Colligative properties definition

This relationship constitutes the basic definition of the activity. If the solution behaves ideally, a, =x, and Equation (18) define Raoult s law. Those four solution properties that we know as the colligative properties are all based on Equation (12) in each, solvent in solution is in equilibrium with pure solvent in another phase and has the same chemical potential in both phases. This can be solvent vapor in equilibrium with solvent in solution (as in vapor pressure lowering and boiling point elevation) or solvent in solution in equilibrium with pure, solid solvent (as in freezing point depression). Equation (12) also applies to osmotic equilibrium as shown in Figure 3.2. 

However, in the equation pV = nRT and in equations involving colligative properties, the entity implied in the definition of n should be an individually translating particle (a whole molecule for a gas), whose nature is unimportant. 

Originally x was stated to be independent of polymer concentration. The X-parameters determined by many investigators using one or another of the methods for measuring colligative properties of polymer-liquid solutions (mentioned below) show that this is not the case (see Tables 3-22 of Reference 43) nor does x vary linearly with 1/T as stated in Eq. 7. Later [44] a quantity Aws representing an entropic contribution from contact interaction was added to the Flory-Huggins definition of x to produce a relationship linear in 1/T. 

Suppo.se that a colligative property of the polymer solution is measured. These are properties that depend on the number of dissolved solute molecules and not on their sizes (see also Section 2.10). Osmotic pressure, vapor pressure lowering, and freezing point depression are some examples of colligative properties. If the value of the property measured is P, then by definition... 

The simplicity and generality of Equation 6.5-3 are surprising. According to the equation, if a solution contains 20 mole% solute, then the solvent partial pressure is 80% of the vapor pressure of pure solvent at the system temperature, regardless of the temperature, the pressure, and what the solute and solvent are. (Hence, vapor pressure lowering is a colligative property, by definition.) The only stipulations are that Raoult s law holds and the solute is nonvolatile, nonreactive, and nondissociative. 

Osmotic pressure is a thermodynamic colligative property that measures the free energy difference between a polymer solution and a pure solvent [see Eq. (4.62) for the proper definition of osmotic pressure]. In practice, the two are separated by a membrane that allows solvent to pass through easily, but restricts polymer to stay on one side, as shown schematically in Fig.1.21. 

The phrase concentration of solute particles in the definition of colligative property needs clarification. There are two kinds of solutes, those that exist in solution as neutral molecules and those that ionize when dissolved and exist in solution as ions. Compounds that ionize in water are called electrolytes. Those that do not ionize are nonelectrolytes. Glucose is a nonelectrolyte and exists as neutral molecules in solution. A 1.0 M solution of glucose is 1.0 M in solute particles. Sodium chloride, NaCl, is an electrolyte and exists in solution as separated sodium and chloride ions, NaClfo) — Na+(aq) + CV(aq). A 1.0 M solution of NaCl is 2.0 M in solute particles, 1.0 M Na+(aq) plus 1.0M CV(aq). The concentration of solute particles for compounds that ionize in solution will be some whole number multiple of the concentration of the compound itself. For those solutes that do not ionize when dissolved in water, the concentration of the compound and the concentration of the solute particles (molecules) will be the same. A listing of common nonelectrolytes and electrolytes in water appears in the following table. 

Definitions. Define briefly (a) mole fraction, (b) molality, (c) molarity, (d) solubility, (e) saturated solution, (f) supersaturated solution, (g) ideal solution, (h) activity, (i) colligative property, (j) freezing-point depression, (k) osmotic pressure. 

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