Lecture Notes: Units of Energy
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Objectives
• Explain which phases (solid, liquid, and/or gas) are present in each region of a heating-cooling
curve
• Provide an intermolecular-force-based argument why temperature remains constant at a phase
transition
• Describe why heat absorbed/liberated during phase transitions is calculated differently than the
regions of positive slope
• Define the terms heat of fusion and heat of vaporization
• Explain the role of the First Law of Thermodynamics in our calculation of the molar heat of
fusion of ice
• Identify the three processes which must be highlighted in our calculation of the heat of fusion of
ice
Important Definitions
• Energy the ability to do work (thermal, electrical, mechanical, nuclear, light)
• Heat: energy transferred between a system and its surroundings as a result of temperature
difference
• Thermal energy: energy due to the random motion of molecules
• Temperature: measure of average molecular
CHM1016: Chemical Principles 2 Laboratory CJT 12/09
Lecture Notes: Units of Energy
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• Enthalpy Change (∆H): heat lost or gained at constant pressure (∆H = qP); the sum of the
internal-energy change and P-V work at constant pressure: ∆H = ∆E + p∆V
• Endothermic: a process which consumes or absorbs energy from the surroundings
• Exothermic: a process which releases or liberates heat into the surroundings
• Molar Enthalpy of Fusion (∆Ho
fus): amount of energy required to melt one mole of solid
Key Constants & Formulae:
1 Joule = 1 kg m2
/s2
4.184 J = 1.00 cal 1000 J = 1 kJ 1000 cal = 1 kcal
Cwater = 4.184 J/goC dwater = 1.00 g/oC
• Temperature Change: ∆T = Tfinal – Tinitial
• First Law of Thermodynamics: ∆Euniverse = ∆Esystem + ∆Esurroundings
• Heat-Flow Calculation: q=mC∆T
• Work calculation: w = -p∆V
• Energy Required to Melt Ice: q = n∆Ho
fus
• Safety glasses must be worn at all times!
• Ammonium Chloride - slightly toxic by ingestion
• Calcium Chloride - slightly toxic by ingestion
• Use caution when handling open flames.
Calculations:
Heat of Solution of NH4Cl
• The heat of solution NH4Cl is an endothermic process: NH4Cl(s) + heat NH4
+
(aq) + Cl-
(aq)
• This means heat is absorbed by this system from the surroundings.
• Heat is absorbed by the system, so the final temperature, Tf
, will be lower than the initial
temperature, Ti
-qsurr = + qsystem
qsurr = - (msys)(Csys)(Tf-Ti)
If we let the mass of the system equal the mass of the water plus the salt (50g + 5 g = 55 g) and the
specific-heat capacity of the system, C equal that of pure water (4.184 J/goC), calculating the heat
absorbed by the system is easy:
CHM1016: Chemical Principles 2 Laboratory CJT 12/09
Lecture Notes: Units of Energy
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qsurr = -(55.0g)(4.184 J/goC)(Tf-Ti)
To calculate the amount of heat absorbed per mole of NH4Cl, we need to include the molar mass of
NH4Cl ( ` = 53.4916 g/mol).
∆Ho
soln = qsys/nsalt =
−
molNH Cl
gNH Cl
gNH Cl
qsys
4
4
4 1_
53.4916
.5 00
• The above calculation generates a value in J/mol.
• Division by 1000J/1 kJ, generates the more commonly reports units of kJ/mol.
Heat of Solution of CaCl2
• The heat of solution of CaCl2 is an exothermic process: CaCl2(s) Ca2+
(aq) + 2 Cl-
(aq) + heat
• This means heat is released by this system and absorbed by surroundings.
