EXPERIMENT 9
Thermochemistry:
Hess’ Law and the Heat of Formation of MgO
Outcomes
After completing this experiment, the student should be able to:
1. Differentiate between exothermic and endothermic reactions.
2. Demonstrate the use of Hess’ Law to determine heat of formation.
3. Write balanced thermochemical equations.
Introduction
In this experiment, you will measure the heat effect of a chemical reaction. In addition to chemical
change, reactions also involve differences in energy between products and reactants. For instance, a
combustion reaction such as:
CH4(g) + 2O2(g) → CO2(g) + 2 H2O(l)
releases a lot of “chemical energy”, which is given off to the surroundings in the form of heat. We call
this an exothermic reaction, exothermic means heat is released by the reaction. On the other hand for
instance the reaction:
CaCO3(s) → CaO(s) + CO2(g)
needs a lot of heat to proceed. We call this an endothermic reaction, as the reaction proceeds we have
to provide heat energy from the outside.
Heat effects of chemical and biological processes are measured using an instrument called a
calorimeter. A calorimeter can be a very simple instrument or set-up, such as in this experiment, or it
can be a very sophisticated (and expensive) instrument used for research purposes, or even large and
complex instruments for measuring whole body heat effects such as used for instance in sports
medicine.
When a chemical reaction takes place, some bonds are broken, and new bonds are made. The net
result is an overall energy change which manifests itself in the form of heat. The energy change for a
reaction Products → Reactants is given the symbol ΔE, where Δ stand for the difference in internal
energy content: ΔE(products − reactants). Most of the textbooks use the symbol ΔE, many other
textbooks will use the symbol U and ΔU for energy.
The SI unit for both heat and energy is the joule (J). J = N.m (force x distance). For heat effects we
commonly use the symbol q. An older unit used for heat is the calorie: 1 calorie is the amount of heat
needed to increase the temperature of 1 g of liquid water by 1 oC.
1 cal = 4.184 J
In some disciplines including organic chemistry the calorie and kilocalorie (kcal = 1000 cal)) are still
commonly used. In particular in food science, you will still see the unit Cal (note the capital C), which
is in fact a kcal! The packaged food industry now also reports energy content in kilojoules, kJ.
When a chemical reaction takes place in an open beaker or flask in the laboratory, the pressure P is
constant (at 1 atm, or 760 mm Hg, or 101,325 Pa), and when the reaction involves a volume change
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for instance when gases are produced, the energy change of the reaction is used to produce heat, but
also do work, because the gas formed has to “push away” the atmosphere around it. As a result, the
measured heat effect at constant pressure, qp equals the enthalpy change, ΔH:
ΔHreaction ≡ qp,reaction
(1)
Where qp stand for the heat effect at constant pressure. In other words, the enthalpy change ΔH equals
the heat effect as measured at constant pressure.
We remember that when a reaction produces heat, meaning that the reaction gives off heat to the
surroundings, we speak of an exothermic reaction, and we define the sign of qp and therefore also ΔH
as negative, because the system loses this enthalpy.
For exothermic reactions:
ΔH and qp are negative; the system loses heat (enthalpy) and the
surroundings gains this heat.
And the opposite, when the reaction takes up heat from the outside we speak of an endothermic
reaction, and ΔH is define as positive, because the system gains this enthalpy.
For endothermic reactions
ΔH and qp are positive; the system gains heat (enthalpy) and the
surroundings transfer this heat to the system.
We can speak of enthalpy of reaction, enthalpy of combustion, enthalpy of dissociation, enthalpy of
evaporation, etc., it always means the heat effect of a particular process carried out at constant
pressure conditions.
We define the enthalpy of formation as “the heat effect (at constant pressure again) of an (often
hypothetical) reaction where a compound is formed from its constituent elements under standard
conditions, and in the form in which the elements naturally occur under standard conditions”, symbol
ΔHfo. For instance, the formation reaction of magnesium oxide, MgO is:
Mg(s) + ½O2(g) → MgO(s)
ΔHrxn = ΔHfo(MgO) = −601.7 kJ/mol
Note the minus sign: heat is evolved (given off) in this formation reaction. Standard enthalpies of
formation are tabulated for tens of thousands of compounds, and we can use these tabulated values to
predict the enthalpy change of chemical reactions, as shown below. Note that by the definition,
enthalpies of formation of elements in the form in which they naturally occur (e.g. H2 not H, I2(s), not
I, Fe(s), etc.) are always zero.
The enthalpy change for a reaction, ΔH, is the difference between the standard enthalpy of formation
of the products and the standard enthalpy of formation of the reactants
ΔHreaction = Σ(ΔHoproducts) – Σ(ΔHoreactants)
(2)
If, in addition, the reaction is carried out at constant pressure, we have already seen that the enthalpy
of reaction is equal to the heat of reaction, qp
ΔHreaction = qp,reaction
(constant P)
(3)
Hess’s Law states, ″Heats of reactions are additive in the same way as the reactions to which they
pertain are additive″.
