Dilute solutions freezing point

Calculate the following colligative properties of a dilute solution boiling-point elevation, freezing-point depression, and osmotic pressure. 

Reality Check Actually, the freezing point is somewhat lower, about — 37°C (—35°F), which reminds us that the equation used, ATf = kftn, is a limiting law, strictly valid only in very dilute solution. 

The data in Table 10.3 suggest that the situation is not as simple as this discussion implies. The observed freezing point lowerings of NaQ and MgS04 are smaller than would be predicted with t = 2. For example, 0.50 m solutions of NaCl and MgS04 freeze at —1.68 and —0.995°C, respectively the predicted freezing point is — 1.86°C. Only in very dilute solution does the multiplier i approach the predicted value of 2. 

Let OA, AS represent the vapour-pressure curves of the ice and liquid solvent respectively, BS that of the dilute solution. AC is the vapour-pressure curve of supercooled liquid. T0 is the freezing-point of pure solvent, T that of the solution. Along CS, OA we have /... 

The equations for the vapour pressures and freezing-points of dilute solutions are also readily deduced from Planck s equation. 

In the development of the theory of freezing-points for very dilute solutions (Chap. XI.) it was assumed that both the change of total volume and the heat absorption on further dilution are zero. With solutions of moderate concentration (say up to 5N), neither assumption is true, but we know that the change of volume is always very small, and possibly negligible, whilst the heat absorption is not usually of such small magnitude. It... 

Freezing point methods are often applied to the measurement of activities of electrolytes in dilute aqueous solution because the freezing point lowering, 6= T — T, can be determined with high accuracy, and the solute does not dissolve in the solid to any appreciable extent. Equations can be derivedgg relating a to 9 instead of T and T. The detailed expressions can be found in the literature.16... 

In an electrolyte solution, each formula unit contributes two or more ions. Sodium chloride, for instance, dissolves to give Na+ and Cl ions, and both kinds of ions contribute to the depression of the freezing point. The cations and anions contribute nearly independently in very dilute solutions, and so the total solute molality is twice the molality of NaCl formula units. In place of Eq. 5a we write... 

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... 

The question asks for the freezing point of a solution. The phrase to prevent the waterfrom freezing reveals that we are dealing with depression of the freezing point of water. Equation describes this process for a dilute solution A Zf —. A coolant solution is quite concentrated, so this equation... 

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... 

In a comparable solution of benzoic acid the freezing point is depressed only twice the predicted amount, indicating only a normal acid-base reaction. Further, a sulfuric acid solution of methyl mesitoate when poured into water gave mesitoic acid, while a similar solution of methyl benzoate similarly treated did not.534 The AacI mechanism is also found when acetates of phenols or of primary alcohols are hydrolyzed in concentrated (more than 90%) H2SO4 (the mechanism under the more usual dilute acid conditions is the normal Aac2).535... 

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