Dilute solution freezing point depression

Here, i, the van t Hoff i factor, is determined experimentally. In a very dilute solution (less than about 10 3 mol-I. ), when all ions are independent, i = 2 for MX salts such as NaCl, i = 3 for MX2 salts such as CaCl2, and so on. For dilute nonelectrolyte solutions, i =l. The i factor is so unreliable, however that it is best to confine quantitative calculations of freezing-point depression to nonelectrolyte solutions. Even these solutions must be dilute enough to be approximately ideal. 

In physical chemistry, we apply the term colligative to those properties that depend upon number of molecules present. The principal colligative properties are boiling point elevation, freezing point depression, vapour pressure lowering, and osmotic pressure. All such methods require extrapolation of experimental data back to infinite dilution. This arises due to the fact that the physical properties of any solute at a reasonable concentration in a solvent are... 

Colligative1 properties of dilute polymer solutions depend only on the number of dissolved molecules and not on properties of the molecules themselves, such as mass or size. Osmotic pressure, freezing point depression, boiling point elevation, and vapour pressure lowering are the most prominent examples. These methods essentially allow one to count the number n of solute molecules. From n and the known total mass m of the solute the molar mass M is readily obtained as... 

The depression of the freezing point of a solvent due to the presence of a dissolved solute is an example of a colligative property, that is, a property of a dilute solution that depends on the number of dissolved particles and not on the identity of the particles. Water has a freezing point depression constant, Kf, of 1.86 K kg mol-1. In other words, for every mole of nonvolatile solute dissolved in a kilogram of water, the freezing point of water is lowered by 1.86°C. The change in freezing point, A T, can be calculated from the equation... 

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 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... 

FREEZING-POINT DEPRESSION. The freezing point of a solution is. in general, lower than that of (he pure solvent. The depression is proportional to the active mass of the solute. For dilute (ideal) solutions... 

Concentrations expressed as molality or mole fractions are temperature-independent and are most useful when a physical measurement is related to theory over a range of temperature, e.g., in freezing point depression or boiling point elevation measurements (Chapter 11). Since the density of water is close to 1 g/cm3, molal and molar concentrations are nearly equal numerically for dilute aqueous solutions (<0.1 M). 

Particularly simple forms of the equations for the freezing-point depression, boiling-point elevation, and osmotic pressure are obtained when the solution is ideal or when it is sufficiently dilute, so that the ideally dilute solution approximation is appropriate. In both of these cases, the activity of the solvent is equal to its mole fraction, so that... 

Freezing-point depression, boiling-point elevation and osmotic pressure are known as colligative properties, because they are dependent on the properties of the solvent and the total mole fraction of all solutes, but are independent of any particular property of the solutes. Equations (61)-(63) are usually written in terms of mB, the sum of the molalities of all the solutes, which for ideally dilute solutions is related to xB by... 

A few values of Kf and Kb are given in Table 2. For a macromolecular solution, the ideally dilute approximation holds only up to such low molality that freezing-point depression and boiling-point elevation are useless for determining... 

In the ideally dilute limit, colligative properties depend on the total solute mole fraction or molality. If there are a number of different solutes present, this can be expressed as (for the case of freezing-point depression)... 

Pure benzene freezes at 5.50°C and has a density of 0.876 g/mL. A solution of 1.7 g of nitrobenzene in 250 mL benzene freezes at 5.18°C. What is the molality-based freezing-point depression constant of benzene and at what temperature does a solution containing 3.2 g of bromobenzene in 250 mL of benzene freeze (You may make the ideally dilute approximation for both these solutions.)... 

Solutions of arsenic pentafluoride have conductivities and freezing point depressions (Dean et al., 1970) that are only approximately one-half those of SbF5 at the same concentration and it has been shown that even in dilute solutions there is essentially complete formation of the As2Ff1 ion according to equation (14). 

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 ... 

Since we know how the solution vapor pressure varies with concentration (the relationship being given by Equation 6.5-2) and temperature (through the Clausius-Clapeyron equation. Equation 6.1-3), we can determine the relationships between concentration and both boiling point elevation and freezing point depression. The relationships are particularly simple for dilute solutions x — 0, where x is solute mole fraction). 

Since the coefficients of x in these two equations are constant, it follows that for dilute solutions of nonvolatile, nonreactive, nondissociative solutes, both boiling point elevation and freezing point depression vary linearly with solute mole fraction. 

Nonelectrolytes in nonaqueous solvents Activity coefficients of dilute solutions of solutes can be studied experimentally by liquid-liquid chromatography as well as techniques such as solvent extraction, light scattering, vapor pressure, and freezing point depression. 

II. Molecular freezing-point depression and latent heat of fusion of dilute solutions. 

An alternative approach is based on the theoretical foundation described earlier for the colligative properties. If the solution is isotonic with blood, its osmotic pressure, vapor pressure, boiling-point elevation, and freezing-point depression should also be identical to those of blood. Thus, to measure isotonicity, one has to measure the osmotic pressure of the solution and compare it with the known value for blood. However, the accurate measurement of osmotic pressure is difficult and cumbersome. If a solution is separated from blood by a true semipermeable membrane, the resulting pressure due to solvent flow (the head) is accurately measurable, but the solvent flow dilutes the solution, thus not allowing one to know the concentration of the dissolved solute. An alternative is to apply pressure to the solution side of the membrane to prevent osmotic solvent flow. In 1877, Pfeffer used this method to measure osmotic pressure of sugar solutions. With the advances in the technology, sensitive pressure transducers, and synthetic polymer membranes, this method can be improved. However, results of the search for a true semipermeable membrane are still... 

Molality is used in certain physical chemical calculations (e.g., calculations of boiling-point elevation and freezing-point depression). For dilute aqueous solutions, m and M will be quite close. In order to interconvert m and M, we need to know % w/w. 

The expressions for boiling-point elevation and freezing-point depression apply accurately to dilute solutions only. A saturated aqueous solution of Nal (sodium iodide) in water has a boiling point of 144°C. The mole fraction of Nal in the solution is 0.390. Compute the molality of this solution. Compare the boiling-point elevation predicted by the expression in this chapter with the elevation actually observed. 

Melting point also changes when a solute is added, but it is not related to the vapor pressure. Instead, it is a factor of crystallization. Impurities (the solute) interrupt the crystal lattice and lower the freezing point. Freezing point depression for an ideally dilute solution is given by the equation ... 

The freezing-point constant, kf, depends on the solvent and has units of K-kg-mol (Table 8.8). -> The freezing-point depression equation holds for nonvolatile solutes in dilute solutions that are approximately ideal. 

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