General Chemistry 2
Science, Technology, Engineering, and Mathematics
Try It!
Calculate the amount of energy needed
to raise the temperature of 300 grams
of water in the liquid state from 20 ºC to
27 ºC.
2
Lesson 2.3
Heating and Cooling
Curves
General Chemistry 2
Science, Technology, Engineering, and Mathematics
When you take the ice out of the refrigerator, it starts to
melt.
4
Water can be further
heated in a kettle to
boil, forming water
vapor rushing out
and mixing with the
air.
5
As water changes
phase, hydrogen
bonds are broken,
along with weaker
intermolecular forces
of attraction.
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But how much heat is needed to transform ice into water
vapor? Is there a way to represent these heat changes and
interpret the energetics of phase changes more
systematically?
In this lesson, you will learn how to construct and interpret
heating and cooling curves and calculate the associated
heat changes at each step.
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How do you interpret
heating and cooling curves?
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Energetics of Phase Changes: A Recall
Changes in phases are
accompanied by energy
changes → molar
enthalpies
The phase changes and their energy
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Energetics of Phase Changes: A Recall
Phase changes only occur at specific temperatures and
pressures
○ freezing of water: at 0 OC and 1 atm
○ evaporation of water: at 100 OC and 1 atm
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Energetics of Phase Changes: A Recall
For phase changes at constant P,
where q= heat absorbed or released (J);
n = amount of substance (moles), and
ΔH =molar heat associated with phase change (J/mol).
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Energetics of Phase Changes: A Recall
For temperature changes,
where q = heat absorbed or released, J;
m =mass, g;
c = specific heat, J/(g x OC-1); and
ΔT = change in temperature.
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Heating and Cooling Curves
● Transformations of substances in real life involve
multiple phase changes and temperature changes.
● There are instances when a substance in its solid state
is converted into its gaseous state.
● In between phase changes, additional heat is needed
to satisfy temperature changes.
13
Heating and Cooling Curves
The amount of heat in
complex phase
transformations can be
tracked in heating and
cooling curves.
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Heating and Cooling Curves
In these curves, the
temperature (y-axis) is
plotted against total heat
changes (x-axis).
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Heating and Cooling Curves
This heating curve shows
the heat associated with
the transformation of 1
mol of ice initially set at –
25 ºC and 1 atm to steam
at 125 ºC and 1 atm.
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Heating and Cooling Curves
How do we calculate the
amount of heat associated
with the entire process?
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How can one calculate the
heat associated with
consecutive phase
transformations?
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Heating and Cooling Curves
The amount of heat can be
calculated by adding all
heat absorbed from each
phase and temperature
change.
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Heating and Cooling Curves
The process can be divided
as represented by the
segments.
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Heating and Cooling Curves
Blue segments represent
temperature changes
without phase change,
while red segments
represent phase changes
without temperature
change.
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Heating and Cooling Curves
Segment AB
Segment AB represents a
change in temperature of
ice from –25 ºC to 0 ºC.
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Heating and Cooling Curves
Segment BC
The ice cube starts to melt
from point B and ends with
point C.
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Heating and Cooling Curves
Segment CD
Segment CD represents a
change in temperature of
water from 0 ºC to 100 ºC.
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Heating and Cooling Curves
Segment DE
Water starts to boil from
point D and ends with
point E.
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Heating and Cooling Curves
Segment EF
Segment EF represents a
change in temperature of
steam from 100 ºC to 125
ºC.
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Heating and Cooling Curves
Total Heat
Total heat is additive, from
point A to F.
What is the total heat of the
phase change of ice to steam
from point A to F?
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Heating and Cooling Curves
Constructing Heating Curves
● To create a heating curve, one must plot temperature
(y-axis) against heat (x-axis).
● Processes, where heat is absorbed to increase
temperature, are represented by lines slanted
upright, while horizontal lines represent phase
changes at a constant temperature.
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Heating and Cooling Curves
Constructing Cooling Curves
● Cooling curves are the exact reverse of heating curves.
● Processes that require the release of heat are
represented by lines sloping downwards, while
horizontal lines still represent phase changes.
● A cooling curve can be produced from the heating
curve by reading the plot from the top right to bottom
left.
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Remember
In heating curves, processes with
temperature changes without phase change
are represented by a line slanting upward,
while horizontal lines represent processes
with phase changes without temperature
change.
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How can you describe the
cooling curve when steam at
150 ºC is transformed into
–15 ºC?
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Let’s Practice!
Calculate the heat required to transform 5 grams of
ice at -10 ºC to liquid water at 80 ºC. Use the following
specific heats: cice = 2.108 J/(g ✕ ºC), cwater = 4.186 J/(g ✕
ºC), cvapor = 1.97 J/(g ✕ ºC). Water has a heat of fusion
(ΔHfus) of 6 000 J/mol, and a heat of vaporization
(ΔHvap) of 40 700 J/mol.
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Let’s Practice!
Calculate the heat required to transform 5 grams of
ice at -10 ºC to liquid water at 80 ºC. Use the following
specific heats: cice = 2.108 J/(g ✕ ºC), cwater = 4.186 J/(g ✕
ºC), cvapor = 1.97 J/(g ✕ ºC). Water has a heat of fusion
(ΔHfus) of 6 000 J/mol, and a heat of vaporization
(ΔHvap) of 40 700 J/mol.
