Molar mass boiling-point elevation

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. 

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 freezing point depression and boiling point elevation techniques are useful in calculating the molar mass of a solute or its van t Hoff factor. In these cases, you will begin with the answer (the freezing point depression or the boiling point elevation), and follow the same steps as above in reverse order. 

A boiling point elevation measurement can be used to estimate the molar mass of a solute. 

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. 

Molality (m) is a temperature-independent measure of concentration, defined as the number of moles of solute per kilogram of solvent. It differs from molarity (M) in that it is based on a mass of solvent, rather than a volume of solution. Like molarity, molality can be used as a factor to solve problems (Section 15.4). Molality is also used in problems involving freezing-point depression and boiling-point elevation. 

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. 

Calculate the molar mass of a nonvolatile solute from the changes it causes in the colligative properties (vapor-pressure lowering, boiling-point elevation, freezing-point lowering, or osmotic pressure) of its dilute solution (Section 11.5, Problems 41-56). 

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 ... 

When 1.645 g of white phosphorus are dissolved in 75.5 g of CS2, the solution boils at 46.709°C, whereas pure CS2 boils at 46.300°C. The molal boiling-point elevation constant for CS2 is 2.34°C/m. Calculate the molar mass of white phosphorus and give the molecular formula. 

The accuracy in the temperature measurements hardly justifies using the correction factor in the brackets. Nonetheless, a plot of 0/c versus yields an extrapolated value of (VlRTl/MAH°), from which M can be calculated. Because the effects are very small, freezing point depression and boiling point elevation are not often used for molar mass... 

Calculating the Molar Mass by Boiling-Point Elevation... 

A common application of freezing-point depression and boiling-point elevation experiments is to provide a means to calculate the molar mass of a nonvolatile solute. What data are needed to calculate the molar mass of a nonvolatile solute Explain how you would manipulate these data to calculate the molar mass of the nonvolatile solute. 

Hence, any colligative method should yield the number average molar mass M of a polydisperse polymer. Polymer solutions do not behave in an ideal manner, and nonideal behavior can be eliminated by extrapolating the experimental (F/c) data to c = 0. For example, in the case of boiling point elevation measurements (ebullio-scopy) Equation 9.2 takes the form... 

Analyze Our goal is to calculate the molar mass of a solute based on knowledge of the boiling-point elevation of its solution in CCI4, ATj = 0.357 °C, and the masses of solute and solvent. Table 13.3 gives fCj for the solvent (CCI4), fCj = 5.02 °C/m. 

Thus the relation between the two quantities is roughly where is the molar molecular mass of the solvent A. Therefore, the boiling point elevation of the solution can be expressed simply as follows ... 

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. 

Analyze and Plan We are given the boiling-point elevation of the solution, ATj, = 0.357°C, and Table 13.4 gives fCj, for the solvent (CC ), Kf, = 5.02°C/w . Thus, we can use Equation 13.11, AT, = Ki/ii, to calculate the molality of the solution. Then we can use molality and the quantity of solvent (40.0 g CCI4) to calculate the number of moles of solute. FinaUj the molar mass of the solute equals the number of grams per mole, so we divide the number of grams of solute (0.250 g) by the number of moles we have just calculated. 

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