Pressure and freezing point depression

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

Nonelectrolytes in nonaqueous solvents Activity coefficients of dilute solutions of solutes can be studied experimentally by liquid-liquid chromatography as well as techniques such as solvent extraction, light scattering, vapor pressure, and freezing point depression. 

Solutions have two fundamental property changes compared with pure water lowering the vapor pressure and freezing point depression. In cloud microphysics, these changes are crucial for droplet growth and precipitation formation. 

Previous chapters have emphasized the important role of the MWD in determining many functional properties of cereal proteins. Measurement of MWD has met two main problems. The first one is the difficulty of solubilization, particularly of the glutelins. The second is that many of the standard methods for measurement lose their sensitivity above a certain MW. Colligative properties such as osmotic pressure and freezing point depression are related to the number of molecules and therefore give a measure of the number-average MW (MJ. 

Very small coefficients of friction are observed on ice. A typical value is p sa 0.03. There have been several attempts to explain this extremely low friction (for a history of research on this topic, see Ref. [918]). One attempt is related to the abnormal behavior of ice with respect to pressure and density. James Thompson in 1850 developed an expression showing the hnear dependence between pressure and freezing point depression, which was verified experimentally by his brother Lord Kelvin. In 1886, John Joly calculated that the local pressure below skater slides leads to... 

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 depression of the activity may be measured in various ways. The most obvious would involve a measurement of the vapor pressure lowering, but this method is superseded by others both in accuracy and in simplicity of execution. The boiling point elevation and freezing point depression methods relegated vapor pressure measurement... 

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. 

ACTIVITY COEFFICIENT. A fractional number which when multiplied by the molar concentration of a substance in solution yields the chemical activity. This term provides an approximation of how much interaction exists between molecules at higher concentrations. Activity coefficients and activities are most commonly obtained from measurements of vapor-pressure lowering, freezing-point depression, boiling-point elevation, solubility, and electromotive force. In certain cases, activity coefficients can be estimated theoretically. As commonly used, activity is a relative quantity having unit value in some chosen standard state. Thus, the standard state of unit activity for water, dty, in aqueous solutions of potassium chloride is pure liquid water at one atmosphere pressure and the given temperature. The standard slate for the activity of a solute like potassium chloride is often so defined as to make the ratio of the activity to the concentration of solute approach unity as Ihe concentration decreases to zero. 

X V iution), the determination of the molar mass of a solute requires a measurement of mass, volume, temperature, and osmotic pressure. Osmotic pressures are generally large and can be determined quite accurately, thus yielding accurate molar masses. Boiling-point elevations and freezing-point depressions are usually small and not very accurate, so molar mass determinations based on those measures often are not accurate. 

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 fundamental cause of boiling-point elevation and freezing-point depression in solutions is the same as the cause of vapor-pressure lowering (Section 11.6) the entropy difference between the pure solvent and the solvent in a solution. Let s take boiling-point elevations first. We know that liquid and vapor phases are in equilibrium at the boiling point (Tb) and that the free-energy difference between the two phases (AGvap) is therefore zero (Section 8.14). 

Vapor-pressure lowering, boiling-point elevation, and freezing-point depression are very similar thermodynamically. For example, the increase in boiling point ATh is interpreted thermodynamically by using the boiling-point elevation constant Kb to obtain the molality of the solution, as stated in the equation... 

Suppo.se that a colligative property of the polymer solution is measured. These are properties that depend on the number of dissolved solute molecules and not on their sizes (see also Section 2.10). Osmotic pressure, vapor pressure lowering, and freezing point depression are some examples of colligative properties. If the value of the property measured is P, then by definition... 

Since we know how the solution vapor pressure varies with concentration (the relationship being given by Equation 6.5-2) and temperature (through the Clausius-Clapeyron equation. Equation 6.1-3), we can determine the relationships between concentration and both boiling point elevation and freezing point depression. The relationships are particularly simple for dilute solutions x — 0, where x is solute mole fraction). 

