Calculating Freezing-Point Depression

Sample Problem C what is the freezing-point depression of water in a solution of 17.1 g of sucrose, Cj2H220jj, in 200. g of water What is the actual freezing point of the solution  

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Table 18.1 Values for the calculated freezing point depression (FPD) for NaCl, KC1, CaCl2, and...

Kb is the boiling point elevation constant, and for water equals 0.52°C/m. Each solvent has its own unique value for Kb, and the value of Kb for water indicates that a 1.0 m solution of glucose, a nonelectrolyte, would boil 0.52°C higher than that of pure water, 100.52°C. As with the equation used to calculate freezing point depressions, if the solute is an electrolyte, the molality of the ions will be a whole number multiple of the molality of the compound. 

New material on using molality to calculate freezing point depression and boiling point elevation was added. 

Table 2.4 Calculated freezing-point depressions of citric acid solutions, osmotic and activity coefficients of citric acid...

To calculate freezing point depression, boiling point elevation, and osmotic pressure of ionic solutions we use the van t Hoff factor in each equation as follows ... 

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 presence of a solute lowers the freezing point of a solvent if the solute is nonvolatile, the boiling point is also raised. The freezing-point depression can be used to calculate the molar mass of the solute. If the solute is an electrolyte, the extent of its dissociation, protonation, or deprotonation must also be taken into account. 

If we calculate the H values for various water temperatures, we see results as shown in Table 4.4. The importance of the information content encoded in the H value in these studies is that it is a single-numerical description of the system, water in this case, that can be used to relate to physical property changes occurring at different temperatures. This approach can be used to evaluate a property change such as the freezing point depression. 

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... 

Table XXVII.—Comparison of Calculated Boiling Point Elevation, Freezing Point Depression, and Osmotic Pressure...

Compare the freezing point depression values you calculated to the... 

The depression of the freezing point of a solvent due to the presence of a dissolved solute is an example of a colligative property, that is, a property of a dilute solution that depends on the number of dissolved particles and not on the identity of the particles. Water has a freezing point depression constant, Kf, of 1.86 K kg mol-1. In other words, for every mole of nonvolatile solute dissolved in a kilogram of water, the freezing point of water is lowered by 1.86°C. The change in freezing point, A T, can be calculated from the equation... 

Step 3 Since 0.9% sodium chloride has a freezing point depression of 0.52, one can calculate the percentage concentration of sodium chloride required to lower the difference in freezing points, i.e., the value obtained in Step 2, ATf, by the method of proportion. The calculations involved in this method are explained best by following examples. 

Freezing point depression of 1% atropine sulfate is 0.074°C. Calculate the volume of iso-osmotic solution produced by 1 g of atropine sulfate. Since a freezing point depression of 0.074°C is caused by 1 g of atropine sulfate in 100 mL of water, a depression of 0.52°C will be produced by a solution containing 1 g in X mL can be calculated by as follows ... 

Freezing point depression of 1% pilocarpine nitrate is 0.14°. Calculate the volume of iso-osmotic solution produced by 1 gram of pilocarpine nitrate by U.S.P. method. 

We can enter the given values along with the calculated molality into the freezing point depression equation ... 

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. 

Raoult s law, osmotic pressure, and freezing point depression calculations use, without conversion, which of the following respective concentration units... 

The freezing-point depression technique is also commonly used to calculate the molar mass of a solute. 

In freezing-point depression and boiling-point elevation problems, to find the actual freezing/boiling point, calculate the AT (change in temperature), then subtract that amount from the solvent s freezing point, or add it to the solvent s boiling point. 

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—Freezing-point depression is a colligative property, which depends on the number of particles present. The solution with the greatest concentration of particles will have the greatest depression. The concentration of particles in E (a non electrolyte) is 0.10 m. All other answers are strong electrolytes, and the concentration of particles in these may be calculated by multiplying the concentration by the van t Hoff factor. 

Calculate the molality of the solution by dividing the change in temperature (AT) by the freezing-point depression constant (A)). 

Salt is a strong electrolyte that produces two ions, Na+ and Cl, when it dissociates in water. Why is this important to consider when calculating the colligative property of freezing point depression ... 

As we saw in Section 17.5, the activity coefficient of a nonelectrolyte solute can be calculated from the activity coefficient of the solvent, which, in turn, can be obtained from the measurement of colligative properties such as vapor pressure lowering, freezing point depression, or osmotic pressure. We used the Gibbs-Duhem equation in the form [Equation (17.33)]... 

Measuring and Using Numbers Calculate the freezing point depression constant for BHT. (Ar = K m)... 

A solution also exhibits a depression in its freezing point. The freezing point depression is the decrease in the temperature of the freezing point due to the addition of a solute. It is calculated using the equations ATj. = Kjm, where ATj. is the decrease in freezing point for the solution, Kj. is the molal freezing point depression constant, and m is the molality of the solution. Water s K. value is 1.86°C/m. 

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