Freezing-point depression molar mass from

When determining a molar mass from freezing-point depression, it is possible to make each of the following errors (among others). In each case, predict whether the error would cause the reported molar mass to be greater or less than the actual molar mass. 

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

Molar Mass from Freezing-Point Depression... 

How to Calculate the Molar Mass of a Solute from Freezing-Point Depression or Boiling-Point Elevation Data... 

In carrying out a molar mass determination by freezing point depression, we must choose a solvent in which the solute is readily soluble. Usually, several such solvents are available. Of these, we tend to pick one that has the largest kf. This makes ATf large and thus reduces the percent error in the freezing point measurement From this point of view, cyclohexane or other organic solvents are better choices than water, because their kf values are larger. 

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... 

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. 

A 4.51 g sample of an unknown compound was dissolved in 98.0 g of solvent. From the freezing point depression, the concentration was found to be 0.388 mol/kg. Calculate the molar mass of the unknown. 

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. 

We wish to derive expressions for calculating the molality m of the solution (or the molar mass Mof the solute) from a measured freezing-point depression AT. The molality of the solution is given by... 

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 elemental analysis of an organic solid extracted from gum arabic (a gummy substance used in adhesive, inks, and pharmaceuticals) showed that it contained 40.0 percent C, 6.7 percent H, and 53.3 percent O. A solution of 0.650 g of the solid in 27.8 g of the solvent diphenyl gave a freezing-point depression of 1.56°C. Calculate the molar mass and molecular formula of the solid. K for diphenyl is 8.00°C/ot.)... 

Two grams of benzoic acid dissolved in 25 g of benzene, Xy = 4.90 Kkg/mol, produce a freezing-point depression of 1.62 K. Calculate the molar mass. Compare this with the molar mass obtained from the formula for benzoic acid, CgHjCOOH. 

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... 

Reserpine is a natural product isolated from the roots of the shrub Rauwolfia serpentina. It was first synthesized in 1956 by Nobel Prize winner R. B. Woodward. It is used as a tranquilizer and sedative. When 1.00 g reserpine is dissolved in 25.0 g camphor, the freezing-point depression is 2.63X Kf for camphor is 40.x kg/mol). Calculate the molality of the solution and the molar mass of reserpine. 

The molar mass of CH3COOH is 60.05 g/mol. Since the molar mass of the solute calculated from the freezing point depression is twice this value, the structure of the solute most likely is a dimer that is held together by hydrogen bonds. 

Following Eq. (8.12) the freezing point depression is proportional to the cryoscopic constant and the concentration of the solute (m2 (mol/kg)) in the molality scale. Since the cryoscopic constant K ry of the solvent depends on the molar mass, the melting temperature T and the enthalpy of fusion, the various liquids show different values. From Eq. (8.12) it can be seen that the measurement of the freezing point depression allows the determination of the molar mass of unknown compounds, if the melting temperature and the enthalpy of fusion is known. 

Strategy Solving this problem requires three steps. First, we calculate the molality of the solution from the freezing-point depression. Next, from the molality we determine the number of moles in 7.85 g of the compound and hence its molar mass. Finally, comparing the experimental molar mass with the empirical molar mass enables us to write the molecular formula. 

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. 

His first measurements of freezing-point depressions appeared in 1878. He pointed out the advantages of determining the molar mass of a substance from the freezing point of its dilute solution, and gave specific examples of this procedure. He was the first to show experimentally that the freezing-point depression of a dilute aqueous solution of an electrolyte is proportional to the number of ions per solute formula unit (Eq. 12.4.12). 

Given (a) the mass of solute and solvent in a solution (b) the freezing-point depression or hoiling-point elevation, or data from which they may be found and (c) the molal freezing/boiling-point constant of the solvent, find the approximate molar mass of the solute. 

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