For instance, if for the formation reaction:
H2(g) + ½O2(g) → H2O(l)
Then for the reaction:
2H2 + O2 → 2H2O
And for the reverse reaction:
ΔH = −286 kJ
ΔH = −572 kJ (2x(−286))
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H2O(l) → H2(g) + ½O2(g)
ΔH = +285 kJ (−(−285))
Hess’s law is the basis for using enthalpies of formation to calculate enthalpies of reaction:
ΔHreaction = Σ(ΔHoproducts) – Σ(ΔHoreactants)
(4)
Determining the heat of reaction, qp,reaction
In this experiment you will use an open adiabatic calorimeter. Open because we perform the reaction
at constant atmospheric pressure, and adiabatic because we insulate the reacting system so that no
heat is transferred to or from the laboratory environment. This means that for an exothermic reaction
(ΔHreaction negative) the heat produced by the reaction is used only to increase the temperature of the
calorimeter and its contents, since no heat is transferred to the outside. For an endothermic reaction
(ΔHreaction positive), the heat needed to make the reaction proceed is taken up from the calorimeter
content, and the temperature of the calorimeter and its content decreases.
For an adiabatic calorimeter:
q = qreaction + qcalorimeter = 0
(5a)
qp,reaction = −qp,calorimeter
(5b)
or:
The heat capacity C (J/K = J/oC) is defined as the amount of heat (in Joules) needed to increase the
temperature of the calorimeter by 1 oC (1 oC = 1K).
qp,calorimeter = CΔT
(ΔT in oC)
(6)
qp,reaction = −qcalorimeter = −C ΔT
(7)
Since qp.rxn = ΔHrxn, we find that for an open adiabatic calorimeter as used in this experiment:
ΔHreaction = –CΔT
(8)
Calculating the enthalpy of formation of MgO
In this experiment, you will first determine the heat of reaction of magnesium metal reacting with
aqueous hydrochloric acid (reaction 1), and the heat of reaction of magnesium oxide reacting with
aqueous hydrochloric acid (reaction 2). We also know the heat of formation (ΔHo298) of water
(reaction 3) and can then apply Hess’ Law and calculate the heat of formation of solid magnesium
oxide:
Reaction 1:
Mg(s) + 2HCl(aq)
→ MgCl2(aq) + H2(g)
Reaction 2:
MgO(s) + 2HCl(aq)
→ MgCl2(aq) + H2O(l)
Reaction 3: formation reaction of H2O(l)
H2(g) + ½O2(g) → H2O(l)
ΔH(1) (kJ/mol)
ΔH(2) (kJ/mol)
ΔH(3) = −286 (kJ/mol)
By rearranging above equations, we can calculate heat of formation of MgO:
Mg(s) + ½O2(g) → MgO(s)
ΔH = ΔH(1) −ΔH(2) + ΔH(3)
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Safety Precautions
Handle concentrated HCl in the fumehood only, wear gloves and safety glasses (as always!). Rinse
any spills immediately.
Materials and Equipment
Balance, styrofoam cup, graduated cylinder, wire stirrer, thermometer, 2.0 M HCl, magnesium metal,
magnesium oxide.
Procedure
Part A: Reaction of magnesium metal with aqueous hydrochloric acid
1) Assemble the “styrofoam cup” calorimeter as instructed.
2) Weigh approximately 0.4 g of magnesium metal on an analytical balance and record the
mass.
3) Using a graduated cylinder place 50 mL of 2.0 M HCl in the calorimeter (remember, HCl
will be in excess, so the volume does not need to be accurate). Add 150 mL of water.
While slowly stirring the HCl solution with the wire stirrer, record the temperature of the
solution at ½ minute intervals for 5 minutes or until the temperature remains constant for
2 minutes. NOTE: Be sure to record both temperature and time since you will be plotting
temperature vs. time for the purpose of calculating the heat evolved in the reaction.
4) Open the calorimeter, add the weighed magnesium metal (note the time at which the
magnesium metal is added to the solution). Continue to stir or swirl the solution and
record the temperature at ½ minute intervals. Continue recording the temperature and
time for at least 12 minutes after the addition of the magnesium metal.
5) Discard the solution in the sink with large volumes of water.
6) Repeat steps (2) through (4) for a second determination. If time permits after you have
completed the next step, carry out a third trial with magnesium.
Part B: Reaction of magnesium oxide with aqueous hydrochloric acid
Repeat steps (2) through (4) above using 0.7 g of powdered MgO instead of 0.4 g Mg metal. Repeat
for a second determination.
