Properties, colligative prediction

Completely ah initio predictions can be more accurate than any experimental result currently available. This is only true of properties that depend on the behavior of isolated molecules. Colligative properties, which are due to the interaction between molecules, can be computed more reliably with methods based on thermodynamics, statistical mechanics, structure-activity relationships, or completely empirical group additivity methods. 

Rudin s aim was to predict the size of dissolved polymer molecules and the colligative properties of polymer solutions (hydrodynamic volume, second virial coefficient, interaction parameter, osmotic pressure, etc) from viscometric data (average molar mass, intrinsic viscosity, etc.). 

Despite the above shortcomings, the Flory-Huggins theory has served as a useful model for predicting a large number of colligative properties, and has had remarkable success in providing qualitative if not quantitative descriptions of polymer-solvent systems. 

Any physical effect of the solute on the solvent is a colligative property. The lowering of the freezing point and the raising of the boiling point are examples of colligative properties. Only nonvolatile solutes have predictable effects on boiling point, but besides that requirement, the identity of the solute is relatively unimportant. 

As we have emphasized, colligative properties depend on the number of solute particles in a given mass of solvent. A 0.100 molal aqueous solution of a covalent compound that does not ionize gives a freezing point depression of 0.186°C. If dissociation were complete, 0.100 m KBr would have an ejfective molality of 0.200 m (i.e., 0.100 m K+ + 0.100 m Br ). So we might predict that a 0.100 molal solution of this 1 1 strong electrolyte would have a freezing point depression of 2 X 0.186°C, or 0.372°C. In fact, the observed depression is only 0.349°C. This value for ATf is about 6% less than we would expect for an effective molarity of 0.200 m. 

For solutions that contain electrolytes, the change from the pure solvent to a solution is different from what is predicted by the above equations. Due to their ionic nature, these substances will dissociate to put many more ions in solution than their molal concentration would predict. The total number of ions affects the colligative properties just as the number of molecules would for a nonpolar solute. 

In Chapter 4, we classified solutes by their ability to conduct an electric current, which requires moving ions to be present. Recall that an electrolyte is a substance that dissociates into ions in aqueous solution strong electrolytes dissociate completely, and weak electrolytes dissociate very little. Nonelectrolytes do not dissociate into ions at all. To predict the magnitude of a colligative property, we refer to the solute formula to find the number of particles in solution. Each mole of nonelectrolyte yields 1 mol of particles in the solution. For example, 0.35 M glucose contains 0.35 mol of solute particles per liter. In principle, each mole of strong electrolyte dissociates into the number of moles of ions in the formula unit 0.4 M Na2S04 contains 0.8 mol of Na ions and 0.4 mol of S04 ions, or 1.2 mol of particles, per liter (see Sample Problem 4.1). 

A colligative property is a physical property of a solution that depends on the number of solute particles present in solution and usually not on the identity of the solutes involved. Colligative properties may be predicted by imagining ourselves shrinking down to the size of molecules in a solution and visualizing the impact of an increasing number of generic solute particles around us. 

Raoult s law predicts that when we increase the mole fraction of nonvolatile solute particles in a solution, the vapor pressure over the solution will be reduced. In fact, the reduction in vapor pressure depends on the total concentration of solute particles, regardless of whether they are molecules or ions. Remember that vapor-pressure lowering is a colligative property, so it depends on the concentration of solute particles and not on their kind. In our applications of Raoult s law, however, we will limit ourselves to solutes that are not only nonvolatile but nonelectrolytes as well. We consider the effects of volatile substances on vapor pressure in the "Closer Look" box in this section, and we will consider the effects of electrolytes in our discussions of freezing points and boiling points. 

We predict the magnitude of a colligative property from the solute formula, which shows the number of particles in solution and is closely related to our classification of solutes by their ability to conduct an electric current (Chapter 4) ... 

Now that you have the chemical potential, you can follow the same procedures you use for the lattice model of simple solutions to predict the colligative properties and phase separations of polymer solutions. 

There are several interesting consequences of equation (54). Since the melting point depression is a colligative property the influence of a high molecular weight diluent will be expected to be relatively small as predicted. This expectation is widely observed experimentally. ... 

Certain solutes produce a greater effect on colligative properties than expected. For example, consider a 0.0100 m aqueous solution. The predicted freezing-point depression of this solution is... 

EXAMPLE 14-11 Predicting Colligative Properties for Electrolyte Solutions... 

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