Vapor Pressure
Vapor Pressure
Pressure of the vapor present when equilibrium is achieved
between the rate of vaporization and the rate of condensation.
At the boiling point, the Patm = Pvapor
As the vapor pressure on a pot of water is reduced, the energy
needed to boil that water is also reduced.
Pressure Cooker: By increasing the vapor pressure, additional
energy is needed for the water to boil, therefore the water can
boil at temperatures above 100C.
Effect of Pressure on Boiling Point
Vapor Pressure vs. Temperature
As the temperature increases, a greater number of molecules
have sufficient kinetic energy to convert from the liquid to the
vapor phase.
There is a nonlinear relationship between the vapor pressure of
a liquid and temperature.
Vapor Pressure vs. Temperature
The Clausius – Clapeyron Equation
• A mathematical expression which relates the variation of
vapor pressure to temperature
• ln P = (-DHvap/RT) + C where C is a constant
• IMPORTANCE:
• When the ln P is plotted vs (1/T) you create a line where the
slope is equal to the –DHvap/R
• Which means you can calculate the enthalpy of vaporization
from the slope of the line.
• R = 8.314 J/Kmol
Convert all Temps to Kelvin
Vapor Pressure of Solutions
• A nonvolatile solute lowers the vapor pressure of the solution.
• The molecules of the solvent
must overcome the force of
both the other solvent
molecules and the
solute molecules.
Raoult’s Law:
•Psoln = csolvent x Psolvent
• Vapor pressure of the solution = m ole fraction of solvent x
vapor pressure of the pure solvent
• Applies only to an ideal solution where the solute doesn’t
contribute to the vapor pressure.
• Water has a higher vapor pressure than a solution
Aqueous
Solution
Pure water
• Water evaporates faster from for water than solution
Aqueous
Solution
Pure water
• The water condenses faster in the solution so it should all
end up there.
Aqueous
Solution
Pure water
Practice Problem
• A solution of cyclopentane with a nonvolatile compound has
vapor pressure of 211 torr. If vapor pressure of the pure liquid
is 313 torr, what is the mole fraction of the cyclopentane?
• Psoln = XcpPcp
• 211 torr = Xcp (313 torr)
• .674
Try one on your own
• Determine the vapor pressure of a solution at 25 C that has
45 grams of C6H12O6, glucose, dissolved in 72 grams of H2O.
The vapor pressure of pure water at 25 C is 23.8 torr.
• Psolution= Xsolvent Psolvent
• Psolution = .941(23.8 torr)
• Psolution = 22.4 torr
Ideal solutions
• Liquid-liquid solutions where both are volatile.
• Modify Raoult’s Law to
• Ptotal = PA + PB =
cAPA0 + cBPB0
• Ptotal = vapor pressure of mixture
• If this equation works then the solution is ideal.
Vapor Pressure of solution
Deviations
•
•
•
•
If solvent has a strong affinity for solute (H bonding).
Lowers solvent’s ability to escape.
Lower vapor pressure than expected.
Negative deviation from Raoult’s law.
• DHsoln is large and negative exothermic.
• Endothermic DHsoln indicates positive deviation.
Vapor Pressure
Positive deviationsWeak attraction between
solute and solvent
Positive ΔHsoln
χA
χb
Vapor Pressure
Negative deviationsStrong attraction between
solute and solvent
Negative ΔHsoln
χA
χb
Problem #1
• The vapor pressure of a solution containing 53.6g of glycerin
C3H8O3 in133.7g ethanol C2H5OH is 113 torr at 40C. Calculate
the vapor pressure of pure ethanol at 40C assuming that the
glycerin is a non volatile, nonelectrolyte solute in ethanol.
Answer to #1
Psoln = Xeth Peth
113torr = 2.90mol/3.48mol (Peth)
135.6 torr = Peth
Problem #2
• At a certain temperature, the vapor pressure of pure benzene
C6H6 is 0.930atm. A solution was prepared by dissolving 10.0g
of a nondissociating, nonvolatile solute in 78.11g of benzene
at that temperature. The vapor pressure was found to be
0.900atm. Assuming the solution behave ideally, determine
the molar mass of the solute.
Answer #2
Psoln = XbenzenePbenzene
.900atm = Xbenzene (.930atm)
Xbenzene = .9677
Xsolute = .0323
MM = 10.0g/.0323mol = 310g/mol
Problem #3
A solution of NaCl in water has a vapor pressure of 19.6 torr at
25C. What is the mol fraction of solute particle in this solution if
the vapor pressure of water is 23.8 torr at 25C?
Answer #3
Psoln = XwaterPwater
19.6torr = Xwater(23.8torr)
.824 = Xwater therefore Xsolute = .176
Problem #3
For the same problem as #3:
What is the vapor pressure of the solution at 45C if the vapor
pressure of water is 71.9 torr at 45C?
Answer #3
Psoln = .824(71.9torr)
Psoln = 59.2 torr
Problem #4
A solution is made from 0.0300mol CH2Cl2 and 0.0500mol CH2Br2
at 25C. Assuming that the solution is ideal, calculate the %
composition of the vapor at 25C.
PCH2Cl2 = 133 torr
PCH2Br2 = 11.4 torr
Answer #4
Psoln = XCH2Cl2 P + XCH2Br2 P
Psoln = (.03/.08)(133torr) + (.05/.08)(11.4 torr)
Psoln = 57.0 torr
XCH2Cl2 = 49.9 / 57 = .875 = 87.5%
XCH2Br2 = 7.13 / 57 = .125 = 12.5%