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For instance, for solutions of magnesium chloride, the vapor pressure is slightly greater than that predicted by Raoult's law up to a concentration of 0.7 mol/kg, after which the vapor pressure is lower than Raoult's law predicts. For aqueous solutions, the osmotic coefficients can be calculated theoretically by Pitzer equations [4] or TCPC model.
where is osmotic pressure, i is the dimensionless van 't Hoff index, c is the molar concentration of solute, R is the ideal gas constant, and T is the absolute temperature (usually in kelvins). This formula applies when the solute concentration is sufficiently low that the solution can be treated as an ideal solution .
Similarly, the combined ideal gas law, =, has as an analogue for ideal solutions =, where is osmotic pressure; V is the volume; n is the number of moles of solute; R is the molar gas constant 8.314 J K −1 mol −1; T is absolute temperature; and i is the Van 't Hoff factor.
For most non-electrolytes dissolved in water, the van 't Hoff factor is essentially 1. For most ionic compounds dissolved in water, the van 't Hoff factor is equal to the number of discrete ions in a formula unit of the substance. This is true for ideal solutions only, as occasionally ion pairing occurs in solution. At a given instant a small ...
where ln denotes the natural logarithm, is the thermodynamic equilibrium constant, and R is the ideal gas constant. This equation is exact at any one temperature and all pressures, derived from the requirement that the Gibbs free energy of reaction be stationary in a state of chemical equilibrium .
where is the concentration in molarity of the solute, is the van 't Hoff factor, the ratio of amount of particles in solution to amount of formula units dissolved, is the ideal gas constant, and is the absolute temperature. The water diffuses across the osmotic membrane to where the water potential is lower
A variant of this single set approach is using a special parameter set fitted for the examined temperature range. The second solution is switching to another vapor pressure equation with more than three parameters. Commonly used are simple extensions of the Antoine equation (see below) and the equations of DIPPR or Wagner. [2] [3]
It is used in assessing the osmotic strength of colloids as well as solutions. [2] The freezing point depression osmometer operates by using the solution's freezing point to determine the concentration of the solution. It uses a nanoliter nanometer, a device that facilitates the establishment of the solution's melting and freezing points ...