Molecular weights from freezing-point depression

Calculating the Molecular Weight from Freezing-Point Depression... 

Again, Kf values can be calculated from 7 , AHr, and Mi for the solvent Some results. are shown in Table 5.4. The agreement with the direct determination of Kf from freezing-point depressions is very satisfactory. The very large value of Kf for camphor means that this substance is. frequently a very suitable solvent for molecular weight determinations. 

Compare the experimental molecular weight of aspirin as calculated from freezing-point depression measurements with that calculated from NaOH titration data. Explain the difference. 

Fig. 6. Concentration dependences of a apparent molecular weights ", and b freezing-point depression 6 per unit concentration c in benzene of poly(a-phenylethyl isocyanide) of Mn = 34800. [Reproduced from Ref. (21), with permission of J. Wiley and Sons, Publ.]...

We recall from Chapter 10 that the percentages of the elements in a compound can be used to compute the simplest formula for the compound. When the substance is soluble in some suitable liquid, we can combine the empirical formula with a molecular-weight determination by freezing-point depression to get the true formula. 

In other instances, the values did not correlate with those provided from other sources and in at least one instance no freezing point depression was noted. These effects have not been well explained, although similar anomalies have been observed with other high polymers. For example, in the case of cellulose derivatives, Freudenberg has shown that the freezing point method is very susceptible to error, due both to a tendency of the solute to crystallize and to the probable presence of small amounts of impurities of low molecular weight. 

Thus the molality, m, of a solution may be determined from the depression of freezing point. If the weight of solute, w, dissolved in 1 kg of solvent is known the molecular mass of the solute may be calculated from the relation M2 = 1000w/m. K iis is called the freezing-point-depression constant for the solvent. It may be readily calculated if the relevant properties of the solvent are known (Table 6.1), thus enabling the freezing-point equation to be used in a convenient form. 

The advantage of the osmotic-pressure difference method of determining the molecular weights of macromolecules over alternative methods, such as the freezing-point depression method, is evident from a comparison of the magnitudes of the effects to be measured. In Illustration 12.3-1 it will be shown that the addition of 0.01 g/naL of a 60 000 molecular-weight protein results in a freezing-point depression of water of only... 

At one time, the molecular weight of a compound was determined by its vapor density or its freezing-point depression, and molecular formulas were determined by elemental analysis, a technique that determined the relative proportions of the elements present in the compound. These were long and tedious techniques that required relatively large amounts of a very pure sample. Today, molecular weights and molecular formulas can be rapidly determined by mass spectrometry from a very small amount of a sample. 

The measurement of an osmotic pressure can also be carried out more accurately than can the measurement of a boiling-point elevation or a freezing-point depression. One difficulty in measuring very small osmotic pressures is the long time required for the system to reach equilibrium. This difficulty is sometimes overcome by imposing a pressure on the solution side of the membrane and observing how the rate of flow of liquid varies over time. The osmotic pressure can be calculated from this variation. Molecular weights of up to 3 000000 have been measured by the use of such techniques. 

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