CH1810 Lecture #2

Vapor Pressure of Liquids and Solutions

Vaporization and

Condensation

Kinetic Energy and Temperature

Molecules in a liquid are constantly in motion

Types of motion: vibrational, and limited rotational and translational

The average kinetic energy is proportional to the

temperature.

Some molecules have more kinetic energy than average,

and others have less.

Vaporization

If high energy molecules are at the surface, they may have enough energy

to overcome the attractive forces.

This will allow them to escape the liquid and become a vapor.

Note: The larger the surface area, the faster the rate of evaporation.

Only a small fraction of the molecules in a liquid have enough energy to escape.

Distribution of Thermal Energies

But, as the temperature increases, the fraction of the

molecules with “escape energy” increases.

Distribution of Thermal Energies

The higher the temperature, the faster the rate of evaporation.

Distribution of Thermal Energies

Condensation

Molecules of the vapor will lose energy through molecular collisions.

Some of the molecules will get captured back into the liquid.

Some may stick and gather together to form droplets of liquid.

Evaporation vs. Condensation

Vaporization and condensation are opposite processes.

In an open container, the vapor molecules generally spread out faster than they can condense, and there is a

net loss of liquid.

In a closed container, the vapor is not allowed to spread out indefinitely; at some time the rates of vaporization and

condensation will be equal.

Effect of Intermolecular Attraction

The weaker the attractive forces, the faster the rate of evaporation.

Liquids that evaporate easily are said to be volatile. e.g., gasoline

Liquids that do not evaporate easily are called nonvolatile.

e.g., motor oil

Dynamic Equilibrium

When two opposite processes reach the same rate so that there is no gain or loss of material, we call it a dynamic equilibrium.

This does not mean there are equal amounts of vapor and liquid – it means that they are changing by equal amounts.

Vapor Pressure

The pressure exerted by the vapor when it is in dynamic equilibrium with its liquid is called the

vapor pressure.

The weaker the attractive forces between the molecules, the more molecules will be in the vapor.

Therefore, the weaker the attractive forces, the higher the vapor pressure.

Vapor Pressure of Water at Various Temperatures

Vapor Pressure vs. Temperature

Increasing the temperature increases the number of molecules able to escape the liquid.

The net result is that as the temperature increases, the vapor pressure increases.

Small changes in temperature can make big changes in vapor pressure.

Boiling Point

When the temperature of a liquid reaches a point where its vapor pressure is the same as the external pressure,

vapor bubbles can form anywhere in the liquid.

This phenomenon is what is called boiling and the temperature at which the vapor pressure = external

pressure is the boiling point.

Vapor Pressure Curves

760 mmHg

Which of the liquids is the most volatile?Which liquid has the strongest intermolecular forces?

Which of the liquids has the highest normal boiling point?

The normal boiling point is the temperature at which the vapor pressure of the liquid = 1 atm.

The lower the external pressure, the lower the boiling point.

Normal Boiling Point

(a) The vapor pressures of water, ethanol, and diethyl ether show a nonlinear rise when plotted as a function of temperature.

(b) A plot of ln Pvap versus 1/T (Kelvin) for water shows a linear relationship.

(c) The slope of the plot of ln Pvap and (1/T) is proportional to the heat of vaporization of the liquid.

Vapor Pressure and Temperature

Clausius–Clapeyron Equation

The graph of vapor pressure vs. temperature is an exponential

growth curve.

The logarithm of the vapor pressure vs. inverse absolute

temperature is a linear function.

y  =  ax  +b

Clausius–Clapeyron Equation

The equation below can be used with just two measurements of vapor pressure and temperature.

It can also be used to predict the vapor pressure if you know the heat of vaporization and the normal boiling point.

Clausius–Clapeyron Equation 2-Point Form

The vapor pressure of a liquid is the pressure exerted by a gas in equilibrium with its liquid phase in a sealed container.

The rates of evaporation and condensation are equal.

Vapor Pressure of a Liquid

Factors Affecting Vapor Pressure

Temperature: as T increases, KE increases, V.P. increases

Intermolecular forces: Stronger forces, higher KE needed to enter gas phase, V.P. decreases

Presence of nonvolatile solute: Affects rate of evaporation, decreases V.P. of solution compared to pure solvent

Raoult’s Law: The vapor pressure of solution is equal to the vapor

pressure of the pure solvent multiplied by the mole fraction of the solvent in the solution.

Psolution = 𝛘solvent• Psolvent

Vapor pressure lowering:

The vapor pressure of solution of a nonvolatile solute is decreased because some of the surface area of the solution is occupied by solute molecules

A colligative property of solutions

Ideal solution: One that obeys Raoult’s law

Vapor Pressure of Solutions

A Demonstration

Mixing of Volatile Solutes

Fractional Distillation

Method of separating a mixture of compounds on the basis of their different

boiling points.

Vapor phase enriched in more volatile component

Fractional Distillation

Boiling  points:        -­‐  Heptane  =  98C        -­‐  Octane  =  126  C  

(a) Ideal situation. Fractional distillation of a mixture of heptane and octane produces two plateaus at the boiling points of the two components.

Boiling  points:        -­‐  Heptane  =  98C        -­‐  Octane  =  126  C  

Fractional Distillation

Solutions of Volatile Components

For mixtures containing more than one volatile component:

Partial pressure of each volatile component contributes to total vapor pressure of solution.

Ptotal = 𝛘1P1º+ 𝛘2P2º + 𝛘3P3º + …

Where 𝛘i = mole fraction of component i, and

Piº = equilibrium vapor pressure of pure volatile component at a given temperature

Ideal Solutions

In ideal solutions, the resulting solute-solvent interactions are equal to the sum of the broken dilute-

solute and solvent-solvent interactions.

Raoult’s Law

Real (Nonideal) SolutionsDeviations from Raoult’s Law:

Due to differences in solute–solvent and solvent–solvent interactions (dashed lines = ideal behavior)

Negative deviations Positive deviations

Practice Problem: Vapor Pressure of Solution

1) A solution contains 100.0 g of water (MW = 18.0 g/mol) and 25.00 g of ethanol (MW = 44.0 g/mol). What are the mole fractions of water and ethanol, and the vapor pressure of the solution at 25oC? (Pwater = 23.8 torr; Pethanol = 58.7 torr)

100.0 g H2O x = 5.549 mol H2O1.00 mol H2O

18.02 g H2O

25.00 g C2H6O x = 0.5426 mol C2H6O1.00 mol C2H6O

46.07 g C2H6O 6.092 total moles

Pwater = (𝛘water)(23.8 torr) = ( )(23.8 torr) = 21.7 torr5.5496.092

Pethanol = (𝛘water)(58.7torr) = ( )(58.7 torr) = 5.23 torr0.54266.092

26.9 torr