An alternative approach is based on the theoretical foundation described earlier for the colligative properties. If the solution is isotonic with blood, its osmotic pressure, vapor pressure, boiling-point elevation, and freezing-point depression should also be identical to those of blood. Thus, to measure isotonicity, one has to measure the osmotic pressure of the solution and compare it with the known value for blood. However, the accurate measurement of osmotic pressure is difficult and cumbersome. If a solution is separated from blood by a true semipermeable membrane, the resulting pressure due to solvent flow (the head) is accurately measurable, but the solvent flow dilutes the solution, thus not allowing one to know the concentration of the dissolved solute. An alternative is to apply pressure to the solution side of the membrane to prevent osmotic solvent flow. In 1877, Pfeffer used this method to measure osmotic pressure of sugar solutions. With the advances in the technology, sensitive pressure transducers, and synthetic polymer membranes, this method can be improved. However, results of the search for a true semipermeable membrane are still... 

This phase diagram shows how temperature and pressure affect the solid, liquid, and gas phases of a pure solvent (solid lines) and a solution (dashed lines). The difference between the solid and dashed lines corresponds to vapor pressure lowering (AP), boiling point elevation (AT[,), and freezing point depression (ATf). 

A solution containing 4.22 g of a nonelectrolyte polymer per hter of benzene solution has an osmotic pressure of 0.646 torr at 20.0°C. (a) Calculate the molecular weight of the polymer, (b) Assume that the density of the dilute solution is the same as that of benzene, 0.879 g/mL. What would be the freezing point depression for this solution (c) Why are boiling point elevations and freezing point depressions difficult to use to measure molecular weights of polymers ... 

Under conditions typical of competitive speedskating, frictional melting, squeeze flow and heat conduction into the ice all play an important role in determining skate blade lubrication. Pressure-induced freezing point depression and the quasi-liquid layer are accounted for in the model, but they play only a minor role in determining the kinetic ice friction coefficient. 

Like boiling-point elevation and freezing-point depression, osmotic pressure is directly proportional to the concentration of solution. This is what we would expect, because all colligative properties depend only on the number of solute particles in solution. If two solutions are of equal concentration and, hence, have the same osmotic pressure, they are said to be isotonic. If two solutions are of unequal osmotic pressures, the more concentrated solution is said to be hypertonic and the more dilute solution is described as hypotonic (Figure 12.14). 

Explain why molality is used for boiling-point elevation and freezing-point depression calculations and molarity is used in osmotic pressure calculations. 

Vapor Pressure Lowering Freezing Point Depression and Boiling Point Elevation Osmotic Pressure A Clinical Perspective ... 

In a similar fashion, solubility measurements (of a gas in a liquid, a liquid in a liquid, or a solid in a liquid) can be used to determine the activity coefficient of a solute in a solvent at saturation. Also, measurements of the solubility of a solid solute in two liquid phases can be used to relate the activity coefficient of the solute in one liquid to a known activity coefficient in another liquid, and freezing-point depression or boiling-point elevation measurements are frequently used to determine the activity of the solvent in a solute-solvent mixture. We have also showed that osmotic-pressure measurements can be used to determine solvent activity coefficients, or to determine the molecular weight of a large polymer or protein. 

Describe how the difference between the solid lines and dashed line corresponds to vapor pressure lowering, boiling point elevation, and freezing point depression. 

The quantities Aj and Aj can be determined from the properties of pure systems containing only component 1. They are functions of pressure alone. Equation (11-155) is an expression for log (./ix,) as a function of pressure p and freezing-point depression 9. Thus, measurement of the temperature at which solid component 1 first appears in the system at pressurep is sufficient to determine/,. Equation (11-155) is useful when the solution is dilute and 9jTi < 1. 

When a non-volatile solute is dissolved in a solvent, the vapour pressure of the solvent is lowered. Consequently, at any given pressure, the boiling point of a solution is higher and the freezing point lower than those of the pure solvent. For dilute ideal solutions, i.e. such as obey Raoult s law, the boiling point elevation and freezing point depression can be calculated by an equation of the form... 

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