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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.


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?


23.4 torr

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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

Questions & Answers

who are the alchemist?
Victor Reply
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read Corinthians 5 verses 50 to the end of the chapter then read revelations chapter 2 verse 17
The word "Alchemy" comes from the forgotten name for Ancient Egypt, Khemmet. Khem was the name for the Egyptian Empire, but the actual land of Egypt was called Khemmet because the "T" on the end of a word denoted a physical location on Earth and not just an idea.
What's the mass number of carbon
Charlie Reply
first Faraday's law
mass number of carbon is 12.
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atomic number of oxygen is 8
which quantum number divides shell into orbitals?
Tomiwa Reply
what is atom
Desmond Reply
an atom is a smallest indivisible part of an element
an atom is the smallest part of an element that takes part in a chemical reaction
wat is neutralization
Dubem Reply
when any acid reacts with base to decrease it's acidity or vice-versa to form salt and solvent.. which is called neutralization
explain buffer
buffer is a solution which resists changes in pH when acid or alkali added to it..
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buffer is the solution which resist the change in pH by addition of small amount of acid or alkali to it
neutralisation is the process of mixing of a acid and a base to form water and corresponding salt
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Princewill Reply
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what is gases
Wesike Reply
Its one of the fundamental sate of matter alone side with liquid, solid and plasma
What is chemical bonding
To my own definitions. It's a unit of measurement to express the amount of a chemical substance.
Ozoaniehe Reply
What is mole
It's the unit of measurements used to express the amount of chemical substance.
What is pressure
Stellamaris Reply
force over area
force applied per unit area
force applied per unit area
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Aditya Reply
Why does carbonic acid don't react with metal
Some metals will react depending on their Standard Electrode Potential. Carbonic acid is a very weak acid (i.e. a low hydrogen ion concentration) so the rate of reaction is very low.
sample of carbon-12 has a mass of 6.00g. How many atoms of carbon-12 are in the sample
Emokiniovo Reply
a sample of carbon-12 has a mass of 6.00g. How many atoms of carbon-12 are in the sample
Sharmin Reply
an object of weight 10N immersed in a liquid displaces a quantity of d liquid.if d liquid displaced weights 6N.determine d up thrust of the object
ugonna Reply
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We don't fall off. If set off in any direction in a straight line and keep going. You'll end up back where you started.
earth is spherical
Also, every other planet is spherical as that is the most energy efficient shape. gravity pulls equally on all areas. Sphere.

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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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