives should make it possible to calculate Thus, for example, osmotic pressure measurements were used to characterize PS/PVME blends... 

The conclusion is that equation (11) is inadequate for calculating the osmotic pressure of a sol. It is more Ukcly that this pressure will, for a diluted sol, approach the value p = kT.n (sol particle plus counter-ions one kinetic unit). Besides, there are other objections to the use of equation (11), for example the fact that the potential due to the ionic atmosphere at a considered (colloid) ion under consideration is really proportional to... 

Strategy We are asked to calculate the molar mass of Hb. The steps are similar to those outlined in Example 12.10. From the osmotic pressure of the solution, we calculate the molarity of the solution. Then, from the molarity, we determine the number of moles in 35.0 g of Hb and hence its molar mass. What units should we use for tt and temperature ... 

If the osmotic pressure is measured, it can be used for the determination of the molar masses of complex substances by reversing the calculation in Example 9.1. 

One way to overcome such problems is to consider solvent(l)/polymer(2)/ polymer(3) ternary systems any method that determines either AG or its derivatives should make it possible to calculate Xi3- Thus, for example, osmotic pressure measurements were used to characterize PS/PVME blends dissolved in either toluene or ethylbenzene (Shiomi et al. 1985). The Xi3 was found to depend on the blends composition. Elimination of the solvent effects gave X23/E1 = —10 (7.41 — 11.0103). Thus, the system was expected to remain miscible up to a PVME volume fraction of 03 = 0.67. Osmotic pressure has also been used to determine X23 = 0.070 for PS with poly(p-chloro styrene) in toluene, 2-butanone, and cumene (Ogawa et al. 1986). For the same system, X23 = 0.087 was calculated from intrinsic viscosity measurements. Thus, the system is thermodynamically immiscible. More recently, osmotic pressure measurements in cyclohexanone of a ternary system resulted in X23ipoly(vinylchloride-co-vinylacetate) blends with a series of acrylic copolymers (Sato et al. 1997). 

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