Aqueous solutions freezing-point depression

Colligative properties can be sources of insight into not only the properties of solutions, but also the properties of the solute. For example, acetic acid, CH.COOH, behaves differently in two different solvents, (a) The freezing point of a 5.00% by mass aqueous acetic acid solution is — l.72°C. What is the molar mass of the solute Explain any discrepancy between the experimental and the expected molar mass, (b) The freezing-point depression associated with a 5.00% by mass solution of acetic acid in benzene is 2.32°C. Whar is the experimental molar mass of the solute in benzene What can you conclude about the nature of acetic acid in benzene ... 

Which of the following aqueous solutions would have the greatest freezing point depression ... 

ACTIVITY COEFFICIENT. A fractional number which when multiplied by the molar concentration of a substance in solution yields the chemical activity. This term provides an approximation of how much interaction exists between molecules at higher concentrations. Activity coefficients and activities are most commonly obtained from measurements of vapor-pressure lowering, freezing-point depression, boiling-point elevation, solubility, and electromotive force. In certain cases, activity coefficients can be estimated theoretically. As commonly used, activity is a relative quantity having unit value in some chosen standard state. Thus, the standard state of unit activity for water, dty, in aqueous solutions of potassium chloride is pure liquid water at one atmosphere pressure and the given temperature. The standard slate for the activity of a solute like potassium chloride is often so defined as to make the ratio of the activity to the concentration of solute approach unity as Ihe concentration decreases to zero. 

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. 

In Equation 4.21, the activity of pure water (a) is unity and the activity of the water with the inhibitor (a ) is the product of the water concentration (xw) and the activity coefficient (xw). The water concentration is known and the activity coefficient is easily obtained from colligative properties for the inhibitor, such as the freezing point depression. For instance the activity of water in aqueous sodium chloride solutions may be obtained from Robinson and Stokes (1959, p. 476) or from any of several handbooks of chemistry and physics. 

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). 

Equilibria among water ice, liquid water, and water vapor are critical for model development because these relations are fundamental to any cold aqueous model, and they can be used as a base for model parameterization. For example, given a freezing point depression (fpd) measurement for a specific solution, one can calculate directly the activity of liquid water (or osmotic coefficient) that can then be used as data to parameterize the model (Clegg and Brimblecombe 1995). These phase relations also allow one to estimate in a model the properties of one phase (e.g., gas) based on the calculated properties of another phase (e.g., aqueous), or to control one phase (e.g., aqueous) based on the known properties of another phase (e.g., gas). 

The freezing-point depression of a 32% by weight aqueous solution of ethylene glycol is 16.23°C. What is the activity coefficient of water in this solution ... 

You used 0.5 M glucose and 3% NaCl aqueous solutions in your tonicity experiments. What would be the freezing points of each of these solutions, considering that the freezing point depression constant of water is 1.86°C/osmol ... 

Table 6-2 Freezing Point Depressions of Aqueous Solutions...

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. 

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. 

Freezing point depression 0.14°C (1% w/v aqueous solution) Melting point decomposition at 252°C for the dihydrate. Refractive index 1.33 (1% w/v aqueous solution)... 

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. 

Problem The freezing point depression of 0.1 molal aqueous KCl solution is 0.345 C. Determine the activity of the water in this solution at the freezing point, with reference to pure water as the standard state. 

The freezing point depressions (ff) of dilute aqueous solutions of potassium chlonde are given below ... 

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 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]. 

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