Determining Molar Mass Using Freezing Point Depression

Determining Molar Mass Using Freezing Point Depression... 

The expressions commonly used for determination of molalities or molar mass from freezing-point depressions are derived with the following approximations ... 

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 ... 

The freezing point depression constants of the solvents cyclohexane and naphthalene are 20.1°C/ and 6.94°C/ , respectively. Which solvent would give a more accurate result if you are using freezing point depression to determine the molar mass of a substance that is soluble in either one Why ... 

Colligative properties, particularly freezing point depression, can be used to determine molar masses of a wide variety of nonelectrolytes. The approach used is illustrated in Example 10.9. 

The freezing-point depression data are used to determine the molar mass. 

When using the freezing-point depression method of determining the molar mass of a nonelectrolyte, what information is needed in addition to the above ... 

D—To calculate the molar mass, the mass of the solute and the moles of the solute are needed. The molality of the solution may be determined from the freezing-point depression, and the freezing-point depression constant (I and II). If the mass of the solvent is known, the moles of the solute may be calculated from the molality. These moles, along with the mass of the solute, can be used to determine the molar mass. 

One of the laboratory requirements for the course, and also the topic of former test questions, is the determination of the molar mass of a substance from the freezing-point depression. Actually, any of the colligative properties can be used to determine the molar mass, but the only one that you are required to know is the freezing-point depression method. It is easier to illustrate the technique within the framework of a problem, so the discussion of this process will be done within a sample problem. 

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. 

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

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. 

In principle, any of the colligative properties can be used to find the solute s molar mass, but in practice, some systems provide more precise data than others. For example, to determine the molar mass of an unknown solute by freezing point depression, you would select a solvent with as large a molal freezing point depression constant as possible (see Table 13.5). If the solute is soluble in acetic acid, for instance, aim concentration of it depresses the freezing point of acetic acid by 3.90°C, more than twice the change in water (1.86°C). 

Equation (13.22) provides a simple relation between the freezing-point depression and the molal concentration of solute in a dilute ideal solution, which is often used to determine the molar mass of a dissolved solute. If W2 kg of a solute of unknown molar mass, M2, are dissolved in w kg of solvent, then the molality of solute is m = W2/WM2. Using this value... 

Because of this peculiarity, the colligative properties can be used to determine the amount of substance Wb of sample of an unknown substance B and, therefore, if the mass of the sample is known, also the molar mass Mb = m /n. Let us take a quick look at this by considering the example of lowering of freezing point. Xb ns/riA is valid at high dilution, and because of a = rriA/MA, we have Xb Wb MA/rriA- The quotient n- IrriA corresponds to the molality b- (compare Sect. 1.5). Inserting these expressions in Eq. (12.14) for the freezing-point depression results in... 

Strategy The steps needed to calculate the molar mass of Hb are similar to those outlined in Example 9.10, except we use osmotic pressure instead of freezing-point depression. First, we must calculate the molarity of the solution from the osmotic pressure of the solution. Then, from the molarity, we can determine the number of moles in 35.0 g of Hb and hence its molar mass. Because the pressure is given in mmHg, it is more convenient to use R in terms of L atm instead of L bar because the conversion factor from mm Hg to atm is simpler. 

The colligative properties of nonelectrolyte solutions provide a means of determining the molar mass of a solute. Theoretically, any of the four colhgative properties are suitable for this purpose. In practice, however, only freezing-point depression and osmotic pressure are used because they show the most pronounced changes. 

---