Freezing point, pure aqueous solutions

The solubility of proteins in nonaqueous solvents makes it possible to study them in homogeneous solution at temperatures below the freezing point of aqueous solutions, since many pure nonaqueous solvents have freezing points well below 0°C (Table I). Freezing temperatures can be lowered even further by the use of solvent mixtures. This opens a new dimension in protein chemistry the significance of which can only dimly be appreciated at the present time. Several possible problems of interest may be mentioned, however. 

Phase diagrams for pure water (red lines) and for an aqueous solution containing a nonvolatile solute (blue lines). Note that the boiling point of the solution is higher than that of pure water. Conversely, the freezing point of the solution is lower than that of pure water. The effect of a nonvolatile solute is to extend the liquid range of a solvent. 

Some physical properties of solutions differ in important ways from those of the pure solvent. For example, pure water freezes at 0 °C, but aqueous solutions freeze at lower temperatures. We utilize this behavior when we add ethylene glycol antifreeze to a car s radiator to lower the freezing point of the solution. The added solute also raises the boiling point of the solution above that of pure water, making it possible to operate the engine at a higher temperature. 

F ure 12.10 Phase diagreim illustrating the boiling-point elevation and teezing-point depression of aqueous solutions. The dashed cunres pertain to the solution, and the solid curves to the pure solvent. 4s you can see, the boiling point of the solution is higher than that of water, and the freezing point of the solution is lower them that of water. 

Consider a binary solution of solvent A and solute B. We assume that when this solution is cooled at constant pressure and composition, the solid that first appears is pure A. For example, for a dilute aqueous solution the solid would be ice. The temperature at which solid A first appears is Tf, the freezing point of the solution. This temperature is lower than the freezing point T of the pure solvent, a consequence of the lowering of /za by the presence of the solute. Both Tf and T can be measured experimentally. 

C12-0097. When an aqueous solution cools to low temperature, part of the water freezes as pure ice. What happens to the freezing point of the remaining solution when this occurs A glass of wine placed in a freezer at -10 C for a very long time forms some ice crystals but does not completely freeze. Compute the molality of ethanol in the remaining liquid phase. 

Similarly, concepts of solvation must be employed in the measurement of equilibrium quantities to explain some anomalies, primarily the salting-out effect. Addition of an electrolyte to an aqueous solution of a non-electrolyte results in transfer of part of the water to the hydration sheath of the ion, decreasing the amount of free solvent, and the solubility of the nonelectrolyte decreases. This effect depends, however, on the electrolyte selected. In addition, the activity coefficient values (obtained, for example, by measuring the freezing point) can indicate the magnitude of hydration numbers. Exchange of the open structure of pure water for the more compact structure of the hydration sheath is the cause of lower compressibility of the electrolyte solution compared to pure water and of lower apparent volumes of the ions in solution in comparison with their effective volumes in the crystals. Again, this method yields the overall hydration number. 

A great variety of aqueous—organic mixtures can be used. Most of them are listed in Table I with their respective freezing point and the temperature at which their bulk dielectric constant (D) equals that of pure water. These mixtures have physicochemical properties differing from those of an aqueous solution at normal temperature, but some of these differences can be compensated for. For example, the dielectric constant varies upon addition of cosolvent and cooling of the mixture in such a way that cooled mixed solvents can be prepared which keep D at is original value in water and are isodielectric with water at any selected temperature (Travers and Douzou, 1970, 1974). 

Plot the change in the saturated vapour pressure of water over pure water and an aqueous solution of sugar (sodium chloride) against the temperature. How does the freezing (boiling) point of water change when it contains solutes (sugar, sodium chloride) Define the cryoscopic and ebullioscopic constants of water. What is their numerical value State Raoult s laws and write their mathematical expression. How can the molecular masses of solids be determined ... 

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. 

Penicillins have several properties that are characteristic of /i-lactam antibiotics. They are obtained in relatively pure form as off-white, tan, or yellow freeze-dried or spray-dried solids that are usually amorphous. Alternatively they are sometimes obtained as crystalline solids, often as hydrates. Penicillins do not usually have sharp melting points, but decompose upon heating to elevated temperatures. Most natural members have a free carboxyl group and commercial preparations are generally either supplied as salts, most frequently as sodium salts, or in zwitterionic form as hydrates, e.g.. amoxicillin trihydrate. The acid strength of the carboxyl group in aqueous solution varies from pAT = 2.73 for oxacillin to p= 3.06 for carbenicillin. 

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. 

Values of for several common solvents are found in Table 15-5. As with K values, values are specific to their solvents. With water s value of 1.86°C/m, a Im aqueous solution containing a nonvolatile, nonelectrolyte solute freezes at -1.86°C rather than at pure water s freezing point of 0.0°C. 

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. 

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