Electrolyte solutes freezing point depression

The presence of a solute lowers the freezing point of a solvent if the solute is nonvolatile, the boiling point is also raised. The freezing-point depression can be used to calculate the molar mass of the solute. If the solute is an electrolyte, the extent of its dissociation, protonation, or deprotonation must also be taken into account. 

ATt is the number of degrees that the freezing point has been lowered (the difference in the freezing point of the pure solvent and the solution). Kt is the freezing-point depression constant (a constant of the individual solvent). The molality (m) is the molality of the solute, and i is the van t Hoff factor, which is the ratio of the number of moles of particles released into solution per mole of solute dissolved. For a nonelectrolyte such as sucrose, the van t Hoff factor would be 1. For an electrolyte such as sodium sulfate, you must take into consideration that if 1 mol of Na2S04 dissolves, 3 mol of particles would result (2 mol Na+, 1 mol SO) ). Therefore, the van t Hoff factor should be 3. However, because sometimes there is a pairing of ions in solution the observed van t Hoff factor is slightly less. The more dilute the solution, the closer the observed van t Hoff factor should be to the expected one. 

A—Freezing-point depression is a colligative property, which depends on the number of particles present. The solution with the greatest concentration of particles will have the greatest depression. The concentration of particles in E (a non electrolyte) is 0.10 m. All other answers are strong electrolytes, and the concentration of particles in these may be calculated by multiplying the concentration by the van t Hoff factor. 

A unitless correction factor that relates the relative activity of a substance to the quantity of the substance in a mixture. Activity coefficients are frequently determined by emf (electromotive force) or freezing-point depression measurements. At infinite dilution, the activity coefficient equals 1.00. Activity coefficients for electrolytes can vary significantly depending upon the concentration of the electrolyte. Activity coefficients can exceed values of 1.00. For example, a 4.0 molal HCl solution has a coefficient of 1.76 and a 4.0 molal Li Cl has a value of... 

Electrolytes, depending upon their strength, dissociate to a greater or less extenl in polar solvents. The extent to which a weak electrolyte dissociates may be determined by electrical conductance, electromotive force, and freezing point depression methods. The electrical conductance method is the most used because of its accuracy and simplicity. Arrhenius proposed that the degree of dissociation, a. of a weak electrolyte at any concentration in solution could be found from the rutio of the equivalent conductance. A. of the electrolyte at the concentration in question to (he equivalent conductance at infinite dilution A0 of the electrolyte. Thus... 

Just as we discussed in Chapter 9, we can use measured activities of solvents (determined from vapor pressure, freezing-point depression, boiling-point elevation, or osmotic pressure) to determine activity coefficients of electrolytes in solution. For an ionic substance, the Gibbs-Duhem equation is... 

There are many measurement techniques for activity coefficients. These include measuring the colligative property (osmotic coefficients) relationship, the junction potentials, the freezing point depression, or deviations from ideal solution theory of only one electrolyte. The osmotic coefficient method presented here can be used to determine activity coefficients of a 1 1 electrolyte in water. A vapor pressure osmometer (i.e., dew point osmometer) measures vapor pressure depression. 

Partial Molar Volume 1 0. Cryoscopic Determination of Molar Mass 1 1. Freezing-Point Depression of Strong and Weak Electrolytes 12. Chemical Equilibrium in Solution... 

In this experiment, the freezing-point depression of aqueous solutions is used to determine the degree of dissociation of a weak electrolyte and to study the deviation from ideal behavior that occurs with a strong electrolyte. 

Why is the observed freezing-point depression for electrolyte solutions sometimes less than the calculated value Is the error greater for concentrated or dilute solutions ... 

The Osmotic Coefficient.—Instead of calculating activity coefficients from freezing-point and other so-called osmotic measurements, the data may be used directly to test the validity of the Debye-Hiickel treatment. If 6 is the depression of the freezing point of a solution of molality m of an electrolyte which dissociates into v ions, and X is the molal freezing-point depression, viz., 1.858° for water, a quantity , called the osmotic coefficient, may be defined by the expression... 

A good deal of confusion and much controversy between early workers 54, 55, 77) resulted from a lack of understanding of the nature and extent of the self-dissociation of sulfuric acid, which is repressed by most solutes and thus affects the freezing-point depressions that they produce. Following Hammett and Deyrup 56) it became common practice to carry out cryoscopic measurements in sulfuric acid containing sufficient water to depress the freezing point to approximately 10.0° in order to repress largely the solvent self-dissociation. This is not, however, an entirely satisfactory procedure. The self-dissociation is not completely repressed (J), and allowance for it should still in principle be made. Moreover water has been found, in the case of nonelectrolytes and weak electrolytes at least, to have an effect on the depression... 

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. 

Table 14-3 lists actual and ideal values of i for solutions of some strong electrolytes, based on measurements of freezing point depressions. 

Many weak electrolytes are quite soluble in water, but they ionize only slightly. The percent ionization and i value for a weak electrolyte in solution can also be determined from freezing point depression data (Example 14-12). 

Boiling Point Elevation and Freezing Point Depression Solutions of Electrolytes... 

For aqueous electrolyte solutions, both electrostatic interaction between dissociated ions and ionic hydration induce the deviation of freezing-point depression from that of the ideal solution at high concentrations. In the case of aqueous zwitterion solutions where each ion within a molecule carmot... 

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]. 

Kb is the boiling point elevation constant, and for water equals 0.52°C/m. Each solvent has its own unique value for Kb, and the value of Kb for water indicates that a 1.0 m solution of glucose, a nonelectrolyte, would boil 0.52°C higher than that of pure water, 100.52°C. As with the equation used to calculate freezing point depressions, if the solute is an electrolyte, the molality of the ions will be a whole number multiple of the molality of the compound. 

---