Phase Changes

Courtesy www.lab-initio.com

The BIG Idea

• Students know energy is released when a material condenses or freezes and is absorbed when a material evaporates or melts.

Water phase changes

Temperature remains __________during a phase change.

constant

Phase Changes

Energy must be absorbed to change from a solid to a liquid; heat of fusion or enthalpy of fusion, DHfus

Energy must be absorbed to change from a liquid to a gas; heat of vaporization or enthalpy of vaporization, DHvap

Phase Changes

For water, the DHfus = 6.02 kJ/mol

the DHvap = 40.7 kJ/mol

Why is the DHvap much higher than DHfus?

Example #1

How much energy is needed to convert 25g of ice at -15C to 200C steam?

Plan: Follow the heating curve to determine where the energy goes at each step in the process

Can you identify the FIVE steps in the process?

Example #1 Continued

Step 1: heat ice from -15C to 0C Cice = 2.03J/gC

q = mCDT q = 25g (2.03J/gC)(15C) = 761.25J = .761kJ

Step 2: phase change (s) (l) 25g (1mol/18.02g) (6.02kJ/mol) = 8.35kJ

Step 3: heat water from 0C to 100C Cwater = 4.18J/gC

q=mCDT q=25g (4.18J/gC)(100C)= 10450J = 10.4kJ

Example #1 Continued

Step #4: phase change (l) (g) 25g (1mol/18.02g)( 40.7kJ/mol) = 56.5kJ

Step #5: heat steam from 100C to 200C Csteam = 2.0J/gC

q=mCDT q = 25g (2.0J/gC)(100C) = 5000J = 5kJ

Total heat required: 0.761kJ + 8.35kJ + 10.4kJ + 56.5kJ + 5kJ = 81kJ

Now let’s try one:

The molar heat of fusion for benzene, C6H6, is 9.92kJ/mol. The molar heat of vaporization is 30.7kJ/mol.

Calculate the heat required to melt 8.25g of benzene at its normal melting point.

1.05kJCalculate the heat required to vaporize 8.25g of benzene at its normal boiling point.

3.24kJWhy is the heat of vaporization more than 3 times the heat of fusion?

Another Example

You have a 75g sample of water at 125C. What phase(s) are present when 215kJ of energy is removed from the sample?

Hint: Identify the steps on the cooling curve that may occur: Energy to cool from 125C to 100C Energy to phase change from a vapor to a liquid Energy to cool from 100C to 0C Energy to phase change from a liquid to a solid Energy to cool the solid

A mixture of H2O(l) and H2O(s) will be present

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 PointBoiling Point of Water at Various Locations

Location Feet above sea level

Patm (kPa) Boiling Point (C)

Top of Mt. Everest, Tibet 29,028 32 70

Top of Mt. Denali, Alaska 20,320 45.3 79

Top of Mt. Whitney, California 14,494 57.3 85

Leadville, Colorado 10,150 68 89

Top of Mt. Washington, N.H. 6,293 78.6 93

Boulder, Colorado 5,430 81.3 94

Madison, Wisconsin 900 97.3 99

New York City, New York 10 101.3 100

Death Valley, California -282 102.6 100.3

Water

Phase Diagram Represents phases as a function of temperature and pressure. Critical temperature: temperature above which the vapor can not be liquefied. Critical pressure: pressure required to liquefy AT the critical temperature. Critical point: critical temperature and pressure (for water, Tc = 374°C and 218 atm).

Phase changes by Name

Carbon dioxidePhase

Diagram for

Carbondioxide

CarbonPhase

Diagram for

Carbon

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 heat of vaporization from the slope of the line.

• R = 8.314 J/Kmol Convert all Temps to Kelvin

Example #1

Calculate the heat of vaporization of a compound that has a vapor pressure of 560 torr at 25C and a normal boiling point of 45C.

Hint: normal BP occurs at 1atm (760 torr)Variation of the C-C Equation is used:

ln (P1/P2) = (DHvap/R )(1/T2 – 1/T1)

ln(560torr/760torr) = (DH/8.314J/Kmol) (1/318 – 1/298) 12033J, 12kJ = DH

Example #2

In Breckenridge, CO, the typical atmospheric pressure is 520 torr. What is the boiling point of water (DH=40.7kJ/mol) in Breckenridge? Hint: 760torr BP=100C / 373K

ln(520torr/760torr)= (40,700J mol-1 /8.314)(1/373 - 1/T) -0.379 = 4896(1/373 - 1/T)

-7.75 E -5 = (1/373 - 1/T)1/T = 2.76 E -3T = 363K

Example #3The temperature inside a pressure cooker is 115C. Calculate the vapor pressure of water inside the pressure cooker.

ln (P/1atm) = (40,700kJ mol-1 / 8.314)(1/373 – 1/388) lnP = 0.51 P = e.51 = 1.7atm

What would be the temperature inside the pressure cooker if the vapor pressure of water was 3.50atm?

ln(3.50/1.00) = (40.7kJ mol-1 / 8.314)(1/373 – 1/T) 413K = T

Example #4

The normal boiling point for acetone is 56.5C . At an elevation of 5600ft, the atmospheric pressure is 630 torr. What would be the boiling point of acetone at this elevation? (DHvap = 32.0kJ/mol).

ln(760/630) = (32kJ mol-1/8.314)(1/T – 1/330) 325K = T

What would be the vapor pressure of acetone at 25C at this elevation?

ln(630/P) = (32kJ mol-1/8.314)(1/298 – 1/325) P = 221 torr