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Graphs
A typical “thermogram” for an exothermic reaction (qreaction –ve, qcalorimeter +ve, temperature of the
calorimeter + contents go up) would look as follows:
:
27.00
Tf
26.50
T / oC
26.00
Ti and Tf are calculated at
time, t1/2, half-way through
the Reaction Period.
25.50
25.00
Ti
24.50
Pre-Mixing Period
Reaction
Period
Post-Mixing Period
24.00
0
100
t1/2
200
300
400
t /sec
Figure: A typical “thermogram” for an exothermic reaction.
For each determination:
Prepare a graph of the temperature-time readings Excel (time (sec) and temperature (oC)) and prepare
the thermogram as shown above.
Draw the best straight line representing the temperature before the reaction, and extend this line to the
time the reaction was started.
Draw the best straight line representing the final steady temperature after the reaction. Extend this line
back to the time at which the reaction was started.
Measure the difference in temperature indicated by the displacement of the two lines at the time of
reaction.
Calculations
Compute the heat liberated during the reaction for each trial. Assume that the heat gained by the
stryrofoam cup calorimeter is negligible, the density of the solution is 1.00g/mL, the heat capacity of
the solution is 4.184 J/goC, and the volume of solution is 200 mL:
C = 200(mL)x1.00(g/mL)x4.184(J/g.oC) (J)
(9)
Using equations (8) and (9) calculate first ΔHrxn (J) and ΔHm,rxn (J/mol):
ΔHrxn = –CΔT
(J)
ΔHm,rxn = ΔHrxn/moles
(10)
ΔHm,rxn is caled the molar enthalpy of reaction.
Calculate the average molar enthalpy of reaction for the trials with Mg and the average molar
enthalpy of reaction for the trials with MgO.
Sample calculations of the enthalpy of formation of MgO(s)
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From your data in parts A and B, you will be able to calculate the enthalpy of formation of MgO(s).
The formation reaction is:
1.
Mg(s) + ½O2(g) → MgO(s)
ΔH = ?
You determine the heat effect (enthalpy change) of the reactions:
2.
Mg(s) + 2HCl(aq) → MgCl2(aq) + H2(g)
ΔH from part A
3.
MgO(s) + 2HCl(aq) → MgCl2(aq) + H2O(l)
ΔH from part B
And we know:
4.
H2(g) + ½O2(g) → H2O(l)
ΔH = − 285.6 kJ
Combine the three reactions 2, 3, and 4 and use and use Hess’ law to find ΔH for the formation
reaction 1. Compare your result to the value reported for ΔHf in the thermodynamic tables in your
textbook. Discuss possible experimental errors, compare the random errors, and draw conclusions
about the experimental results
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Experimental General Chemistry 1
Experiment 10: Thermochemistry, the Enthalpy of
Formation of MgO
Laboratory Data Sheet
Name: ______________________________________________ Section:
_________
Part A, the reaction of Mg(s) with excess HCl
Trial 1
Trial 2
Trial 3 (if time
available)
Mass of Mg
Moles Mg
g solution
Cp,calorimeter (J/oC)
(g solution x 4.184)
ΔT (from graph)
qp (J)
ΔHreaction (kJ/mol) =
qp/(moles Mg)
Average ΔH (kJ/mol)
Temperature (oC)
S. #
Time (sec)
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
0
30
60
90
120
150
180
210
240
270
300
330
360
390
420
450
480
Trial 1
Trial 2
Trial 3 (if time
available)
Attach the thermogram graph (Excel plot) to the report.
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Part B, the reaction of MgO with excess HCl
Trial 1
Trial 2
Trial 3 (if time
available)
Mass of MgO
Moles MgO
g solution
Cp,calorimeter (J/K)
(g solution x 4.184)
ΔT (from graph)
qp (J)
ΔHreaction (kJ/mol) =
qp/(moles Mg)
Average ΔH (kJ/mol)
Temperature (oC)
S. #
Time (sec)
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
0
30
60
90
120
150
180
210
240
270
300
330
360
390
420
450
480
Trial 1
Trial 2
Trial 3 (if time
available)
Attach the thermogram graph (Excel plot) to the report.
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Calculations
Mg(s) + 2HCl(aq) → MgCl2(aq) + H2(g)
ΔH = ______ kJ
MgO(s) + 2HCl(aq) → MgCl2(aq) + H2O(l)
ΔH = ______ kJ
H2(g) + ½O2(g) → H2O(l)
ΔH = − 285.6 kJ
Apply Hess’ law by combining these reactions to find:
Mg(s) + ½O2(g) → MgO(s)
ΔH = ΔHfo(MgO)
Result:
ΔHfo(MgO(s))
= _________ kJ/mol
Compare to literature value (textbook tables):
= _________ kJ/mol
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