Osmotic pressure equation

This equation is sometimes called the van t Hoff isochore, to distinguish it from van t Hoff s osmotic pressure equation (Section 8.17). An isochore is the plot of an equation for a constant-volume process. 

A We use the osmotic pressure equation, converting the mass of solute to amount in moles, the temperature to Kelvin, and the solution volume to liters. 

B We use the osmotic pressure equation along with the molarity of the solution. 

We have assumed that the solution is so dilute that its volume closely approximates the volume of the solvent constituting it. Note that this volume corresponds to the STP molar volume of an ideal gas. The osmotic pressure equation also resembles the ideal gas equation. 

In these equations ns is the solvent refractive index, dn/dc the refractive index increment, c the polymer concentration in g/ml, T the temperature in K, R the gas constant, NA Avogadro s number, and n the osmotic pressure. Equation (B.8) follows from Eq. (B.7) by using the familiar virial expansion of the osmotic pressure... 

The molar concentration can now be determined from the osmotic pressure equation. 

The assumption that the molality and molarity are equal does not introduce serious error into the calculations for dilute aqueous solutions. The relationships discussed in Chapter 12 show that M m when the density is 1 g/mL (1 g/cm3) and M < 1000/m. Urea has a molar mass of 60.0 g/mol. Then, 0.280 mol/L may be used for the molarity in the osmotic pressure equation. 

If we solve the osmotic pressure equation for molarity, and insert our known values ... 

The second virial coefficient A2 in the osmotic pressure equations can also be used to determine random coil dimensions (see Chap. 10). 

The term in the second derivative of the free energy with respect to composition (or first derivative of the chemical potential or osmotic pressure), brings in a virial equation, usually expressed in a slightly different form than we used in our discussion of osmotic pressure (Equation 12-35) ... 

The theory of electrolytic dissociation, AVhereas the osmotic pressure and the other colligative properties of aqueous solutions of substances, such as cane sugar, obey van t Hoff s laws, marked deviations are met with in aqueous solutions of acids, bases, and salts, even at great dilutions. The osmotic pressure and lowering of the freezing point for these solutions are still found to be approximately proportional to the molecular concentration, but are considerably greater than the theoretical values. To allow for this van t Hoff introduced a new term into his osmotic pressure equation, writing for such solutions... 

By using the simple osmotic pressure equation (Equation 27) we assume that no moisture change occurs in the wood when it is completely restrained from swelling during exposure to water. According... 

The molar mass can be calculated using the osmotic pressure equation n = iRT X molarity... 

From the results of Exercise 19, show that it is possible to derive the van t Hoff osmotic pressure equation IIV = RT for a very dilute solution V is the volume of solution containing 1 mole of solute. 

When the van t Hoff factor, i, is included, the boiling point elevation equation becomes ATj, = i K m. The van t Hoff factor can be inserted in a similar fashion in the freezing point depression equation and the osmotic pressure equation. The van t Holf factor, however, cannot be inserted in the same way into the vapor... 

Osmotic pressures (Equation 18.50, with two ions per NaCl molecule). 

Urea has a molar mass of 60.) Then 0.280 mol/L may be used for the molar concentration in the osmotic pressure equation. 

Nonideality of solutions is discussed in Section 2.2.5. It can be expressed as the deviation of the colligative properties from that of an ideal, i.e., very dilute, solution. Here we will consider the virial expansion of osmotic pressure. Equation (2.18) can conveniently be written for a neutral and flexible polymer as... 

One unique scaling behavior has been uncovered in this chapter for the low shear limit viscosity, equation 64, Bingham yield stress, equation 65, and the compressive yield stress-osmotic pressure, equation 74, for... 

Polyelectrolyte molecules in highly dilute aqueous solutions exert strong electrical repulsions on each other. These repulsive forces are long range (proportional to l/r ) by comparison with normal dispersion forces (proportional to 1/r ), and as a consequence the intermolecular interactions persist down to the lowest measured concentrations. In osmotic-pressure measurements on polyelectrolytes, the Donnan membrane equilibrium must be satisfied and experimental results indicate that the second virial coefficient in the osmotic-pressure equation (p. 915) becomes very large. 

What is osmotic pressure How is osmotic pressure calculated Molarity units are used in the osmotic pressure equation. When does the molarity of a solution approximately equal the molality of the solution Before refrigeration was common, many foods were preserved by salting them heavily, and many fruits were preserved by mixing them with a large amount of sugar (fruit preserves). How do salt and sugar act as preservatives Two applications of osmotic pressure are dialysis and desalination. Explain these two processes. 

What is osmotic pressure How is osmotic pressure calculated Molarity units are used in the osmotic pressure equation. When does the molarity of a solution approximately equal the molality of the solution ... 

Recently, Schulz and Stockmayer [9] have remarked that the empirical osmotic pressure equation proposed by one of them over 50 years ago, which reads... 

Combining equation (2.23) with that for osmotic pressure (equation 2.14) gives ... 

Van t Hoff proved by thermodynamics that Raoult s law of vapour pressure lowering and the formula for the molecular depression of freezing-point follow from the osmotic pressure equation. L. G. Gouy and G. Chaperon, Duhem, and Arrhenius, also showed by thermodynamics that the osmotic pressure and vapour pressure lowering are connected, and hence osmotic pressure and vapour pressure and freezing-point lowerings. 

Thus, the char2M ter of the concentration dependence of such quantities as the mean square end-to-end distance expansion factor (Equation 39), the correlation length (Equation 40), and the osmotic pressure (Equation 43) coincides with the results of familiar scaling laws (see Table 4.1). 

While the Debye-Huckel derivation was based on a charging process which took into account the distance of closest approach, a, the kinetic effect of the hard core could not adequately be dealt with. In order to include these effects. Pitzer proposed using the osmotic pressure equation (PI) ... 

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