Boiling-point elevation molar mass determination

X V iution), the determination of the molar mass of a solute requires a measurement of mass, volume, temperature, and osmotic pressure. Osmotic pressures are generally large and can be determined quite accurately, thus yielding accurate molar masses. Boiling-point elevations and freezing-point depressions are usually small and not very accurate, so molar mass determinations based on those measures often are not accurate. 

Table 3.6 lists Kf and Kb for several solvents. In general, the higher the molar mass of the solvent, the larger the values of Kf and Kb. If the freezing point depression and boiling point elevation constants are known, the molecular weight of the dissolved solute, M2, can be determined ... 

For the determination of very high molar masses, freezing-point depressions, boiling-point elevations, and vapor-pressure lowerings are too small for accurate measurement. Osmotic pressures are of a convenient order of magnitude, but measurements are time-consuming. The technique to be used in this experiment depends on the determination of the intrinsic viscosity of the polymer. However, molar-mass determinations from osmotic pressures are valuable in calibrating the viscosity method. 

The molar mass of a solute can be determined from the observed boiling-point elevation, as shown in Example 17.2. 

Like the boiling-point elevation, the observed freezing-point depression can be used to determine molar masses and to characterize solutions. 

The normal boiling point of a pure liquid T, or a solution is the temperature at which the vapor pressure reaches 1 atm. Because a dissolved solute reduces the vapor pressure, the temperature of the solution must be increased to make it boil. That is, the boiling point of a solution is higher than that of the pure solvent. This phenomenon, referred to as boiling-point elevation, provides a method for determining molar masses. 

Both freezing-point depression and boiling-point elevation can be used to determine whether a species of known molar mass dissociates in solution (Fig. 11.13), as the following example shows. 

Describe how you would use freezing-point depression and osmotic pressure measurements to determine the molar mass of a compound. Why are boiling-point elevation and vapor-pressure lowering normally not used for this purpose ... 

Note that the boiling point elevation of a solution is only dependent of molality of solute but not on its chemical composition and it can be used to determine the molality of the solute and its molar mass. A selection of ebullioscopic constants is given in Table 20.9. 

Historically, chemists have used the group of colligative properties— vapor pressure lowering, freezing-point depression, boiling-point elevation, and osmotic pressure—for molecular mass determinations. In Example 14-9, we showed how this could be accomplished with osmotic pressure. Example 14-10 shows how freezing-point depression can be used to determine a molar mass and, with other information, a molecular formula. To help you understand how this is done, we present a three-step procedure in the form of answers to three separate questions. In other cases, you should be prepared to work out your own procedure. 

Molar mass determination by freezing-point depression or boiling-point elevation has its limitations. Equations (14.5) and (14.6) apply only to dilute solutions of nonelectrolytes, usually much less than 1 mol kg . This requires the use of special thermometers so that temperatures can be measured very precisely, say to 0.001 °C. Because boiling points depend on barometric pressure, precise measurements require that pressure be held constant. As a consequence, boiling-point elevation is not much used. The precision of the freezing-point depression method can be improved by using a solvent... 

Freezing-point depression and boiling-point elevation (Fig. 14-23) are colligative properties having many familiar practical applications. For reasonably dilute solutions, their values are proportional to the molality of the solution (equations 14.5 and 14.6). The proportionality constants are Kf and K, respectively (Table 14.3). Historically, freezing-point depression was a common method for determining molar masses. 

Measurements of the drop in the freezing point, like those of elevation of the boiling point, can be used to determine molar masses of unknown substances. If a substance dissociates in solution, the total molality of all species present (ionic or neutral) must be used in the calculation. 

Colligative properties are related to the number of dissolved solute particles, not their chemical nature. Compared with the pure solvent, a solution of a nonvolatile nonelectrolyte has a lower vapor pressure (Raoult s law), an elevated boiling point, a depressed freezing point, and an osmotic pressure. Colligative properties can be used to determine the solute molar mass. When solute and solvent are volatile, the vapor pressure of each is lowered by the presence of the other. The vapor pressure of the more volatile component is always higher. Electrolyte solutions exhibit nonideal behavior because ionic interactions reduce the effective concentration of the ions. 

Colligative properties arise from the number, not the type, of solute particles. Compared to pure solvent, a solution has lower vapor pressure (RaoulLs law), elevated boiling point, and depressed freezing point, and it gives rise to osmotic pressure. Colligative properties are used to determine solute molar mass osmotic pressure gives the most precise measurements. 

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