Freezing point pressure dependence

Vapor-pressure lowering depends on concentration expressed as mole fraction, x-Boiling-point elevation depends on concentration expressed as molality, m. Freezing-point depression depends on concentration expressed as molality, m. Osmotic pressure depends on concentration expressed as molarity, M. 

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. 

A liquid boils and condenses - the change between the liquid and gaseous states - at a temperature which depends on its pressure, within the limits of its freezing point and critical temperature. In boiling it must obtain the latent heat of evaporation and in condensing the latent heat must be given up again. 

The properties of a solution differ considerably from those of the pure solvent Those solution properties that depend primarily on the concentration of solute particles rather than their nature are called colligative properties. Such properties include vapor pressure lowering, osmotic pressure, boiling point elevation, and freezing point depression. This section considers the relations between colligative properties and solute concentration, with nonelectrolytes that exist in solution as molecules. 

The lowering of freezing point and the generation of osmotic pressure both depend on the total concentration of solute particles. Therefore, by using the colligative property to determine the amount of solute present, and knowing its mass, we can infer its molar mass. 

In physical chemistry, we apply the term colligative to those properties that depend upon number of molecules present. The principal colligative properties are boiling point elevation, freezing point depression, vapour pressure lowering, and osmotic pressure. All such methods require extrapolation of experimental data back to infinite dilution. This arises due to the fact that the physical properties of any solute at a reasonable concentration in a solvent are... 

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... 

If gas-liquid and gas-solid separations are dependent on the saturation vapor pressure of the chemical component undergoing equilibration (a) What is the expected effect when the temperature of the system is raised (b) If the system is a gas-liquid system sketch what a plot of log VT vs. 1 IT would look like including when the T is below the freezing point of the stationary phase, (c) Why might it be better to sample the vapor phase above a solution as a sample to determine trace materials in the solution ... 

Colligative properties are those properties of solutions that depend on the number of solute particles present and not their identity. Colligative properties include vapor pressure lowering, freezing point depression, boiling point elevation, and osmotic pressure. Colloids are homogeneous mixtures, in which the solute particles are intermediate in size between suspensions and true solutions. We can distinguish colloids from true solutions by the Tyndall effect. 

At a given (low) temperature and pressure a crystalline phase of some substance is thermodynamically stable vis a vis the corresponding amorphous solid. Furthermore, because of its inherent metastability, the properties of the amorphous solid depend, to some extent, on the method by which it is prepared. Just as in the cases of other substances, H20(as) is prepared by deposition of vapor on a cold substrate. In general, the temperature of the substrate must be far below the ordinary freezing point and below any possible amorphous crystal transition point. In addition, conditions for deposition must be such that the heat of condensation is removed rapidly enough that local crystallization of the deposited material is prevented. Under practical conditions this means that, since the thermal conductivity of an amorphous solid is small at low temperature, the rate of deposition must be small. 

The colligative properties of solutions are those properties that depend upon the number of dissolved molecules or ions, irrespective of their kind. They are the lowering of the vapor pressure, the depression of the freezing point, the elevation of the boiling point, and the osmotic pressure. These properties may be used in determining molecular weights of dissolved substances. 

As with vapor-pressure lowering (Section 11.6), the actual amount of boiling-point elevation and freezing-point depression observed for solutions of ionic substances depends on the amount of dissociation, as given by a van t Hoff factor. The formulas for both boiling-point elevation and freezing-point depression can be modified to take dissociation into account ... 

The up to now most frequently used techniques as, for example, vapour pressure osmometry (VPO) or freezing point depression (with its limitation regarding the solvent dependent measuring temperature) are based upon the colligative properties of the system the classical absolute light-scattering and ultracentrifugation techniques are only occasionally and approximately applicable with respect to the determination of CMC values. Evaluation of critical micelle concentrations which are based on these latter methods suffer considerably from the insensitivity of these techniques if measurements below the CMC, i.e., below about 10-3 mol dm-3, are carried out. More sensitive methods will be discussed below. 

Both vapour pressure osmometry and depression of the freezing point are the standard techniques probably most frequently used to determine the apparent number average molecular weight of the aggregates. The former method is preferred since the temperature of the sample is easily varied, thus allowing the investigation of the temperature dependence of the aggregate size. The accuracy of the commercially available equipment is rather different, and this has to be carefully considered below... 

A somewhat surprising result was that 1460 bars of pressure had little effect on the eutectic temperature (238.65 K vs. 237.45 K) (Fig. 5.22). A pressure of 1460 bars, per se, would decrease the freezing point of pure water by about —14.8K (Fig. 3.3). Dropping the temperature at which ice first formed by 12K had only a minor effect on the eutectic (AT = 1.2K) (Fig. 5.22). This is not, however, always the case. For example, for the simpler NaCl-H20 system, the calculated eutectic temperature at lbar is —21.3°C at 1460bars of pressure, the calculated eutectic temperature is —31.3°C (AT = 10.OK). As we point out repeatedly, chemical systems and their response to temperature and pressure depend, ultimately, on thermal and volumetric properties of individual constituents, which makes every system response highly individualistic. 

The molality scale is useful for experiments in which physical measurements (freezing point, boiling point, vapor pressure, osmotic pressure, etc.) are made over a wide range of temperatures. The molality of a given solution, which is determined solely by the masses of solution components, is independent of temperature. In contrast, the molar concentration (or the normality) of a solution is defined in terms of volume it may vary appreciably as the temperature is changed, because of the temperature-dependence of the volume. As a point of interest, in dilute aqueous solutions (less than 0.1M), the molality is very close numerically to the molarity. 

Freezing-point depression, boiling-point elevation and osmotic pressure are known as colligative properties, because they are dependent on the properties of the solvent and the total mole fraction of all solutes, but are independent of any particular property of the solutes. Equations (61)-(63) are usually written in terms of mB, the sum of the molalities of all the solutes, which for ideally dilute solutions is related to xB by... 

---