Ideal solutions boiling-point elevation

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. 

BOILING POINT ELEVATION. The boiling point of a solution is, in general, higher than that of pure solvent, and the elevation is proportional to the active mass of the solute for dilute (ideal) solutions,... 

Here R(T )2/A/fv ] is a property of the pure solvent. Equation (10.92) is the basic equation for the simpler expressions involving the mole fraction or molality of the solute of the equation for the boiling point elevation, but it must be emphasized that it is only an approximate equation, valid in the limit as xx approaches unity. Even for the approximation of ideal solutions, Equation (10.90) should be used for the calculation of the boiling point when Xj is removed from unity. 

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... 

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 Chemistry Lecture 4, we saw that the addition of a nonvolatile solute will lower tire vapor pressure of the solution in direct proportion to the number of particles added, as per Raoult s law. The vapor pressure has an important relationship to the normal boiling point. When the vapor pressure of a solution reaches the local atmospheric pressure, boiling occurs. Thus, the boiling point of a substance is also dranged by the addition of a solute. The addition of a nonvolatile solute lowers the the vapor pressure and elevates the boiling point. The equation for the boiling point elevation of an ideally dilute solution due to the addition of a nonvolatile solute is ... 

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

Boiling point elevation constant, A constant that corresponds to the change (increase) in boiling point produced by a one-molal ideal solution of a nonvolatile nonelectrolyte. CoUigative properties Physical properties of solutions that depend on the number but not the kind of solute particles present. Colloid A heterogeneous mixture in which solute-like particles do not settle out also called colloidal dispersion. 

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). 

If strong electrolyte solutions behaved ideally, the factor i would be the amount (mol) of particles in solution divided by the amount (mol) of dissolved solute that is, i would be 2 for NaCl, 3 for Mg(N03)2, and so forth. Careful experiment shows, however, that most strong electrolyte solutions are not ideal. For example, comparing the boiling point elevation for 0.050 m NaQ solution with that for 0.050 m glucose solution gives a factor i of 1.9, not 2.0 ... 

What is the direction of the influence of nonideality (for example, positive deviations from Raoult s law) on (a) freezing-point depression, (b) boiling-point elevation, and (c) osmotic pressure compared to the ideal solution case ... 

Equation (6.77) is known as the van t Hoff equation, who pointed out already the analogy between solutions and gases, because the form resembles much to the ideal gas law [18, 19]. By the way, in this highly interesting paper, van t Hojf points out relations between osmotic pressure, vapor pressure depression, freezing point depression, and boiling point elevation, i.e., what we address nowadays in short as colligative properties. 

Hence, any colligative method should yield the number average molar mass M of a polydisperse polymer. Polymer solutions do not behave in an ideal manner, and nonideal behavior can be eliminated by extrapolating the experimental (F/c) data to c = 0. For example, in the case of boiling point elevation measurements (ebullio-scopy) Equation 9.2 takes the form... 

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... 

Calculation of the freezing-point depression of the solvent and hence the molecular weight of the solute by this method proceeds exactly the same way as for the boiling-point elevation. For cryoscopy of ideal solutions, equations corresponding to those for Ar and ke are AT/ = -kftnz and = (RT Mi)l(l000Lf), where ATf = T - Tf Hhe freezing-point depression. Tf is the... 

Figure 12.3 Freezing-point depression and boiling-point elevation of an aqueous solution. Solid curves dependence on temperature of the chemical potential of H2O (A) in pure phases and in an aqueous solution at 1 bar. Dashed curves unstable states. The fiA values have an arbittary zero. The solution curve is calculated for an ideal-dilute solution of composition xa = 0.9.

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