The freezing-point depression

The freezing point and boiling point of a solution depend on the equilibrium of the solvent in the solution with pure solid solvent or pure solvent vapor. The remaining possible equilibrium is that between solvent in solution and pure liquid solvent. This equilibrium can be established by increasing the pressure on the solution sufficiently to raise the /x of the solvent in solution to the value of the /x of the pure solvent. The additional pressure on the solution that is required to establish the equality of the /x of the solvent both in the solution and in the pure solvent is called the osmotic pressure of the solution. 

Consider a solution that is in equilibrium with pure solid solvent. The equilibrium condition requires that 

Since is the chemical potential of the pure liquid, p°(T, p) — PsoUd(T, p) = AGf s, where AGfuj is the molar Gibbs energy of fusion of the pure solvent at the temperature T. Equation (13.11) becomes 

To discover how T depends on x, we evaluate (dT/dx)p. Differentiating Eq. (13.12) with respect to x, p being constant, we obtain 

The lower limit x = 1 corresponds to pure solvent having a freezing point Tq. The upper limit X corresponds to a solution that has a freezing point T. The first integral can be evaluated immediately the second integration is possible if AH, is known as a function of temperature. For simplicity we assume that AH, is a constant in the temperature range from Tq to T then Eq. (13.14) becomes 

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Many chemicals when added to water cause a freezing point depression, as shown in Table 1, and thus are termed antifreezes. The antifreeze properties of these chemicals vary widely as a function of their coUigative, or concentrative, properties. The reduction in freeze point depends both on the chemical itself and the concentration of the chemical in water. The freeze point depression increases as the antifreeze chemical is added to the water, until a characteristic concentration is achieved. Further addition of the antifreeze chemical to water will either result in insolubility or serve to increase the freezing point of the mixture, as illustrated in Figure 1. 

The toxicity of antifreeze and deicing fluids is predorninantly a function of the main component, the freezing point depressant. Eor ethylene glycol-based fluids, the toxicity is well-defined, as the toxicity of ethylene glycol has been studied extensively because of its wide usage in varied appHcations (16). 

It is found empirically and can be justified thermodynamically that the freezing-point depression for an ideal solution is proportional to the molality of the solute. For a nonelectrolyte solution. 

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. 

Colligative properties can be sources of insight into not only the properties of solutions, but also the properties of the solute. For example, acetic acid, CH.COOH, behaves differently in two different solvents, (a) The freezing point of a 5.00% by mass aqueous acetic acid solution is — l.72°C. What is the molar mass of the solute Explain any discrepancy between the experimental and the expected molar mass, (b) The freezing-point depression associated with a 5.00% by mass solution of acetic acid in benzene is 2.32°C. Whar is the experimental molar mass of the solute in benzene What can you conclude about the nature of acetic acid in benzene ... 

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. 

Using the information content, H, to describe the structure at any temperature, it is possible to estimate the new temperature of water when a solute has been added. An increase in this temperature corresponds to the freezing point depression because the water must experience a greater decrease in temperature in order to arrive at the point of solidification. 

Example 4.6. Modeling the freezing point depression due to a solute... 

A = Kj- Cflj A 7b = Ki) Cflj We use molality in these equations because they describe temperature changes. The constant Zf is called the freezing point depression constant, and is called the boiling point elevation constant. These constants are different for different solvents but do not depend on the identity of the solutes. For water, Zf is 1.858 °C kg/mol and is 0.512 °C kg/mol. 

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... 

In the freezing point depression method, one measures the temperature lowering AT/ required to render the activity of the solvent in the solution equal to that of the pure crystalline solvent (referred to the pure liquid as the standard state see above). Then... 

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. 

Freezing point depression follows the colligative laws of thermodynamics at low concentrations added to water. At the same time the boiling point generally will be increased. The freezing point depression can be readily explained from the theory of phase equilibria in thermodynamics. 

What is the freezing point depression constant of naphthalene ... 

The solution in question 3 freezes at -0.192°C. Because water normally freezes at 0°C, this means that the freezing point has decreased by 0.192°C. Thus, ATf = -0.192°C. What is the freezing point depression constant of water, Kfl... 

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

The freezing point depression of a solvent is proportional to the concentration of solute particles and may be used to measure the extent of ionization once the new particles have been identified qualitatively as ions. The method has the obvious disadvantage of not allowing measurements over a range of temperatures in a single solvent. It is almost certainly not worth while to compute an enthalpy of ionization from ionization constants at two different temperatures in two different solvents. Usable solvents are limited not only by the requirement that the melting point be at a convenient temperature but also by the requirement that the solvent be capable of producing ions yet not be sufficiently nucleophilic to react irreversibly with them once they are formed. For this reason most cryoscopic work has been done in sulfuric acid or methanesulfonic acid.170... 

Triphenylcarbinol in sulfuric acid solution has a spectrum indicating the presence of the same carbonium ion responsible for the conductivity of triphenylmethyl chloride in liquid sulfur dioxide.171 In confirmation of this the freezing point depression is four times that of substances dissolving to give only one mole of particles per mole of dissolved substance.171-173... 

In contrast to the simple olefins, aryl-substituted olefins dissolve in sulfuric acid to give comparatively stable carbonium ions, as is shown by the -factors, the spectra, and the recovery of the olefin on dilution.262 In some cases it is neccessary to extrapolate the freezing point depression to zero time owing to a slow sulfonation. Because of the similarity in the spectra it is believed that these carbonium ions have the classical structures shown below.263... 

The freezing point depression is proportional to the product of the solute s molality and the van t Hoff factor. For nonelectrolytes, such as C2H5OH (0.050 m), i = 1, and thus... 

Then we compute the freezing point depression of this solution. 

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

We must appreciate, however, that no chemical reaction occurs between the salt and the water more or less, any ionic salt, when put on ice, will therefore cause it to melt. The chemical identity of the salt is irrelevant - it need not be sodium chloride at all. What matters is the amount of the salt added to the ice, which relates eventually to the mole fraction of salt. So, what is the magnitude of the freezing-point depression ... 

What was the freezing point depression of the solution The standard freezing point for paradichlorobenzene is 53.0°C. 

What was the molality of the naphthalene The freezing point depression constant for paradichlorobenzene is 7.1 °C ml. 

If the freezing point depression of a 5% solution of boric acid is 1.55°C, how many grams of boric acid should be used in preparing a liter of an isotonic solution ... 

ATt is the number of degrees that the freezing point has been lowered (the difference in the freezing point of the pure solvent and the solution). Kt is the freezing-point depression constant (a constant of the individual solvent). The molality (m) is the molality of the solute, and i is the van t Hoff factor, which is the ratio of the number of moles of particles released into solution per mole of solute dissolved. For a nonelectrolyte such as sucrose, the van t Hoff factor would be 1. For an electrolyte such as sodium sulfate, you must take into consideration that if 1 mol of Na2S04 dissolves, 3 mol of particles would result (2 mol Na+, 1 mol SO) ). Therefore, the van t Hoff factor should be 3. However, because sometimes there is a pairing of ions in solution the observed van t Hoff factor is slightly less. The more dilute the solution, the closer the observed van t Hoff factor should be to the expected one. 

Just as the freezing point of a solution is always lower than the pure solvent, the boiling point of a solution is always higher than the solvent. The relationship is similar to the one for the freezing point depression above and is ... 

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