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where P A is the partial pressure exerted by component A in the solution, is the vapor pressure of pure A, and X A is the mole fraction of A in the solution. (Mole fraction is a concentration unit introduced in the chapter on gases.)
Recalling that the total pressure of a gaseous mixture is equal to the sum of partial pressures for all its components (Dalton’s law of partial pressures), the total vapor pressure exerted by a solution containing i components is
A nonvolatile substance is one whose vapor pressure is negligible ( P ° ≈ 0), and so the vapor pressure above a solution containing only nonvolatile solutes is due only to the solvent:
First, calculate the molar amounts of each solution component using the provided mass data.
Next, calculate the mole fraction of the solvent (ethanol) and use Raoult’s law to compute the solution’s vapor pressure.
23.4 torr
As described in the chapter on liquids and solids, the boiling point of a liquid is the temperature at which its vapor pressure is equal to ambient atmospheric pressure. Since the vapor pressure of a solution is lowered due to the presence of nonvolatile solutes, it stands to reason that the solution’s boiling point will subsequently be increased. Compared to pure solvent, a solution, therefore, will require a higher temperature to achieve any given vapor pressure, including one equivalent to that of the surrounding atmosphere. The increase in boiling point observed when nonvolatile solute is dissolved in a solvent, Δ T b , is called boiling point elevation and is directly proportional to the molal concentration of solute species:
where K b is the boiling point elevation constant , or the ebullioscopic constant and m is the molal concentration (molality) of all solute species.
Boiling point elevation constants are characteristic properties that depend on the identity of the solvent. Values of K b for several solvents are listed in [link] .
Boiling Point Elevation and Freezing Point Depression Constants for Several Solvents | ||||
---|---|---|---|---|
Solvent | Boiling Point (°C at 1 atm) | K b (C m −1 ) | Freezing Point (°C at 1 atm) | K f (C m −1 ) |
water | 100.0 | 0.512 | 0.0 | 1.86 |
hydrogen acetate | 118.1 | 3.07 | 16.6 | 3.9 |
benzene | 80.1 | 2.53 | 5.5 | 5.12 |
chloroform | 61.26 | 3.63 | −63.5 | 4.68 |
nitrobenzene | 210.9 | 5.24 | 5.67 | 8.1 |
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