Boiling point elevation ATj

Figure 14-14 Because a nonvolatile solute lowers the vapor pressure of a solvent, the boiling point of a solution is higher and the freezing point lower than the corresponding points for the pure solvent. The magnitude of the boiling point elevation, ATj, is less than the magnitude of the freezing point depression, ATf.

The boiling point elevation (ATj) is also proportional to the solute concentration AT(, = X (solute concentration)... 

A similar change occurs with the boiling point of water. The boiling point elevation (ATj,) is determined from the molality (m) of the particles in the solution and the boiling point constant, K/,. 

AHe = solvent enthalpy of vaporization AHf = solvent enthalpy of fusion A2J = boiling-point elevation ATj- = freezing-point depression % = osmotic pressure p = density... 

The change in temperature, ATf, is once again proportional to the change in vapor pressure, ATj. For sufficiently small concentrations of solute, the freezing-point depression is related to the total molality, m (by analogy with the case of boiling-point elevation), through... 

When the van t Hoff factor, i, is included, the boiling point elevation equation becomes ATj, = i K m. The van t Hoff factor can be inserted in a similar fashion in the freezing point depression equation and the osmotic pressure equation. The van t Holf factor, however, cannot be inserted in the same way into the vapor... 

The term ATj, represents the elevation of the boiling point of the solvent, that is, the boiling point of the solution minus the boiling point of the pure solvent. The m is the molality of the solute, and is a proportionality constant called the molal boiling point elevation constant. This constant is different for different solvents and does not depend on the solute (Table 14-2). 

Analyze Our goal is to calculate the molar mass of a solute based on knowledge of the boiling-point elevation of its solution in CCI4, ATj = 0.357 °C, and the masses of solute and solvent. Table 13.3 gives fCj for the solvent (CCI4), fCj = 5.02 °C/m. 

Analyze and Plan We are given the boiling-point elevation of the solution, ATj, = 0.357°C, and Table 13.4 gives fCj, for the solvent (CC ), Kf, = 5.02°C/w . Thus, we can use Equation 13.11, AT, = Ki/ii, to calculate the molality of the solution. Then we can use molality and the quantity of solvent (40.0 g CCI4) to calculate the number of moles of solute. FinaUj the molar mass of the solute equals the number of grams per mole, so we divide the number of grams of solute (0.250 g) by the number of moles we have just calculated. 

The lowering of the freezing temperature ATj by solute can be treated in the same way as the boiling point elevation in Equations (16.15) to (16.22), with the result... 

In these equations, AHf and AHh are the latent heats of freezing and vaporization Tj and Tf are the boiling and freezing points of the solution Tb and Tf are the boiling and freezing points of the pure solvent ATj, (= Tb — Tb) is the elevation in the boiling point AT/ (= T/ — TJ) is the depression in the freezing point pi is the vapor pressure at temperature T of the solution and p° the vapor pressure over pure solvent at the same temperature II is the osmotic pressure of the solution. 

Figure 13.12 Phase diagrams of solvent and solution. Phase diagrams of an aqueous solution dashed lines) and of pure water solid lines) show that, by lowering the vapor pressure (AP), a dissolved solute elevates the boiling point ATJ and depresses the freezing point (ATf).

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