Ideal solutions freezing-point depression

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. 

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. 

This relationship constitutes the basic definition of the activity. If the solution behaves ideally, a, =x, and Equation (18) define Raoult s law. Those four solution properties that we know as the colligative properties are all based on Equation (12) in each, solvent in solution is in equilibrium with pure solvent in another phase and has the same chemical potential in both phases. This can be solvent vapor in equilibrium with solvent in solution (as in vapor pressure lowering and boiling point elevation) or solvent in solution in equilibrium with pure, solid solvent (as in freezing point depression). Equation (12) also applies to osmotic equilibrium as shown in Figure 3.2. 

FREEZING-POINT DEPRESSION. The freezing point of a solution is. in general, lower than that of (he pure solvent. The depression is proportional to the active mass of the solute. For dilute (ideal) solutions... 

Figure 14.18 shows the experimentally determined phase diagram for (1,4-dimethylbenzene + acetonitrile)14 at ambient pressure, along with the diagram predicted by ideal solution behavior. The actual freezing point depressions are significantly less than those expected for ideal solutions/ We can interpret this... 

Particularly simple forms of the equations for the freezing-point depression, boiling-point elevation, and osmotic pressure are obtained when the solution is ideal or when it is sufficiently dilute, so that the ideally dilute solution approximation is appropriate. In both of these cases, the activity of the solvent is equal to its mole fraction, so that... 

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... 

A few values of Kf and Kb are given in Table 2. For a macromolecular solution, the ideally dilute approximation holds only up to such low molality that freezing-point depression and boiling-point elevation are useless for determining... 

In the ideally dilute limit, colligative properties depend on the total solute mole fraction or molality. If there are a number of different solutes present, this can be expressed as (for the case of freezing-point depression)... 

Pure benzene freezes at 5.50°C and has a density of 0.876 g/mL. A solution of 1.7 g of nitrobenzene in 250 mL benzene freezes at 5.18°C. What is the molality-based freezing-point depression constant of benzene and at what temperature does a solution containing 3.2 g of bromobenzene in 250 mL of benzene freeze (You may make the ideally dilute approximation for both these solutions.)... 

There are many measurement techniques for activity coefficients. These include measuring the colligative property (osmotic coefficients) relationship, the junction potentials, the freezing point depression, or deviations from ideal solution theory of only one electrolyte. The osmotic coefficient method presented here can be used to determine activity coefficients of a 1 1 electrolyte in water. A vapor pressure osmometer (i.e., dew point osmometer) measures vapor pressure depression. 

Real colligative properties are only found in ideal gases and ideal solutions. Examples are osmotic pressure, vapour pressure reduction, boiling-point elevation, freezing-point depression, in other words the osmotic properties. 

The heat of vaporization and the heat of fusion of water are 540 and 80 cal/g respectively, (a) For a solution of 1.2 g of urea in 100 g of water, estimate (i) the boiling point elevation, (ii) the freezing point depression, (iii) the vapor pressure lowering at 100°C. Assume ideal-solution and ideal-gas behavior and assume urea to be nonvolatile. (b) Discuss the foregoing properties of a solution of 1.2 g of a nonvolatile solute of molecular weight 10 in 100 g of water. 

In this experiment, the freezing-point depression of aqueous solutions is used to determine the degree of dissociation of a weak electrolyte and to study the deviation from ideal behavior that occurs with a strong electrolyte. 

Use will be made of the theory developed in Exp. 10 for the freezing-point depression A7 of a given solvent containing a known amount of an ideal solute this material should be reviewed. 

Another method that has proved extremely useful in obtaining information about the nature of solutes in sulfuric acid solution is the measurement of freezing point depressions. The freezing point constant ( ) for sulfuric acid is 6.12 kg °C mol. For ideal solutions, the depression of the freezing point is given by... 

Melting point also changes when a solute is added, but it is not related to the vapor pressure. Instead, it is a factor of crystallization. Impurities (the solute) interrupt the crystal lattice and lower the freezing point. Freezing point depression for an ideally dilute solution is given by the equation ... 

The freezing-point constant, kf, depends on the solvent and has units of K-kg-mol (Table 8.8). -> The freezing-point depression equation holds for nonvolatile solutes in dilute solutions that are approximately ideal. 

The values of Kf for a few solvents are given in Table 14-2. Each is numerically equal to the freezing point depression of a one-molal ideal solution of a nonelectrolyte in that always positive. 

Table 14-3 lists actual and ideal values of i for solutions of some strong electrolytes, based on measurements of freezing point depressions. 

Freezing point depression constant, Kf A constant that corresponds to the change in freezing point produced by a one-molal ideal solution of a nonvolatile nonelectrolyte. 

For aqueous electrolyte solutions, both electrostatic interaction between dissociated ions and ionic hydration induce the deviation of freezing-point depression from that of the ideal solution at high concentrations. In the case of aqueous zwitterion solutions where each ion within a molecule carmot... 

A substance in solution has a chemical potential, which is the partial molar free energy of the substance, which determines its reactivity. At constant pressure and temperature, reactivity is given by the thermodynamic activity of the substance for a so-called ideal system, this equals the mole fraction. Most food systems are nonideal, and then activity equals mole fraction times an activity coefficient, which may markedly deviate from unity. In many dilute solutions, the solute behaves as if the system were ideal. For such ideally dilute systems, simple relations exist for the solubility of substances, partitioning over phases, and the so-called colligative properties (lowering of vapor pressure, boiling point elevation, freezing point depression, osmotic pressure). 

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