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P A = X A P A °

where P A is the partial pressure exerted by component A in the solution, P A ° 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

P solution = i P i = i X i P i °

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:

P solution = X solvent P solvent °

Calculation of a vapor pressure

Compute the vapor pressure of an ideal solution containing 92.1 g of glycerin, C 3 H 5 (OH) 3 , and 184.4 g of ethanol, C 2 H 5 OH, at 40 °C. The vapor pressure of pure ethanol is 0.178 atm at 40 °C. Glycerin is essentially nonvolatile at this temperature.

Solution

Since the solvent is the only volatile component of this solution, its vapor pressure may be computed per Raoult’s law as:

P solution = X solvent P solvent °

First, calculate the molar amounts of each solution component using the provided mass data.

92.1 g C 3 H 5 ( OH ) 3 × 1 mol C 3 H 5 ( OH ) 3 92.094 g C 3 H 5 ( OH ) 3 = 1.00 mol C 3 H 5 ( OH ) 3 184.4 g C 2 H 5 OH × 1 mol C 2 H 5 OH 46.069 g C 2 H 5 OH = 4.000 mol C 2 H 5 OH

Next, calculate the mole fraction of the solvent (ethanol) and use Raoult’s law to compute the solution’s vapor pressure.

X C 2 H 5 OH = 4.000 mol ( 1.00 mol + 4.000 mol ) = 0.800 P solv = X solv P solv ° = 0.800 × 0.178 atm = 0.142 atm

Check your learning

A solution contains 5.00 g of urea, CO(NH 2 ) 2 (a nonvolatile solute) and 0.100 kg of water. If the vapor pressure of pure water at 25 °C is 23.7 torr, what is the vapor pressure of the solution?

Answer:

23.4 torr

Got questions? Get instant answers now!

Elevation of the boiling point of a solvent

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:

Δ T b = K b m

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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Source:  OpenStax, Chemistry. OpenStax CNX. May 20, 2015 Download for free at http://legacy.cnx.org/content/col11760/1.9
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