Freezing-point depression determination

Given the following freezing-point depressions, determine the molality of each solution of an unknown nonelectrolyte in water. (Hint See Sample Problem D.)... 

Beckmann thermometer A very sensitive mercury thermometer with a small temperature range which can be changed by transferring mercury between the capillary and a bulb reservoir. Used for accurate temperature measurements in the determination of molecular weights by freezing point depression or boiling point elevation. 

M depends not on the molecular sizes of the particles but on the number of particles. Measuring colligative properties such as boiling point elevation, freezing point depression, and vapor pressure lowering can determine the number of particles in a sample. 

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. 

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. 

Here, i, the van t Hoff i factor, is determined experimentally. In a very dilute solution (less than about 10 3 mol-I. ), when all ions are independent, i = 2 for MX salts such as NaCl, i = 3 for MX2 salts such as CaCl2, and so on. For dilute nonelectrolyte solutions, i =l. The i factor is so unreliable, however that it is best to confine quantitative calculations of freezing-point depression to nonelectrolyte solutions. Even these solutions must be dilute enough to be approximately ideal. 

The freezing point depression constant for water is known from experiments and can be found in tables Tf = 1.858 ° C kg/mol. To calculate the freezing point, we must first determine the molality of the... 

The solvent s activity can be determined by measuring the saturation vapor pressure above the solution. Such measurements are rather tedious and their accuracy at concentrations below 0.1 to 0.5M is not high enough to produce reliable data therefore, this method is used only for concentrated solutions. The activity can also be determined from the freezing-point depression or boiling-point elevation of the solution. These temperature changes must be ascertained with an accuracy of about 0.0001 K, which is quite feasible. This method is used primarily for solutions with concentrations not higher than 1M. 

To determine freezing point depression, we first need molality, which means we need mass of solvent. 

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

Determination of molar mass by freezing-point depression... 

Experiment 4 Determination of Molecular Mass by Freezing-Point Depression ... 

Scenario A student set up an apparatus to determine the molecular mass through freezing point depression (see Figure 3)... 

Methods for the determination of Molecular weight based on colligative property are vapour-pressure lowering, boiling point elevation (ebulliometry), freezing-point depression (cryoscopy), and the Osmotic pressure (osmometry). 

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. 

A unitless correction factor that relates the relative activity of a substance to the quantity of the substance in a mixture. Activity coefficients are frequently determined by emf (electromotive force) or freezing-point depression measurements. At infinite dilution, the activity coefficient equals 1.00. Activity coefficients for electrolytes can vary significantly depending upon the concentration of the electrolyte. Activity coefficients can exceed values of 1.00. For example, a 4.0 molal HCl solution has a coefficient of 1.76 and a 4.0 molal Li Cl has a value of... 

Colligative properties are dependent on the number of particles present and are thus related to M . M values are independent of molecular size and are highly sensitive to small molecules present in the mixture. Values of are determined by Raoult s techniques, which are dependent on colligative properties such as ebulliometry (boiling point elevation), cryometry (freezing point depression), osmometry, and end-group analysis. 

---