• Heat is released by the system, the final temperature, Tf
, will be higher than the initial
temperature, Ti
+qsurr = -qsystem
q system = -(55.0 g)(4.184 J/goC)(Tf-Ti)
Again, to calculate the amount of heat liberated per mole of CaCl2, we need to include the molar mass of
CaCl2 (` =110.98 g/mol)
∆Ho
soln = qsys/nsalt =
−
2
2
2 1_
110.98
.5 00 molCaCl
gCaCl
gCaCl
qsys
• Again, the above calculation calculates the exothermic heat of solution in terms of J/mol.
• Division by 1000J/1 kJ, generates the more commonly reports units of kJ/mol.
The Molar Enthalpy of Fusion of Ice.
• Calculating the molar enthalpy of fusion of ice is an involved process
• To do this, we must recognize there are three unique processes occurring in this system
A. The Melting of Ice (Calculated as q = n∆Hfus)
B. The Cooling of Warm Water (Calculated as q = -mC(Tf-Ti)
C. The Warming of Ice Melted (Calculated as q = + mC(Tf-Ti)
• We recognize that both the melting and warming processes are endothermic, and involve an
input of energy from the surroundings.
CHM1016: Chemical Principles 2 Laboratory CJT 12/09
Lecture Notes: Units of Energy
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• Accordingly, the cooling of the warm water is an energy-releasing or exothermic process
All three processes are represented in the following diagram, which is called a Heating-Cooling Curve.
They have been coded both by color and letter, for students holding black-and-white copies of these
notes.
Calculating the molar heat of fusion of ice merely requires an algebraic rearrangement of the above
equations.
-qlost = + q gained
- [qwarm water (ww)] = + [qmelt ice (i) + qwarming of melted ice (wmi)]
Please note that the Tf
we use in the calculation below will be the same for both the cooled warm water
and the warmed melted ice.
-mwwCw(Tf-Ti, ww) = + [mi∆Hfus + mwmiCw(Tf-Twmi]
mi∆Hfus = -[mwwCw(Tf-Ti, ww) + mwmiCw(Tf-Ti, wmi)]
+
∆ = −
i
ww w f i, ww wmi w f i, wmi
m
H fus
This lab requires several calculations. Please remember to feature these calculations as part of the “Data
Sheet” portion of your lab write-up.
Instructions:
Heat of Solution of NH4Cl & CaCl2
1.) Measure 5.00 g salt (NH4Cl or CaCl2) on the laboratory balance.
2.) Measure exactly 50.0 mL deionized water in the graduated cylinder.
3.) Add water to the foam cup
4.) Record the initial temperature of the foam cup.
CHM1016: Chemical Principles 2 Laboratory CJT 12/09
Lecture Notes: Units of Energy
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5.) Add entire amount of salt to water in the cup.
6.) Stir mixture slowly with glass stirring rod.
7.) Record the final temperature for the salt—water mixture.
8.) Repeat steps (1.)-(7.) for the other salt.
The Molar Enthalpy of Fusion of Ice.
Preparation of Ice
1.) Weigh approximately 50g crushed ice on the laboratory balance.
2.) Add the ice to the foam cup.
Preparation of Warm Water
1.) Half fill a 250 mL beaker with deionized water.
2.) Place the water-filled beaker over a Bunsen-burner flame and heat until the temperature reaches
60oC.
3.) When the temperature reaches 60oC, pour the warm water up to the top of your 25 mL graduated
cylinder and wait approximately 2 minutes.
4.) Pour off the water in the graduated cylinder and then re-fill it with exactly 25 mL of warmed water.
5.) Record the temperature of the water in the graduated cylinder as Ti, w.
Combining the Ice & Water
1.) Add the warm water to the foam cup containing the ice
2.) Record the final temperature of the ice and water system.
3.) Decant all liquid from the ice-water mixture of the cup into your 100mL graduated cylinder
4.) Record the volume of liquid water.
5.) Calculate the volume of water melted as Vmelted water = V(Step 4) - 25 mL
6.) Calculate the mass of melting water as mmelted water = (dwater)(Vmelted water)
Sample Solution