The total heat required to transform 5 grams of ice at
-10 ºC to liquid water at 80 ºC is 3446.5 J.
33
Try It!
Calculate the heat required to transform
15 grams of ice at -5 ºC to liquid water at
90 ºC. Use the following specific heats: cice
= 2.108 J/(g ✕ ºC), cwater = 4.186 J/(g ✕ ºC),
cvapor = 1.97 J/(g ✕ ºC). Water has a heat of
fusion (ΔHfus) of 6000 J/mol, and a heat of
vaporization (ΔHvap) of 40 700 J/mol.
34
Let’s Practice!
Calculate the heat required to transform a gram of
ice at -50 ºC to steam at 120 ºC. Use the following
specific heats: cice = 2.108 J/(g ✕ ºC), cwater = 4.186 J/(g ✕
ºC), cvapor = 1.97 J/(g ✕ ºC). Water has a heat of fusion
(ΔHfus) of 6 000 J/mol, and a heat of vaporization
(ΔHvap) of 40 700 J/mol.
35
Let’s Practice!
Calculate the heat required to transform a gram of
ice at -50 ºC to steam at 120 ºC. Use the following
specific heats: cice = 2.108 J/(g ✕ ºC), cwater = 4.186 J/(g ✕
ºC), cvapor = 1.97 J/(g ✕ ºC). Water has a heat of fusion
(ΔHfus) of 6 000 J/mol, and a heat of vaporization
(ΔHvap) of 40 700 J/mol.
The total heat required to transform a gram of ice at
-50 ºC to liquid water at 120 ºC is 3157.8 J.
36
Try It!
Calculate the heat required to transform
10 grams of ice at -200 ºC to steam at 200
ºC. Use the following specific heats: cice =
2.108 J/(g ✕ ºC), cwater = 4.186 J/(g ✕ ºC),
cvapor = 1.97 J/(g ✕ ºC). Water has a heat of
fusion (ΔHfus) of 6 000 J/mol, and a heat of
vaporization (ΔHvap) of 40 700 J/mol.
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Let’s Practice!
Calculate the heat required to transform a mole of
ice that underwent the change from A to F described
in the heating curve next slide. Use the following
specific heats: cice = 2.108 J/(g ✕ ºC), cwater = 4.186 J/(g ✕
ºC), cvapor = 1.97 J/(g ✕ ºC). Water has a heat of fusion
(ΔHfus) of 6 000 J/mol, and a heat of vaporization
(ΔHvap) of 40 700 J/mol.
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Let’s Practice!
39
Let’s Practice!
Calculate the heat
required to transform a
mole of ice that
underwent the change
from A to F described in
the heating curve.
The total heat
required is 56069.9 J.
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Check Your Understanding
Identify if the following statements are true or false.
1. When ice melts, the temperature remains at 0 ºC.
2. In a heating curve, the x-axis is temperature, in ºC, and
the y-axis is heat added, in J.
3. Above 100 ºC, the relevant specific heat to be used is
that of steam.
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Check Your Understanding
Use the cooling curve for a
hypothetical substance Z shown
to answer the questions that
follow.
1. What is the boiling point of the
hypothetical substance Z?
2. Which segment represents
condensation?
3. How long does it take for
gaseous Z to completely liquefy?
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Let’s Sum It Up!
● Heating and cooling curves are used to track heat
changes associated with complex phase
transformations.
● A heating curve is produced when the temperature
changes (y-axis) are plotted against heat changes (xaxis).
● A cooling curve can be constructed from a heating curve
by reading the latter from top right to bottom left.
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Key Formulas
Concept
Energy change
without phase
changes
Formula
where
● m is mass (in g);
● c is specific heat (in
J/(g✕0C)), and
● ΔT is the change in
temperature.
Description
Use this formula
when the material
undergoes
temperature
changes but not
phase changes.
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Key Formulas
Concept
Energy change
during phase
changes
Formula
where
● q is the amount of heat,
● n is the number of moles,
and
● ΔH is the molar enthalpy of
the specific process.
Description
Use this formula
when the material
undergoes phase
changes but its
temperature does
not change.
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Challenge Yourself
In a heating curve, temperature (in
ºC) is plotted against heat changes (in
J). Changes in temperatures for a
specific state of a substance are
represented by slanted lines. What
does the slope of these diagonal lines
represent? Briefly explain its
significance.
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Bibliography
Chang, Raymond, and Kenneth A. Goldsby. General Chemistry: The Essential Concepts. New York:
McGraw-Hill, 2014.
Handwerker, Mark J. Science Essentials. San Francisco, CA.: Jossey-Bass, 2005.
Hawe, Alan, Dan Davies, Kendra McMahon, Lee Towler, Chris Collier, and Tonie Scott. Science 5–11: A
Guide for Teachers. 2nd ed. New York, NY: David Fulton Publishers, 2009.
Petrucci, Ralph H. General Chemistry: Principles and Modern Applications. Toronto, Ont.: Pearson
Canada, 2011.
Silberberg, Martin S. Principles of General Chemistry. New York: McGraw-Hill, 2013.
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