Freezing-point elevation

Binary systems are known that form solid solutions over the entire range of composition and which exhibit either a maximum or a minimum in the melting point. The Uquidus-solidus curves have an appearance similar to that of the liquid-vapor curves in systems which f orm azeotropes. The mixture having the composition at the maximum or minimum of the curve melts sharply and simulates a pure substance in this respect just as an azeotrope boils at a definite temperature and distills unchanged. Mixtures having a maximum in the melting-point curve are comparatively rare. 

Suppose that the solid solution is an ideal solid solution, defined, in analogy to ideal gaseous and ideal liquid solutions, by requiring that for every component, fii = 

LetAGi = — i(s), the Gibbs energy of fusion of the pure component at temperature 

If the pure solid were present, then Xi(s) = 1 in this case the second term of the denominator in Eq. (15.8) would be positive so that the fraction in the braces would be less than unity. The freezing point T is therefore less than Tor. If a solid solution is present in equilibrium then if Xi(s) Xi(l), the second term in the denominator will be negative, the fraction in the braces will be greater than unity and the melting point will be greater than Tqi. 

---

The activity a2 of an electrolyte can be derived from the difference in behavior of real solutions and ideal solutions. For this purpose measurements are made of electromotive forces of cells, depression of freezing points, elevation of boiling points, solubility of electrolytes in mixed solutions and other characteristic properties of solutions. From the value of a2 thus determined the mean activity a+ is calculated using the equation (V-38) whereupon by application of the analytical concentration the activity coefficient is finally determined. The activity coefficients for sufficiently diluted solutions can also be calculated directly on the basis of the Debye-Hiickel theory, which will bo explained later on. 

Solutions have lower freezing points than the pure solvent. The freezing point elevation (ATf) is directly proportional to the solvent s freezing point depression constant (Kf) times the molality (m) of the nonelectrolyte solute in moles per kg of solvent ... 

Freezing point elevation in nanospace detected directly by atomic force microscopy... 

Now the research effort goes toward experimental verification of the elevation phenomena in the simplest geometry, a slit. Our main interest is in the range of a few to several nanomenters. Some experimental studies have already reported freezing point elevation in slit pores [8-10], but the materials used were activated carbon fibers (ACFs), which have only micropores less than 2nm. In such small pores the first layer adjacent to the attractive pore wall, which is known to form a frozen phase at a temperature well above the bulk freezing point, will occupy most of the pore spaces, and the freezing behavior in the interior of the pore space is difficult to be detected. Further, there may still remain some controversy if a liquid confined in a larger nanopore would exhibit elevation unless an experimental verification is made over such sizes. 

Unlike the surface force apparatus the AFM measurement does not have a direct method to detect the distance between the surfaces. Instead, one will take the linear signal of cantilever deflection against sample displacement as the origin of the surface distance The linear signal results because the two surfaces are in contact and move together. This manner of wall detection usually works well. However, what would result if the freezing point elevation is the case ... 

Through a simple thermodynamic treatment the following equation was obtained to express the extent of freezing point elevation 5T [3], ffr -A(p... 

DETECTION OF FREEZING POINT ELEVATION IN SLIT NANOSPACE BY ATOMIC FORCE MICROSCOPY... 

An experimental trial for finding foe freezing point elevation phenomena was conducted, employing foe so-called colloidal-probe Atomic Force Microscopy. A carbonaceous nanospace with slit geometry was successfully made up by this technique. 

In this paper we report, first, grand canonical Monte Carlo (GCMC) simulations of LJ fluid modeled on methane in slit-shaped nanopores that are kept equilibrium with saturated vapor, or pure liquid, in bulk phase. Depending on the strength of the attractive potential energy from pore walls, fluid in a pore shows freezing point elevation as well as depression. 

Electrolyte solutions are solutions which can conduct electricity. Colligative properties such as the lowering of the vapour pressure, depression of the freezing point, elevation of the boiling point and osmotic pressure all depend on the number of individual particles present in solution. They thus give information about the number of particles actually present in solution. For some solutes it is found that the number of particles actually present in solution is greater than would be expected from the formula of the compound. 

Interpret the freezing-point elevation in solid solutions in terms of the escaping tendency of the solid in the solid solution. 

However, what of the possibility that the curve might be lowered more than the curve This would happen if more B dissolved into solid A than into liquid A and would result in a freezing point elevation as shown in Figure 17.15. This explains an important feature of many binary systems. 

The presence of solutes in water can have profound effects upon the properties of the solvent. These effects include lowering the freezing point, elevating the boiling point, and osmosis. All such properties are called colligative properties they depend upon the concentration of solute, rather than its particular identity. The effects of solutes and solution concentrations on colligative properties are addressed briefly here. 

A variety of analytical methods have been employed for the estimation of deuterium in biological fluids in the context of total body water measurements. These include the falling drop method [241], freezing point elevation [242], infrared spectroscopy [243], gas chromatography [237] and mass spectrometry [240,244]. A range of accuracy between 0.5-5.0% is claimed from these various techniques in the overall protocol of body water measurement. 

Colligative A colligative property of a solute in a dilute solution is an effect whose magnitude depends only on the concentration of the solute particles (number of particles per unit volume of solution) and not on features such as size, shape or chemical composition. Examples are osmotic pressure, depression of freezing point, elevation of boiling point and the vapour pressure of the solution. If the value of any one of these is known for a particular solution, then the values of the others may readily be calculated. 

Colligative properties include lowering of vapor pressure, depression of freezing point, elevation of boiling point, and osmotic pressure. 

---