Water molal freezing-point depression

IQ = molal freezing-point depression constant Kb = molal boiling-point elevation constant Kf for water = 1.86 K kg mol-1 for water = 0.512 K kg mol-1 AT = iKf x molality ATb = iKb x molality n = MRT... 

A solution also exhibits a depression in its freezing point. The freezing point depression is the decrease in the temperature of the freezing point due to the addition of a solute. It is calculated using the equations ATj. = Kjm, where ATj. is the decrease in freezing point for the solution, Kj. is the molal freezing point depression constant, and m is the molality of the solution. Water s K. value is 1.86°C/m. 

PROBLEM 11.20 Assuming complete dissociation, what is the molality of an aqueous solution of KBr whose freezing point is —2.95°C The molal freezing-point-depression constant of water is given in Table 11.4. 

The molality of the solution is determined from the freezing-point depression and the value of kf for water. The freezing-point depression for this solution is 0.602°C... 

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... 

The cryoscopic method was used in Hantzsch s original work 53, 54) and was later developed by Hammett and Deyrup 56) and by Gillespie et al. 48). Sulfuric acid freezes at 10.371 C and has a relatively large molal freezing-point depression or cryoscopic constant fc = 6.12 32). It is thus a convenient solvent for cryoscopic measurements provided that adequate precautions are taken to prevent absorption of water from the atmosphere. From freezing-point measurements the number, v, of moles of particles (ions and molecules) produced by one mole of any solute may be obtained. Some examples are given in Table IV. 

Glycol (C2H602) is the main component in antifreeze. What mass of glycol must be added to 10 liters of water to prevent freezing down to -18.6°C (The molal freezing point depression constant for water is 1.86°C kg/mol.)... 

In principle, any of the colligative properties can be used to find the solute s molar mass, but in practice, some systems provide more precise data than others. For example, to determine the molar mass of an unknown solute by freezing point depression, you would select a solvent with as large a molal freezing point depression constant as possible (see Table 13.5). If the solute is soluble in acetic acid, for instance, aim concentration of it depresses the freezing point of acetic acid by 3.90°C, more than twice the change in water (1.86°C). 

The values of Kp the molal freezing-point-depression constant, for several common solvents are given in Table 13.3. For water, Kfvs 1.86 °C/m.Therefore, any aqueous solution that is 1 w in nonvolatile solute particles (such as 1 tn C6H12O6 or 0.5 m NaCl) freezes at the temperature that is 1.86 °C lower than the freezing point of pure water. 

The proportionality constants, Kf and K, are, respectively, the molal freezing-point depression constant and the molal boiling-point elevation constant The freezing-and boiling-point constants are properties of the solvent, no matter what the solute may be. The freezing-point constant for water is 1.86°C/m, and the boiling-point constant is 0.52°C/m. 

A = Kj- Cflj A 7b = Ki) Cflj We use molality in these equations because they describe temperature changes. The constant Zf is called the freezing point depression constant, and is called the boiling point elevation constant. These constants are different for different solvents but do not depend on the identity of the solutes. For water, Zf is 1.858 °C kg/mol and is 0.512 °C kg/mol. 

The freezing point depression constant for water is known from experiments and can be found in tables Tf = 1.858 ° C kg/mol. To calculate the freezing point, we must first determine the molality of the... 

As shown in the first diagram in this sidebar (for water), the melting point of solution is also displaced toward lower values by addition of a nonvolatile solute, the freezing-point depression effect. By arguments similar to those given above, the freezing-point depression ATfp = T p — 7fp(.xB) will also be found to be proportional to solute molality ... 

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). 

The dimer is relatively nonpolar and thus more soluble in benzene than in water. Since benzoic acid forms dimers in benzene, the effective solute particle concentration will be less than 1.0 molal. Therefore, the freezing-point depression would be less than 5.12°C (AT, = Kfm). 89. a. 26.6 kj/mol b. -657 kj/mol 91. 0.050... 

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